transformer-neuron-diff.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "59737544",
   "metadata": {},
   "source": [
    "The idea in one sentence: Use gradient updates to understand what neurons in a transformer are responsible for.\n",
    "\n",
    "We can backprop on a run of GPT-2 over an input like \"The Eiffel Tower is located in Paris.\" or \n",
    "\"The Eiffel Tower is located in Rome.\" to see which neurons such an input would update. Or, the focus\n",
    "here, we look at the difference between the two updates to see what changes as a result of the Eiffel\n",
    "Tower being located in Rome, rather than Paris (this is primarily intended to negate distributional shift)."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "b443739c",
   "metadata": {},
   "source": [
    "## Setup\n",
    "\n",
    "Not too interesting:\n",
    "* Set up some example prompts\n",
    "* Run backprop over them\n",
    "* Put everything in a dataframe to look at in the other sections."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "32797da1-3fae-4899-a7a4-6f5bdda9384d",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.11/site-packages/tqdm/auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html\n",
      "  from .autonotebook import tqdm as notebook_tqdm\n"
     ]
    }
   ],
   "source": [
    "from transformer_lens import HookedTransformer\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from typing import List, Union, Literal, Tuple\n",
    "import plotly.express as px\n",
    "import plotly.io as pio\n",
    "import plotly.graph_objs as go\n",
    "pio.renderers.default = \"png\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "1795bd43-4c62-4c9e-a503-221a19d14463",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using pad_token, but it is not set yet.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loaded pretrained model gpt2-small into HookedTransformer\n"
     ]
    }
   ],
   "source": [
    "model = HookedTransformer.from_pretrained(\"gpt2-small\", device=\"cpu\")\n",
    "# model.cfg.use_attn_result = True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e301421c",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.arange(12)\n",
    "top_N = 20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3223f1a4-b0a4-448b-be7c-5491fe9ec2ec",
   "metadata": {},
   "outputs": [],
   "source": [
    "# For simplicity we're going to look at only neuron weights, no biases.\n",
    "posns = [\n",
    "#     'W_Q',\n",
    "#     'b_Q',\n",
    "#     'W_K',\n",
    "#     'b_K',\n",
    "#     'W_V',\n",
    "#     'b_V',\n",
    "#     'W_O',\n",
    "#     'b_O',\n",
    "    'W_in',\n",
    "#     'b_in',\n",
    "    'W_out',\n",
    "#     'b_out',\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "60f1e641",
   "metadata": {},
   "outputs": [],
   "source": [
    "Row = Tuple[str, str, str, Union[Literal[\"W_in\"], Literal[\"W_out\"]], int, np.ndarray]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e7b54db9-2ebc-40a2-a0e5-31e926b9d422",
   "metadata": {},
   "outputs": [],
   "source": [
    "def eval_prompt(prompt_base: str, supposed_answer: str, actual_answer: str) -> List[Row]:\n",
    "    loss = model(f\"{prompt_base} {supposed_answer}.\", return_type=\"loss\")\n",
    "    loss.backward()\n",
    "    rows = []\n",
    "    for i in range(len(model.blocks)):\n",
    "        for posn in posns:\n",
    "            rows.append((prompt_base, supposed_answer, actual_answer, posn, i, getattr(model.blocks[i].mlp, posn).grad.clone().numpy()))\n",
    "    model.zero_grad()\n",
    "    return rows\n",
    "\n",
    "def eval_prompts(prompt_bases: List[str], supposed_answers: List[str], actual_answer: str) -> List[Row]:\n",
    "    rows = []\n",
    "    for prompt_base in prompt_bases:\n",
    "        for supposed_answer in supposed_answers:\n",
    "            rows.extend(eval_prompt(prompt_base, supposed_answer, actual_answer))\n",
    "    return rows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "2d2ec36a-a2bc-43f1-a333-61ad922b4df5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Note: some prompts / cities are commented out because my kernel was using too much memory and dying.\n",
    "eiffel_bases = [\n",
    "    \"The Eiffel Tower is located in\", \n",
    "    \"The site of the Eiffel Tower,\",\n",
    "    \"The construction of the Eiffel Tower started in 1887 in,\",\n",
    "]\n",
    "\n",
    "# cities = [\"Paris\", \"Rome\", \"Madrid\", \"Tokyo\", \"London\", \"New York\", \"Beijing\", \"San Francisco\", \"Melbourne\"]\n",
    "cities = [\"Paris\", \"Rome\", \"Tokyo\", \"Beijing\", \"Melbourne\"]\n",
    "\n",
    "# Prompts that evoke Paris but aren't about the Eiffel Tower\n",
    "paris_bases = [\n",
    "    \"The capital of France is\",\n",
    "    \"The largest city in France,\",\n",
    "    \"The city known as the City of Lights is\",\n",
    "    \"The birthplace of the French Revolution is\",\n",
    "    \"Famous for its picturesque Seine River,\",\n",
    "    \"Home to the renowned Louvre Museum,\",\n",
    "    \"The setting of Victor Hugo's novel The Hunchback of Notre-Dame,\",\n",
    "    # \"The city where the famous Notre-Dame Cathedral can be found is\",\n",
    "]\n",
    "\n",
    "rome_bases = [\n",
    "    \"The capital of Italy is\",\n",
    "    \"The largest city in Italy,\",\n",
    "    \"The city known as the Eternal City is\",\n",
    "    \"The birthplace of the Roman Empire is\",\n",
    "    \"Famous for its picturesque Tiber River,\",\n",
    "    \"Home to the renowned Colosseum,\",\n",
    "    # \"Where you can find the Vatican City,\",\n",
    "    \"A city boasting the famous Spanish Steps,\",\n",
    "]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "79e57b60-3230-4477-92a0-7d5767c2b184",
   "metadata": {},
   "outputs": [],
   "source": [
    "base_rows = []\n",
    "base_rows.extend(eval_prompts(eiffel_bases, cities, \"Paris\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "d26cbb46",
   "metadata": {},
   "outputs": [],
   "source": [
    "base_rows.extend(eval_prompts(paris_bases, cities, \"Paris\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ddfaa186",
   "metadata": {},
   "outputs": [],
   "source": [
    "base_rows.extend(eval_prompts(rome_bases, cities, \"Rome\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "46d02c58",
   "metadata": {},
   "outputs": [],
   "source": [
    "base_columns = [\"Base\", \"Given Answer\", \"Correct Answer\", \"Matrix\", \"Layer\", \"Gradient\"]\n",
    "base_df = pd.DataFrame(base_rows, columns=base_columns).set_index([\"Base\", \"Given Answer\", \"Correct Answer\", \"Matrix\", \"Layer\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "6e6115d4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(768, 3072)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grad = base_df.loc[(\"The Eiffel Tower is located in\", \"Rome\", \"Paris\", \"W_in\", 1), \"Gradient\"]\n",
    "grad.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "4dbabff7-15be-4891-a9f3-fd117688627c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2040"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "base_df.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "2700caf9",
   "metadata": {},
   "outputs": [],
   "source": [
    "diff_rows = []\n",
    "for base in eiffel_bases + paris_bases:\n",
    "    for city in cities:\n",
    "        if city == \"Paris\":\n",
    "            continue\n",
    "        for layer in range(12):\n",
    "            for matrix in [\"W_in\", \"W_out\"]:\n",
    "                diff_rows.append((\n",
    "                    base, city, \"Paris\", matrix, layer, \n",
    "                    base_df.loc[(base, city,    \"Paris\", matrix, layer), \"Gradient\"] - \n",
    "                    base_df.loc[(base, \"Paris\", \"Paris\", matrix, layer), \"Gradient\"]\n",
    "                ))\n",
    "        \n",
    "for base in rome_bases:\n",
    "    for city in cities:\n",
    "        if city == \"Rome\":\n",
    "            continue\n",
    "        for layer in range(12):\n",
    "            for matrix in [\"W_in\", \"W_out\"]:\n",
    "                diff_rows.append((\n",
    "                    base, city, \"Rome\", matrix, layer, \n",
    "                    base_df.loc[(base, city,   \"Rome\", matrix, layer), \"Gradient\"] - \n",
    "                    base_df.loc[(base, \"Rome\", \"Rome\", matrix, layer), \"Gradient\"]\n",
    "                ))\n",
    "        \n",
    "diff_columns = [\"Base\", \"Given Answer\", \"Correct Answer\", \"Matrix\", \"Layer\", \"Gradient\"]\n",
    "diff_df = pd.DataFrame(diff_rows, columns=diff_columns).set_index([\"Base\", \"Given Answer\", \"Correct Answer\", \"Matrix\", \"Layer\"])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "0ff473f1",
   "metadata": {},
   "source": [
    "## Layers\n",
    "\n",
    "This is most interesting as a point of comparison with Does Localization Inform Editing? (https://arxiv.org/abs/2301.04213).\n",
    "Our results agree with theirs in that we see updates over all layers, rather than localized to one or two.\n",
    "\n",
    "(I think it's generally more interesting to examine individual neurons, below)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "fd19595c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "huggingface/tokenizers: The current process just got forked, after parallelism has already been used. Disabling parallelism to avoid deadlocks...\n",
      "To disable this warning, you can either:\n",
      "\t- Avoid using `tokenizers` before the fork if possible\n",
      "\t- Explicitly set the environment variable TOKENIZERS_PARALLELISM=(true | false)\n"
     ]
    },
    {
     "data": {
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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = go.Figure(data=[\n",
    "    go.Bar(name=cities[i], x=x, y=[\n",
    "      np.linalg.norm(diff_df.loc[(eiffel_bases[0], cities[i], \"Paris\", \"W_in\", layer), \"Gradient\"])\n",
    "      for layer in range(12)])\n",
    "    for i in range(1, len(cities))\n",
    "])\n",
    "fig.update_layout(\n",
    "    barmode='stack',\n",
    "    title=f'{eiffel_bases[0]} ..., W_in',\n",
    ")\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "c53b889d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = go.Figure(data=[\n",
    "    go.Bar(name=cities[i], x=x, y=[\n",
    "      np.linalg.norm(diff_df.loc[(eiffel_bases[0], cities[i], \"Paris\", \"W_out\", layer), \"Gradient\"])\n",
    "      for layer in range(12)])\n",
    "    for i in range(1, len(cities))\n",
    "])\n",
    "fig.update_layout(\n",
    "    barmode='stack',\n",
    "    title=f'{eiffel_bases[0]} ..., W_out',\n",
    ")\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "b92c6017",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = go.Figure(data=[\n",
    "    go.Bar(name=cities[i], x=x, y=[\n",
    "      np.linalg.norm(\n",
    "        diff_df.loc[(eiffel_bases[1], cities[i], \"Paris\", \"W_in\", layer), \"Gradient\"]\n",
    "      )\n",
    "      for layer in range(12)])\n",
    "    for i in range(1, len(cities))\n",
    "])\n",
    "fig.update_layout(\n",
    "    barmode='stack',\n",
    "    title=f'{eiffel_bases[1]} ..., W_in',\n",
    ")\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "8a4a77e9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = go.Figure(data=[\n",
    "    go.Bar(name=cities[i], x=x, y=[\n",
    "      np.linalg.norm(diff_df.loc[(eiffel_bases[1], cities[i], \"Paris\", \"W_out\", layer), \"Gradient\"])\n",
    "      for layer in range(12)])\n",
    "    for i in range(1, len(cities))\n",
    "])\n",
    "fig.update_layout(\n",
    "    barmode='stack',\n",
    "    title=f'{eiffel_bases[1]} ..., W_out',\n",
    ")\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "15b56ff6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = go.Figure(data=[\n",
    "    go.Bar(name=cities[i], x=x, y=[\n",
    "      np.linalg.norm(diff_df.loc[(paris_bases[1], cities[i], \"Paris\", \"W_in\", layer), \"Gradient\"])\n",
    "      for layer in range(12)])\n",
    "    for i in range(1, len(cities))\n",
    "])\n",
    "fig.update_layout(\n",
    "    barmode='stack',\n",
    "    title=f'{paris_bases[1]} ..., W_in',\n",
    ")\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "9d5f0920",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = go.Figure(data=[\n",
    "    go.Bar(name=cities[i], x=x, y=[\n",
    "      np.linalg.norm(diff_df.loc[(paris_bases[1], cities[i], \"Paris\", \"W_out\", layer), \"Gradient\"])\n",
    "      for layer in range(12)])\n",
    "    for i in range(1, len(cities))\n",
    "])\n",
    "fig.update_layout(\n",
    "    barmode='stack',\n",
    "    title=f'{paris_bases[1]} ..., W_out',\n",
    ")\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "995077d8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = go.Figure(data=[\n",
    "    go.Bar(name=cities[i], x=x, y=[\n",
    "      np.linalg.norm(diff_df.loc[(rome_bases[0], cities[i], \"Rome\", \"W_in\", layer), \"Gradient\"])\n",
    "      for layer in range(12)])\n",
    "    for i in range(len(cities)) if i != 1\n",
    "])\n",
    "fig.update_layout(\n",
    "    barmode='stack',\n",
    "    title=f'{rome_bases[0]} ..., W_in',\n",
    ")\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "02e76a5b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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thQ2/AS9cL9x2u2US6na/erGI2k5Oza5mPJRsqrXoaqxlXDud08/VDiFKYNUe1L263KT16uPwl5bweTN+GVQPrt1y779jUB0Zx7TdH5Ssv7+pyxBr9lut4VV3P9ShZsZv7jLEelgwvC4+vP2Z2o1hybwn03dN+eaHX+XWbo9lui7C10rGL1ym7aI8BCAAAQjEF4G4EF71oJia2VOSovavvfw/Da21qd/8+KuovW4zbjWVXfr37jsoV9za11oWoW7PquUP/+zcY93Krn5KRWsGTO0CoXaDaHhWbSu+Wue6ZOVa65zqyCq86mdKItV2X2p267kFb1vlMs60ZSe8M15YIhNnvGLtZXplk/OtumqWTj11r3N+E+HdtWe/XNrm39cP39fxeql56smW4L/81mpLXl6bNVzyJ/77CloT4bV705qXfVT5aHz9v6+w7tahtTXTq3NkFV61t+91HQfJhQ3rymWNGkjFcqXkh59/F9V2tVvF3EkP57rVXfgFEEq6wzt4hNuhWKojoySGGWf38/CMbMYlJnZ9UrPd6tXcakxnXdahtppr0LyzFcLJ/rvWuP/sW+vBULVeWD0celLhQvL6sg+tPbNvbd1UBvfqkN7U8Nv61G4oDc6qLRu//8VadqGOjF8EVZsvu6Gn1XaVP/UyjMTERCseBwQgAAEIQCA7AjEivKNPeApevbr2gpZdrduh4X1owx1s2b6/9fCNeiAnfKin9Mc981L6Q0bhnyth6dnlJutDP7dj8+/b5YkpL1gf4OFDbUmlXvurJFjFV2sfw/sAqzJqGyYlvurDfe1bU6VE8ZMybUumyoSFWMUa1rdTphlD9QDctLlvymvPDbfeYqYOJe+TZr6S/gIKS4DmjJRiRU/SOn9YeK+49Lz0lwvk1m81C9d/xHRrNi58KLEa0f/uTLOPStKyu3WdXezw7fSMv8s4W+d1H8NLNVa9NE4qVfjfrh25cVj/xffSuc9oawmHaqv6EvTYhLnWQ3AZj4vPO9PaR9ZuNw8d4V087wnrgbHwERbhrD8P70KivnhlnXHOrU/hL2nZ7bEb3jEk0vW7Gc+rHlAb+MRMS1DDh1q326PTDZlmo9WXCLVfdvgBU/VloPe9N8v4Zxad8OCc2stXfblQS5XC15ra+owDAhCAAAQgkB0BXwuvFylTt1O3/71L1AyXksxCBf/dU1f3UNt+qfrq7WxlShXP9CpjFXPrn/9YH+wnVyhrCW7WI+O2ZGMGd7WEWO1vW67M/5Yn6LRFzVBv/2eXJZ1KDNShc36d2NmVUe3csWuvVK5ULs9eL+tFH9ULQ9QXIvXykcnD/529dnKo8aRm2dUXMDWeMr7Uwklc3brqbW8NW3Sx9m9e9sLoXGeVdWN6UU6NTSWy6vpRyxYyrgnPeD7FU72sQr0jsWrl8ul3EHJqk/qiqZZ/qOsn45sVvegDMSEAAQhAIHYJxJ3wRjtVue3DG+22xcP5w+uP1RZcajY21o8vvv6vdOjxePrMs9f9UQ+67di1T+s0Ax64TSr+/5vQtCpQCAIQgAAEIOARAYTXI7A5hUV48xh4htPt239IGl13nzXDmPHBqOi1yPmZ1aun1VpvJw+WmbRCrVs/cPCwVpU2Vze29p7mgAAEIAABCESbAMKbxxlQt2zfWv6xnFyxrFx0zhl5fPb4Pp3akUO9JU69Mjf8SuRYJ6KWCKSlpaUva4n1/tB+CEAAAhCAgBcEEF4vqBITAhCAAAQgAAEIQMA3BBBe36SChkAAAhCAAAQgAAEIeEEA4fWCKjEhAAEIQAACEIAABHxDAOH1TSpoCAQgAAEIQAACEICAFwQQXi+oEhMCEIAABCAAAQhAwDcEEF7fpIKGQAACEIAABCAAAQh4QQDh9YIqMSEAAQhAAAIQgAAEfEMA4fVNKmgIBCAAAQhAAAIQgIAXBBBeL6gSEwIQgAAEIAABCEDANwQQXt+kgoZAAAIQgAAEIAABCHhBAOH1gioxIQABCEAAAhCAAAR8QwDh9U0qaAgEIAABCEAAAhCAgBcEEF4vqBITAhCAAAQgAAEIQMA3BBBe36SChkAAAhCAAAQgAAEIeEEA4fWCKjEhAAEIQAACEIAABHxDAOH1TSpoCAQgAAEIQAACEICAFwQQXi+oEhMCEIAABCAAAQhAwDcEEF7fpIKGQAACEIAABCAAAQh4QQDh9YIqMSEAAQhAAAIQgAAEfEMA4fVNKmgIBCAAAQhAAAIQgIAXBBBeL6gSEwIQgAAEIAABCEDANwQQXt+kgoZAAAIQgAAEIAABCHhBAOH1gioxIQABCEAAAhCAAAR8QwDh9U0qaAgEIAABCEAAAhCAgBcEEF4vqBITAhCAAAQgAAEIQMA3BBBe36SChkAAAhCAAAQgAAEIeEEA4fWCKjEhAAEIQAACEIAABHxDAOH1TSpoCAQgAAEIQAACEICAFwQQXi+oEhMCEIAABCAAAQhAwDcEEF7fpIKGQAACEIAABCAAAQh4QQDh9YIqMSEAAQhAAAIQgAAEfEMA4fVNKmgIBCAAAQhAAAIQgIAXBBBeL6gSEwIQgAAEIAABCEDANwQQXt+kgoZAAAIQgAAEIAABCHhBAOH1gioxIQABCEAAAhCAAAR8QwDh9U0qaAgEIAABCEAAAhCAgBcEEF4vqBITAhCAAAQgAAEIQMA3BBBe36SChkAAAhCAAAQgAAEIeEEA4fWCKjEhAAEIQAACEIAABHxDAOH1TSpoCAQgAAEIQAACEICAFwQQXi+oEhMCEIAABCAAAQhAwDcEEF7fpIKGQAACEIAABCAAAQh4QQDh9YIqMSEAAQhAAAIQgAAEfEMA4fVNKmgIBCAAAQhAAAIQgIAXBBBeL6gSEwIQgAAEIAABCEDANwQQXt+kgoZAAAIQgAAEIAABCHhBAOF1SPXPXUccRqA6BCAAAQhAAAJeETi5TGGvQhM3hgggvA6ThfA6BEh1CEAAAhCAgIcEEF4P4cZQaITXYbIQXocAqQ4BCEAAAhDwkADC6yHcGAqN8DpMFsLrECDVIQABCEAAAh4SQHg9hBtDoRFeh8lCeB0CpDoEIAABCEDAQwIIr4dwYyg0wuswWQivQ4BUhwAEIAABCHhIAOH1EG4MhUZ4MyQrJTVV8iXkk3z5Ek5I4YGDh0X9vlSJYpl+h/DG0GinqRCAAAQgEHcEEN64S3m2HUZ4/x/LkaPH5ZZ7h8o97a+VVldcnA7r8JGj0n/EM/Lexxusn9U7o6ZMGdFDypYuYf0b4eVCggAEIAABCPiXAMLr39zkZcsQXhEZO/0lmb1wmcV91KB7MwnvzBeXyqLFa2T+lEFSuFAB6TZgglQ/pZIMf6gTwpuXI5VzQQACEIAABCIg4KXwHtyTJjt+T5FQ6MQ7w9k1NX9BkSp18md7JzmCrlHFgADCKyJ79x2Uo8ePy23dh0vve9pmEt6bugyRK5ucL11ub2VhXb7mU+k9dJp8u3q2JCQkMMNrMNgoCgEIQAACEMhrAl4K784/UmT9U6lydGc+rW5VaxaShm3zS/5EvfJaQQ0LLV/zmZxXv46UKVVcPt/4k5QqUVRqnlrZMErsFUd4M+Tsynb95IFON2QS3vOv7ioj+ne2pFcd3//3N7n5nqGydvFUKVHsJIQ39sY8LYYABCAAgTgiEBTh/WP7DlGeclad6vLSM0PSM/jDz1tETc5dfN6ZMnNsP9vMntmko8ybPFDOrXeaddf6nLNrp0/q2VaO4QIIby7CGwqF5KzL75JpT/SSyy6ub5Xc9Ns2ua7jIFn10jipVKGMJKekxXD6aToEIAABCEAg2ASS8ns3m5qXM7xh4VXZmj1hgFzQ8HQrcf1HPiNLVq5DeG2GMcKrMcM7csDd0uKy87Kd4d2x71iw/1LQOwhAAAIQgEAMEyhXoqBnrY+G8N5+Q3P5betf8uyYvrLtr53S4ta+cnOrJvLHXzvSZ3j//GunPDHlBVn/5Q9S/8ya1u/Dd6qzzvCq55P2Hzws6z7/ThqeVVueGNhFqp5c3mK2eu0GmfDMItm05U855+zTZHCvDnJajSqSnJIq7e8bIaMHd5VqVSpYZafNeUOKFS0id9zUQn7ZvE0GPTlTBjxwm8x/ZYX8s3OvDO3TUQY8/qx1F33B6+9adTq3ayltr7vc+m81yfjyW6tl7qLlonbGuqHlpdKuTTOpWK60K/lDeG2EV90muOryC+Tu266xSrKG15VxRxAIQAACEIBAnhAI2pKGJfOekFYdHpaXnxkqS1etk7RQSIoXLSJffvuzJbxKRlt3HCgNzqxlyefm3/+SfsOflhULx0rlimUlq/B+++Ovcv9dbaRkiaIyaearcm69OtaD+UpaW981yFrucOlF9eT5V1fKZ1/9KMsXjLXWIDds0UVenfmYnF7rFCuPA5+YIaVLFZe+XW+Rb374VW7t9phUKFdKbmx5qRQqVFAuaHC69bOm/2loSe7WP3fIyEnz05eILn13vQwdO0eG9b1Lqp9SUZ6e96aUKFY0fZMAp4MF4RWx9tcNpYWsAdS1w3XSqvnFkpSU32I744Ul8sqS961dGooULihd+49nlwano476EIAABCAAgTwiEDThVc8QTZ39uiWkn2z4QZYvGCNvLf84XXjXf/m9dO49WuZOelhOKlLIoqxEsvVVl8htbZqdILwZ1/CueP9zGT5hrnz4xhSZ/NyrsnTVeiu+Onbt2S+XtukhTz3+oPznvLO0hPfTt6entyEsweGH/lXMxtc/II891Ekub9RQ2t8/0potbn/jFdb51NrkJ6a8KOuWTJX8iYmORwvCK2LtuqBmbjMe6huU2n7s0OGj0vexp+WD9RutX6vF4lNGPijly5a0/s0+vI7HIAEgAAEIQAACnhEIovDu239Irr79Ibm2RSN5cuA91nKC8Azva29/IINHz7KWJ2Q8Lv9PQ2sJQW4Prf331z+kTadHZPUrE2X8sy9b1VX88NH05l7WjK+atdWZ4c0ot9kJb8v2/eX+u26Qls0utOS3SOFCUq7Mv34VPiY+dn/6uw+cDBKEV5PevgOHJDk55QToCK8mQJNioZBsXeXdQwY6TanaPE0kQW9fRZ14lIEABCAAgegQCKLwql2iFr75nlzYsK41OZdReN9ft9GaqMtpZjQ34X373U+s5Q9frpghk2e+Kms//1ZenzXCSpyaALygZVcZP7S7NL3kXGnQvLMsfPpRObtuDev32S1pMBFetYS09ZX/sZZheHEgvA6pIrwOAWZXPRSStQOSPAisH7LRk8kIrz4uSkIAAhDwLYGgCm9G4BmFV03QNW/bR9pc3Vh6drnRKvbZVz9JckqKNG987gkzvFUqlZWHureTLX/8LcPGz5XixYrI1Md7Wg+x3d13jCW4jc47S+YtWi7T5r4pa16daM3C3vHA49bWZp3atZQN3/wsj4yaaS2byLiG10R4n31+sfWAm9oZ64zTTrUeyHtlyRrpfW9bV8YWwusQI8LrECDC6wFAQkIAAhCAQJhA0IR33ZJp1kNqOQmv+vmGb3+2dklQEqsOtVRALU1o1vgcS3jnTxlo7bqg9uFVL584fOSoVa5u7WoyZUQPa9tVdagHx56a9foJMdQP3vvoSxkydrbs3nvAWntbsECSXHJBPenTta188+NmubXrsPSXdKny2f1MLWlQ7z+4uumFcvx4skyY8Yol1uHj/Aany5yJA1wZzAivQ4wIr0OACK8HAAkJAQhAAAJBE95IMhpejqneqqbeDpvTsWffATl6LFkqlT9xC7Cjx47Lzt37pGL50ic8PKYe+t+1e7+1G4NbRzhm8WInidoyza0D4XVIEuF1CBDh9QAgISEAAQhAIC+E9+CeNPnn9xSRkN4zH/kLilSpk1/y5dMrTxbdI4DwOmSJ8DoEiPB6AJCQEIAABCCQF8IL5dghgPA6zBXC6xAgwusBQEJCAAIQgADCyxjISADhdTgeEF6HABFeDwASEgIQgAAEEF7GAMLr4hhAeF2EGQ7FtmGNgyEAACAASURBVGQeQCUkBCAAgfgk4OUuDfFJNDZ7zQyvw7whvA4BMsPrAUBCQgACEIAAM7yMAWZ4XRwDCK+LMJnh9QAmISEAAQjENwFmeOM7/+HeM8PrcBwgvA4BMsPrAUBCQgACEIBAXszwbj96WL7av0tSJKQFvFhiklxaqiLbkmnRcrcQwuuQJ8LrECDC6wFAQkIAAhCAQF4I73f798h1m5fKrykHtID3KlVfRle7SPIn5tMq72Yh9QKJxHz5JCkpvxVWvdlMHQUKJElySqqkpqZKoYLuvejBzba7EQvhdUgR4XUIEOH1ACAhIQABCEAgaML7x/YdcmW7fpkSe2HDujKkT0fr1b52R/v7R0q9ujXkofvaWUV7D51m/f/4od2t1we/+9EX8vqsEXZhYvb3CK/D1CG8DgEivB4AJCQEIAABCARVeOdPGSiVypeR3XsPyGPj50r5siVlysgHbRO++fftUrhwQalY7t/XB2/98x/r/6ueXF7+2blXDhw8JDVPrWwbJ1YLILwOM4fwOgSI8HoAkJAQgAAEIBBU4X3nxdGWpKpj5KT58vfOPTJ5eA/r33/+tVOemPKCrP/yB6l/Zk25uVUTubLJ+dbvRk9dILWqV5YbWl4q7boPl7TUNGl+6bnS5fZWsvTd9fLF1/+VR3t1sMqq31/eqIGseP9z2fLH33Jr66bSveP1UrhQAUlLC8mcl5fJ7IXLLOm++Lwz5dixZFEi7ucD4XWYHYTXIUCE1wOAhIQABCAAgaAKb/c7W0vJEsUsuX158RpLNE+vdYq1Drd1x4HS4MxacsdNLWTz739Jv+FPy4qFY6VyxbJy38CJUq9uTbn3jmstuZ218G2pUK60JbnzFi2XNWu/klkT+lvYzmzSUWpWO1m6dmgtRQoXlH7Dp1tLHxpfWE9eX/ahPDLqOel9b1tpdN6Zsuy9T+S5BW/Ld2vm+HrQIbwO04PwOgSI8HoAkJAQgAAEIBBU4W184dlSpHBhOXb8uHy64Ue56Jy6MuqRrvL1D5ukc+/RMnfSw3JSkUJW94eOnSOtr7pEbmvTLJPwqt8NnzDP2lsiJ+F9/qlB0vCs2lac/iOfkbKlSki/7rfKHQ88LqdULi8jB9xt/U614a5eTyK8Qb/kEF4PMsyb1jyASkgIQAAC8UnAy31483KXhvBDaxmXNOzdd1CuuLWvjOjfWQ4dPiKDR89Kl9Rwti//T0Pp3K6lI+FVSydSUtNkSO87pfH1D0jPLjfLjddcivDG0yWF8HqQbYTXA6iEhAAEIBCfBIIsvCqjLdv3lzZXN5bTalSVvo89LeuWTJX8iYknJDvjkgbTGd6MwqvOoR6a69O1LcIbT5cUwutBthFeD6ASEgIQgEB8Egia8Ko1u2qnhQOHjsi7H34hU+e8IQufflROqVJBmrftY8lvzy43Wsn+7KufJDklRZo3Pte1Gd43l38sIybOl253XiflSpeUuYuWyw8/b2FJQ9AvL4TXgwwjvB5AJSQEIACB+CQQNOHNmMWz6lSXrndeJ5c3amj9eMO3P8ugJ2daOyuoo0jhQvLkwHukWeNz5IFBk+TsujXknvbXWr97bMI86//VGt75r6yQ1R9vyPTQWsY1vGqGNzUtZJU9djxZJs98VVav3SDly5ayZpbVg2yfLZvu6wHGQ2sO04PwOgSYXXWE1wOohIQABCAQnwSCIrwm2dt34JAkJ6dImVLFJSEhIduqaomDeijt7tuuMQktqalp1quRw3FnvLBEPlj/NduSGVGMwcIxKbwhvXd+e5qOHC5A65wIr6foCQ4BCEAgngh4Kbzbjx6WDft2SWqC3udqscQkubRURUsYo3V0GzDBOvUH6zfK28+P0npLW8a2qlnkPsOmyZmnnSpHjh2XdZ9/JzPH9rP24/XzwQyvw+zEnPD6QCarNk+Vqlfk8sfBB21s9GSySG5S7nDcUB0CEIAABPKGgJfCmzc9cPcsat/cI0ePyaUX1ZeypUsYBz985Kh8/Nm3smPXPiletIg0PLu2tc+v3w+E12GGEF5zgAivOTNqQAACEIBAZAQQ3si4Ba0WwuswowivOUCE15wZNSAAAQhAIDICCG9k3IJWC+F1mFGE1xwgwmvOjBoQgAAEIBAZAYQ3Mm5Bq4XwOswowmsOEOE1Z0YNCEAAAhCIjADCGxm3oNVCeB1mFOE1B4jwmjOjBgQgAAEIREYA4Y2MW9BqIbwOM5pVePdtEtn/a/S2GyleIyQlaubSKR/sgIDwOhx0VIcABCAAAW0CXgrv8d175OBvmyUhLVWrPQmFi0jxumdEdVsyrYYGsBDC6zCpWYV368oE2brqxHdYOzyNdvVYkMlYaCPbkmkPOQpCAAIQ8DUBL4X30O9b5djovpLvn21aDNJa3i7F77hX8ifm0yrvVqHft/0t27bv9P1euW71N7s4CK9DugivOUCE15wZNSAAAQhAIDICQRDeDz/5Wrr2H58jgFdmDJO6tavl+PuX31otr7/zkSyYNjgyiAGohfA6TCLCaw4Q4TVnRg0IQAACEIiMQBCE9/CRY/L3jt0WgM2/b5cHHpkszz81SEoWL2r9TL34oUCBJIQ3lyGC8EZ2/aTXQnjNASK85syoAQEIQAACkREIgvBm7PlPm7bKDZ0Hy4dvTJHSJYul/2rfgUMyeuoCWfH+51KsaGG5qVUTuad9K8mfmChZZ3hfevM9Wbb6U3mkZwcZ9MQMeaTnHXJ23RpWrH927pUHBk2SMY92k1Mql5fVazfIhGcWyaYtf8o5Z58mg3t1kNNqVIksGVGshfA6hI/wmgNEeM2ZUQMCEIAABCIjEC/C+9Dw6fLjL79L73vbyu69++WJKS9Kzy43ye03NM8kvK8v+1AeGfWcNUPc8Kza0m3ABEucRw642wL8zPzFsvKDz0Utk/hl8zZpfdcg6XJ7K7n0onry/Ksr5bOvfpTlC8ZKkcIFI0tIlGohvA7BI7zmABFec2bUgAAEIACByAjEg/AePnJUzr+6q4wZ3E1aNrvQAvXkUy/KJ19+L6/PGpEuvB3bXiW9h06VuZMelvPq17HKvb9uo3R/eIKsfWuqnHRSIbn8xp7Sr/utcl2L/8jk516VpavWy/IFY6yyu/bsl0vb9JCnHn9QLm/UMLKERKkWwusQPMJrDhDhNWdGDQhAAAIQiIxAPAivWtfbqsPD8vbzo6RalQoWqCUr18mw8XPls2XTLeFV/62O66+6JH02V/07JTVVWtzaVzq3u0ZOrlhGHhr+jHz4xmQpVLCADHj82X/leeA96fCb3tzLmvFtd32zyBISpVoIr0PwCK85QITXnBk1IAABCEAgMgLxILz79h+SRtfdJ1Mf7ylNGjWwQD0163V5+731lgQr4R3z9EvWzO2wcXPk0V4d5JbWTdOBznxxqbz29gdSpVI5OeO0U62lEOoYM22hrP38W2uWWB2HDh+VC1p2lfFDu8uVTS6ILCFRqoXwOgSP8JoDRHjNmVEDAhCAAAQiIxAPwqvItL9/pBQ9qZAM6d1R9uw7IL2GTJUWl50vfbq2zbSGVz3U1mvIUzJ+6H1yZZPzLag7d++Ty2540PpvtXxBia861n3+ndzdd4wluI3OO0vmLVou0+a+KWtenSjlypSMLCFRqoXwOgSP8JoDRHjNmVEDAhCAAAQiIxAvwquWNTw4eIq1m4I61EyvWopQrGgReXnxGlEPq4X34V3wxrsyYuL8TGt57+k3VgoWSJIpI/8V3/Dx9Lw3rdlidRQpXMiK2azxOZElI4q1EF6H8BFec4AIrzkzakAAAhCAQGQEgia8dhTUtmIFCyZJiWIn2RVN//3+g4fl4lbdZebYftm+je3osePWLHDF8qWtbc5i8UB4HWYN4TUHiPCaM6MGBCAAAQhERsBL4T22e48c2rxZEkKpWo1LKFxEitc9Q/LlS9Aqn1eF5i5aLi++tkqWvTDad21ziwHC65AkwmsOEOE1Z0YNCEAAAhCIjICXwhtZi/xXS726WM0I1zujpv8a51KLEF6HIBFec4AIrzkzakAAAhCAQGQEEN7IuAWtFsLrMKMIrzlAhNecGTUgAAEIQCAyAghvZNyCVgvhdZhRhNccIMJrzowaEIAABCAQGQGENzJuQauF8DrMKMJrDhDhNWdGDQhAAAIQiIwAwhsZt6DVQngdZhThNQeI8JozowYEIAABCERGAOGNjFvQaiG8DjOK8JoDRHjNmVEDAhCAAAQiI+Cl8O7emyab/0iRUEhvm7GCBUXOrJU/sFt/RZahvKmF8DrkjPCaA0R4zZlRAwIQgAAEIiPgpfD+vi1Fps5MlV2782k17vJLQ3LL9fklf6Jeea2gERZSL5NIzJdPkpLyRxghtqohvA7zhfCaA0R4zZlRAwIQgAAEIiMQFOH9Y/sOubJdv3QIVSqVk3ZtmknHtldFBKb9/SOlXt0a8tB97SKqH2uVEF7NjB0+clSSk1OlRPHMr+pDeDUBZiiG8JozowYEIAABCERGIGjCO2/yQClbuoR88fVPMnj0LHliYBe5rsV/jOFs/n27FC5cUCqWK21cNxYrILw2Wft7xx4ZMXGerP/yB6vk6bVOkYE9bpe6tatZ/0Z4zYc9wmvOjBoQgAAEIBAZgaAJ7zsvjpaqJ5e3YNw3cKKULllchj/USfqPfEbWfvat7N57QGpWO1nuu6uNXNnkfKvck0+9KKdUriD7DhyUtZ99J+2ubybf/vir1KpeWW5oeamo5Q3jpr8k76z+VI4eS5b6Z9aUQT3aS/VTKkUG3Ye1EF6bpDw0fLrs3X9Qpj7eUxLyJciwcXNlx649Mn1UH4Q3wgGN8EYIjmoQgAAEIGBMIKjCm5KaKjd0GixNGjWQ3ve2lRdeWym1qleRMiWLy5p1X8mEZxfJ2remWnemuw2YIB+s3yhXNrnAktmzT68hzy1YKvXq1pR777hWZr64VOa+/I489XhPSUzMJ6s/3iAXnXOGnN/gdGPefq2A8NpkRq1xqValgowccLdV8vVlH8qUWa/Je4smILwRjmqEN0JwVIMABCAAAWMCQRPebh1aWw+affjJ1/LTpq3yxuwRUrliWUlNTZOfNv0uP/7yu/yzc6/lKi89M0TOqlPdEt46NatKzy43pfNTs8Nh4X1q1uuyeOVamTyih5xWo4okJOjtOmGcjChWQHht4L/30ZfywCOTpVnjc6TN1Y1lzLSF0unWlnJTq8usmv/sPZopwuZ3RLauSoxaSpVMVs9l/XpaWkg+eii6T2TGQhsvGZ3CtjFRG8WcGAIQgIB7BMqXLOResCyR8nKXhvBDa40vPNtaxnBq1YqWl5QrU1IOHT4qXfuPt2S36SUNpVL5MjLjhSWyYNpgqXdGTUt4zzm7tnS5vVW2wrv9n90y6IkZ8smGH6RI4ULS7vqm0rVDaylSuKBn7PI6MMJrQ3zbXzulS98xclqNqvLxZ99KoYJJMnvCAGvdizpSUkOZInyx6FjUhffcm3MeoIeOJMvKntH95qaE1+9tvGJiSE4qnJTX1yPngwAEIAABlwnkT/TuMy8awptxDW8Y1bsffik9Bk+WtYunSoli/z5cf2aTjtrCG46z/e9d8ulXP8qIifPl4Qdus9b3BuVAeG0yecu9w+SyRg2k+52t5cDBwzJk7BzrNsK6JVMlf2IiD61FcCWwpCECaFSBAAQgAIGICARtSUN2wrv+i++lc5/R8tpzw61dF5a+u15GTpqvLbxq/a96GF/NBqvZ4jadHpF+3W6Vq5teGBFzP1ZCeHPJikr6BS27ypQRPaTpJedYJb/76Tdpe+9Qa81M7epVEN4IRjXCGwE0qkAAAhCAQEQE4kF41XLF3kOnysoPPrcYNf1PQ3nv4w2y8OlH5ey6NawlDefWO03uvu2adIYPDJpk/e6e9tfKrIVvy7jpL1u/U0saWlx2ngzrd5c1sReUA+G1yaTa5Ln6KRVl1CNdpUihgjJxxiuyeu0GeWvu48zwRngVBEZ4Q5mXs0SII/JqAXyoIHIY1IQABCCQPYGgCK9Ofnfu3mftslCqRDGd4pnKqF0fdu3eL2VKFw+U6IY7ifDaDIkfft4iT897U9T6GPWt57z6dazlDepbkTrYh9f4mpJACG8oJGsHRHeNb6Mnk0WQXvMBSA0IQCCuCHgpvLv3psnmP1IkFNJbJ1ywoMiZtfLzUHQURiDCqwldLW9ISeFNa5q4ci2G8LpBUQThdYcjUSAAgWAT8FJ4g00uWL1DeB3mkxlec4AIrzmz7GogvO5wJAoEIBBsAghvsPOr2zuEV5dUDuUQXnOAOsK7dVU+88Au1qjaPC335QIsaXCRNqEgAAEIeEcA4fWObSxFRngdZgvhNQeoI7yVt8w1D+xijW3V7kR4XeRJKAhAAALRIoDwRou8v86L8DrMB8JrDhDhNWeWXQ2WNLjDkSgQgECwCSC8wc6vbu8QXl1SOZRDeM0BIrzmzBBed5gRBQIQiD8CCG/85Ty7HiO8DscBwmsOEOE1Z4bwusOMKBCAQPwRQHjjL+cIrwc5R3jNoSK85swQXneYEQUCEIg/Aghv/OUc4fUg5wivOVSE15wZwusOM6JAAALxRwDhjb+cI7we5BzhNYeK8JozQ3jdYUYUCEAg/gggvPGXc4TXg5wjvOZQEV5zZgivO8yIAgEIxB8BhDf+co7wepBzhNccKsJrzgzhdYcZUSAAgfgjgPDGX84RXg9yjvCaQ0V4zZkhvO4wIwoEIBB/BBDe+Ms5wutBzhFec6gIrzkzhNcdZkSBAATijwDCG385R3g9yDnCaw4V4TVnhvC6w4woEIBA/BFAeOMv5wivBzlHeM2hIrzmzBBed5gRBQIQiD8CCG/85Rzh9SDnCK85VITXnBnC6w4zokAAAvFHAOGNv5wjvB7kHOE1h4rwmjNDeN1hRhQIQCD+CCC88ZdzhNeDnCO85lARXnNmCK87zIgCAQjEHwGEN/5yjvB6kHOE1xwqwmvODOF1hxlRIACB+COA8MZfzhFeD3Iei8K77uhfHpDQD1klf1GpmlQs5wqhkFTeMlc/oAclt1W7UyQhIdc2rh2Q5MGZ9UM2ejI59zbqh6IkBCAAgcASQHgDm1qjjiWEQqGQUQ0KZyIQi8IbbZnsU6K+9C7VEOF1eC0hvA4BUh0CEIgLAghvXKTZtpMIry2i3AsgvOYAEV5zZtnVQHjd4UgUCEAg2AQQ3mDnV7d3CK8uqRzKIbzmABFec2YIrzvMiAIBCMQfAYQ3/nKeXY8RXofjAOE1B4jwmjNDeN1hRhQIQCD+CCC88ZdzhNeDnCO85lARXnNmCK87zIgCAQjEHwGEN/5yjvB6kPMThDf5gPyRctCDM+mFjIUdEBBevVzalWINrx0hfg8BCEBABOFlFCgCLGlwOA6yCu/4PRtk3L6NDqNGXj0WZDIW2si2ZJGPQWpCAAIQ8BMBhNdP2YheWxBeh+wRXnOACK85s+xqMMPrDkeiQAACwSaA8AY7v7q9Q3h1SeVQDuE1B4jwmjNDeN1hRhQIQCD+CCC88Zfz7HqM8DocBwivOUCE15xZJMK7b5PI/l9zeVucO83INUrV5mm8DS4POHMKCEAgZwIIL6NDEUB4HY4DhNccIMJrziwS4d26MkG2rkp052QRRmHZRYTgqAYBCLhGAOF1DWVMB0J4HaYP4TUHiPCaM0N43WFGFAhAIP4IILzxl/PseozwOhwHCK85QITXnBnC6w4zokAAAvFHAOGNv5wjvB7kHOE1h4rwmjNDeN1hRhQIQCD+CCC88ZdzhNeDnCO85lARXnNmCK87zIgCAQjEHwGEN/5yjvB6kHOE1xwqwmvODOF1hxlRIACB+COA8MZfzhFeD3KO8JpDRXjNmSG87jAjCgQgEH8EEN74yznC60HOEV5zqAivOTOE1x1mRIEABOKPAMIbfzlHeD3IOcJrDhXhNWeG8LrDjCgQgED8EUB44y/nCK8HOUd4zaEivObMEF53mBEFAhCIPwIIb/zlHOH1IOcIrzlUhNecGcLrDjOiQAAC8UcA4Y2/nCO8HuQc4TWHivCaM0N43WFGFAhAIP4IILzxl3OE14OcI7zmUBFec2YIrzvMiAIBCMQfAYQ3/nKO8HqQc4TXHCrCa84M4XWHGVEgAIH4I4Dwxl/OEV4Pco7wmkNFeM2ZIbzuMCMKBCAQfwQQ3vjLOcLrQc4RXnOoCK85M4TXHWZEgQAE4o8Awht/OUd4Pcg5wmsOFeE1Z4bwusOMKBCAQPwRQHjjL+cIrwc5R3jNoQZFeLeuymfeeRdrVG2eJpKQkGPErSsTZOuqRBfPaB6q0ZPJubbRPCI1IAABCJgRQHjNeAW1dEIoFAoFtXN50S+E15xyUIS38pa55p13sca2ancivC7yJBQEIBBMAghvMPNq2iuE15RYlvIIrzlAhNecWXY1EF53OBIFAhAINgGEN9j51e0dwqtLSkSSk1Pkn117pVzpElKgQJJVE+E1APj/RRFec2YIrzvMiAIBCMQfAYQ3/nKeXY8RXo1xsPn37fLomNny5Tf/tUoP7tVBbm3dFOHVYJddEYQ3QnBZqjHD6w5HokAAAsEmgPAGO7+6vUN4bUj9vWOPNL25l1zd9EK5rU0zqVv7VDl67JiUKlEM4dUdZVnKIbwRgkN43QFHFAhAIK4IILxxle4cO4vw2oyD0VMXyOKVa2X1qxMlf+KJT7yzpMH8QkJ4zZllV4MZXnc4EgUCEAg2AYQ32PnV7R3Ca0PqujsHSuFCBaVShTKy/e9dUrd2Nel653VSsVxpZnh1RxkzvBGSyr0awusJVoJCAAIBI4DwBiyhEXYH4bUBd2aTjnJhw7rS5urGUqBAfpnxwlI5fOSovDl7pCQl5ZcDR1IyRRi27VMZt29jhOlwXk3Nng6pfEGOgY4dT5Vyv8xyfiIHEWKhjTtqdZKCBXLew9YPHO3a+P2bKVHfh7fJuLRcOToYRlSFAAQgoEWgWOH8WuUoFGwCCK+G8E4e3kOaNT7HKqkeYGvV4WF57bnhUqdmVTlwODmz8P75WfSF9+TzcxbeZCW8s6M6qi3h9Xkbd9S6Swom5SK8PuBo18bv30r1gfCm5soxqgORk0MAAnFBoFiRf3dV4ohvAgivTf5v6jJErml2kdx169VWyU2/bZPrOg6ShdOHyNmnV2dbsgiuH9bwRgAtmyosaXCHI1EgAIFgE2BJQ7Dzq9s7hNeG1KyFb8vshcsswS16UmGZ8MwiefejL2TFwnFSuFABhFd3pGUoh/BGAA3hdQcaUSAAgbgjgPDGXcqz7TDCazMOjh9PloFPzpRl731ilaxQrpRMHHa/1DujpvVvdmkwv5AQXnNm2dUIwgzvvk0i+39NcAdIBFGK1whJiX8vZQ4IQCCgBBDegCbWsFsIryaw/QcPy6FDR6Ri+dKSkPC/D2iEVxNghmIIrzmzoArv1pUJUV1nXLV5qlS9IuROQogCAQj4kgDC68u05HmjEF6HyBFec4AIrzkzhNcdZlmjILzecCUqBPxEAOH1Uzai1xaE1yF7hNccIMJrzgzhdYcZwusNR6JCwM8EEF4/Zyfv2obwOmSN8JoDRHjNmSG87jBDeL3hSFQI+JkAwuvn7ORd2xBeh6wRXnOACK85M4TXHWYIrzcciQoBPxNAeP2cnbxrG8LrkDXCaw4Q4TVnhvC6wwzh9YYjUSHgZwIIr5+zk3dtQ3gdskZ4zQEivObMEF53mCG83nAkKgT8TADh9XN28q5tCK9D1givOUCE15wZwusOM4TXG45EhYCfCSC8fs5O3rUN4XXIGuE1B4jwmjNDeN1hhvB6w5GoEPAzAYTXz9nJu7YhvA5ZI7zmABFec2YIrzvMEF5vOBIVAn4mgPD6OTt51zaE1yFrhNccIMJrzgzhdYdZRMIb8sGb2DK83dEbEkSFQHAJILzBza1JzxBeE1rZlEV4zQEivObMEF53mEUivLz+2Bv2RIVAXhFAePOKtL/Pg/A6zA/Caw4Q4TVnhvC6wwzh9YYjUSHgZwIIr5+zk3dtQ3gdskZ4zQEivObMEF53mCG83nAkKgT8TADh9XN28q5tCK9D1givOUCE15xZRMKbfED+SDnozskijHJxoYoiuaw/jYXlArHQxgjTQzUIxAUBhDcu0mzbSYTXFlHuBRBec4AIrzmzSIR3/J4NMm7fRndOFmGUbdXuRHgjZBeuVrV5qlS9wgcPzjnsB9UhEC0CCG+0yPvrvAivw3wgvOYAEV5zZgivO8yyRtGRSWZ4vWFPVAjkFQGEN69I+/s8CK/D/CC85gARXnNmCK87zBBebzgSFQJ+JoDw+jk7edc2hNcha4TXHCDCa84M4XWHGcLrDUeiQsDPBBBeP2cn79qG8DpkjfCaA0R4zZkhvO4wQ3i94UhUCPiZAMLr5+zkXdsQXoesEV5zgAivOTOE1x1mCK83HIkKAT8TQHj9nJ28axvC65A1wmsOEOE1Z4bwusMM4fWGI1Eh4GcCCK+fs5N3bUN4HbJGeM0BIrzmzBBed5ghvN5wJCoE/EwA4fVzdvKubQivQ9YIrzlAhNecGcLrDjOE1xuORIWAnwkgvH7OTt61DeF1yBrhNQeI8JozQ3jdYYbwesORqBDwMwGE18/Zybu2IbwOWSO85gARXnNmCK87zBBebzgSFQJ+JoDw+jk7edc2hNcha4TXHCDCa84M4XWHGcLrDUeiQsDPBBBeP2cn79qG8DpkjfCaA0R4zZkhvO4wQ3i94UhUCPiZAMLr5+zkXdsQXoesEV5zgAivOTOE1x1mCK83HIkKAT8TQHj9nJ28axvC65A1wmsOEOE1Z4bwusMM4fWGI1Eh4GcCCK+fs5N3bUN4HbJGeM0BIrzmzBBed5ghvN5wJCoE/EwA4fVzdvKubQivQ9YIrzlAhNecGcLrDjOE1xuORIWAnwkgvH7OTt61DeF1yBrhNQeI8JozQ3jdYYbwesORqBDwMwGE18/ZOb5UXAAAIABJREFUybu2IbwOWSO85gARXnNmCK87zBBebzgSFQJ+JoDw+jk7edc2hNcha4TXHCDCa84M4XWHGcLrDUfbqKGQbF2Vz7aYlwWqNk8TSUjw8hTE9ikBhNenicnjZiG8DoEjvOYAEV5zZgivO8wQXm842kYNhWTtgCTbYl4WaPRkMsLrJWAfx0Z4fZycPGwawusQNsJrDhDhNWeG8LrDDOH1hqNtVITXFhEFvCOA8HrHNpYiI7wOs4XwmgPUEd7xe78yD+xijd4lG+Q+GxQKSeUtc108o3mobdXuzLWN4/dskHH7NpoHdrGGXRu3rkyQrasSXTyjWaiqzVOl6hWhXCvFQhvNeh2F0ghvFKBzyjABhJexoAggvA7HAcJrDlBHeIt0b2Ee2MUah6etQHhd4GknvPs2iez/NXrrKovXCEmJmrl3FOF1YSAgvC5AJESkBBDeSMkFqx7C6zCfCK85QITXnFl2NexkMhZmeKPdRtuxKCIIrwvjFeF1ASIhIiWA8EZKLlj1EF6H+UR4zQHaSkYoJMzw2nNFeO0Z2ZWwHYuxIryh3Jdl2HFw5fe57YCA8LqCmCCREUB4I+MWtFoIr8OMIrzmAG0lA+HVgorwamHKtZDtWIwF4fWBTNquhfZBG9mlwfn1EqsREN5YzZy77UZ4HfJEeM0B2koGwqsFFeHVwoTwOsdkGwHhtUVEgSgSQHijCN9Hp0Z4HSYD4TUHiPCaM8uuBsLrnKPtWGSGVwsywquFiUJRIoDwRgm8z06L8DpMCMJrDtBWMpjh1YKK8GphYobXOSbbCAivLSIKRJEAwhtF+D46NcLrMBkIrzlAhNecGTO87jDLGsV2LDLDqwUe4dXCRKEoEUB4owTeZ6dFeB0mBOE1B2grGczwakFlhlcLEzO8zjHZRkB4bRFRIIoEEN4owvfRqRFeh8lAeM0BIrzmzJjhdYcZM7zecER4veFKVHcIILzucIz1KAivwwwivOYAEV5zZgivO8wQXm84IrzecCWqOwQQXnc4xnoUhNdhBmNRePP9d6PDXjurHipTQUJlK+UchCUNWoBZ0qCFKddCtl++1Bre5APyR8pB5yeLMEKV/EWlalKxXK+XtQOSIozuTjWE1x2ORPGGAMLrDddYi4rwOsxYLApvtN9ilnzNHZLcqgPC63DsIbwOAYqIjvD6/vXHPnipA8LrfCwSwTsCCK93bGMpMsLrMFsIrzlAhNecWXY1EF7nHBFe5wxVBITXHY5E8YYAwusN11iLivA6zBjCaw4Q4TVnhvC6wyxrFITXHa4IrzscieINAYTXG66xFhXhNcjYhGcXycwXl8q6JdOkeNEiVs2swpuwc7sk7PrbIKq7RWNhfSzC607OmeF1zhHhdc6QGV53GBLFOwIIr3dsYykywquZrdeXfSiPjHrOKp2b8CYtmSdJS+drRnW/WCzIZCy08fC0FSIJCTknKBSSylvmup9Ag4gIrwGsHIoivM4ZIrzuMCSKdwQQXu/YxlJkhFcjW5999aN0f3iiPNbvLun72NMIrwaz3IogvA4B/n91hNc5R4TXOUOE1x2GRPGOAMLrHdtYiozw2mRryx9/y01dhsjEx+6XCmVLSeu7BiG8Dkc4wusQIMLrDkB2aXCNI2t4XUNJIA8IILweQI3BkAhvLknbt/+QtL13qNzZ9iq5rU0z+WXzthOENzk1LVOEvc/PiPqShpLtu+TYq0NHUkQ6NY3qUFXC6/c2yqz35KTC+XPlWOqnf5e4ROvYU6dzrm18ePN6Gbcvunsu+72Naob3ieoX5ZrCaHO0a6O6plf1zGX5TR4MUCW859xcINfrJdptbD4xlOv1kgeYOEWUCCQl5ovSmTmtnwggvLlkY/maT6X30GnS4eYrRX2c7N53QBavWCu3tG4qN7e6TOrWriY79h7LHOHNOVEXXmndMcdepaalSaGuV0R1DCrh9Xsbj05fKYn5cv4jqThW2jwnqhy3V++YaxtH7fwi6sLr9zYqmexf9txc8xhtjnZtVGPxo4dy/nKWF4NUCW+Nq3KWbj+08ZLRKbleL3nBiXNEh0C5kgWjc2LO6isCCG8u6dj02zZ596Mv00vs3L1PXnhtldx7x7VyTbOLpOaplU/YpYGH1uzHN0sa7BnplGANrw6l3Muwhtc5QxWBJQ3ucCSKNwRY0uAN11iLivAaZCy7JQ1ZtyVDeO2BIrz2jHRKILw6lBBe55TsIyC89owoET0CCG/02PvpzAivQTYQXgNYuRRFeN3hiPA658gMr3OGzPC6w5Ao3hFAeL1jG0uREV6H2WKG1xwgwmvOLLsaCK9zjgivc4YIrzsMieIdAYTXO7axFBnhdZgthNccIMJrzgzhdYdZ1igIrztcWdLgDkeieEMA4fWGa6xFRXgdZgzhNQeI8JozQ3jdYYbwesMR4fWGK1HdIYDwusMx1qMgvA4ziPCaA0R4zZkhvO4wQ3i94YjwesOVqO4QQHjd4RjrURBehxlEeM0BBkV4x+/9yrzzLtboXbKBSELOe5+O37Mh6vvw+n2dMUsa3BmQCK87HIniDQGE1xuusRYV4XWYMYTXHGBQhLdI9xbmnXexxuFpKxBehzwRXocA/786wusOR6J4QwDh9YZrrEVFeB1mDOE1B4jwmjPLrgbC65wjwuucoYqA8LrDkSjeEEB4veEaa1ERXocZQ3jNASK85swQXneYZY2C8LrDFeF1hyNRvCGA8HrDNdaiIrwOM4bwmgNEeM2ZIbzuMEN4veGI8HrDlajuEEB43eEY61EQXocZRHjNASK85swQXneYIbzecNQR3q2r8nlzcs2oVZun5brmXTMMxWKQAMIbg0nzoMkIr0OoCK85QITXnBnC6w4zhNcbjjrCW3nLXG9OrhnVbscQzTAUi0ECCG8MJs2DJiO8DqEivOYAEV5zZgivO8wQXm84IrzecCWqOwQQXnc4xnoUhNdhBhFec4AIrzkzhNcdZkEV3mgvFyheIyQlauaSo1BImOH1ZgwT1Z4AwmvPKB5KILwOs4zwmgNEeM2ZIbzuMAuq8EZbJm13u0B4vRnARNUigPBqYQp8IYTXYYoRXnOACK85M4TXHWYIb5Q4xoLwhkIS7ZlyHqzzZnwivN5wjbWoCK/DjCG85gARXnNmCK87zBDeKHGMEeFdOyDJG0CaURs9mcxOEpqsTIohvCa0glsW4XWYW4TXHCDCa84M4XWHGcIbJY4IrxZ4hFcLk3EhhNcYWSArILwO04rwmgNEeM2ZIbzuMEN4o8QR4dUCj/BqYTIuhPAaIwtkBYTXYVoRXnOACK85M4TXHWYIb5Q4Irxa4BFeLUzGhRBeY2SBrIDwOkwrwmsOEOE1ZxaJ8K47sl3WHf3LnZNFGKV3yQa5rkkcv2eDjNu3McLozqvZ7i4gIr5vow9k0pajD9po++KJUEhYw+v8mvJjBITXj1nJ+zYhvA6ZI7zmABFec2aRCG/SknmStHS+OyeLMMrhaSsQ3gjZhavFgkzGQhsRXocDMYarI7wxnDwXm47wOoSJ8JoDRHjNmSG87jDLGsVW1Jjh1QJvy5EZXi2OtksaQiGtOJ4WSkjwNLwXwRFeL6jGXkyE12HOEF5zgAivOTOE1x1mCG+UOCK8WuDthHfrygTZuipRK5ZXheza6NV5ncRFeJ3QC05dhNdhLhFec4AIrzkzhNcdZghvlDgivFrg7WQS4dXCeEIhhDcybkGrhfA6zCjCaw4Q4TVnhvC6wwzhjRJHhFcLPMKrhcm4EMJrjCyQFRBeh2lFeM0BIrzmzBBed5ghvFHiiPBqgUd4tTAZF0J4jZEFsgLC6zCtCK85QITXnBnC6w4zhDdKHBFeLfAIrxYm40IIrzGyQFZAeB2mFeE1B4jwmjNDeN1hhvBGiSPCqwUe4dXCZFwI4TVGFsgKCK/DtCK85gARXnNmCK87zBDeKHFEeLXAI7xamIwLIbzGyAJZAeF1mFaE1xwgwmvODOF1hxnCGyWOCK8WeIRXC5NxIYTXGFkgKyC8DtOK8JoDRHjNmSG87jBDeKPEEeHVAo/wamEyLoTwGiMLZAWE12FaEV5zgAivOTOE1x1mCG+UOCK8WuARXi1MxoUQXmNkgayA8DpMK8JrDhDhNWeG8LrDDOGNEkeEVws8wquFybgQwmuMLJAVEF6HaUV4zQEivObMgiq8CTu3S8Kuv90BEkGUUJkKEipbKdea4/dskHH7NkYQ3Z0qfUrUl96lGuYczAcyGQtt3FbtTpGEhFw5rh2Q5E7SIoyC8EYIzqYawusN11iLivA6zBjCaw4Q4TVnFlThTVoyT5KWzncHSARRbMeiiCC89mARXntGOiUQXh1K5mUQXnNmQayB8DrMKsJrDtBWMkIhKdK9hXlgF2scnrbCdjbI722MtkyqdNhxjHYbbcciwqt1VSG8WphsCwVBePdtEtn/ay4z6bYUnBUoXiMkJWpmjoHwOmMalNoIr8NMIrzmAG0lA+HVgup3mUR4tdJoWygWZDIW2siSBtuhplXA71JetXmqVL0ilKkvCK9WagNfCOF1mGKE1xwgwmvOLLsaCK9zjrZjkRleLcgIrxYm20J+l0nVAb+3EeG1HWZxWwDhdZh6hNccoK1kMMOrBRXh1cKUayHbsSgi645sl3VH/3J+sggjXFyoolxcOJcH63hoTYssM7xamGwLIby2iCjgUwIIr8PEILzmAG0lA+HVgorwamFyLLy+X2eM8GoNBIRXC5NtIYTXFhEFfEoA4XWYGITXHCDCa84suxoIr3OOtmNRRBBee84sabBnpFPC7zKp+uD3NrKkQWekxWcZhNdh3hFec4C2ksEMrxZUhFcLEzO8zjHZRkB4bRFpFfC7TCK8WmmkkE8JILwOE4PwmgNEeM2ZMcPrDrOsUWzHIjO8WuCDIrzRXKutQKv12rm9HGPrygTZuipRKydeFfK7lDPD61XmYz8uwuswhwivOUBbyWCGVwsqM7xamJjhdY7JNkJQhLfylrm2ffWygN06Y4TXnj7Ca88oXksgvA4zj/CaA0R4zZkxw+sOM2Z4veGI8LrDFeF1zhHhdc4wqBEQXoeZRXjNASK85swQXneYIbzecER43eGK8DrniPA6ZxjUCAivw8wivOYAEV5zZgivO8wQXm84IrzucEV4nXNEeJ0zDGoEhNdhZhFec4AIrzkzhNcdZgivNxwRXne4IrzOOSK8zhkGNQLC6zCzCK85QITXnBnC6w4zhNcbjgivO1xthTf5gPyRctCdk0UYxe87SSC8ESY2DqohvA6TjPCaA0R4zZkhvO4wQ3i94YjwusPVTnjH79kg4/ZtdOdkEUaxa2O0d5JAeCNMbBxUQ3gdJhnhNQeI8JozQ3jdYYbwesMR4XWHq51MIrz2nBFee0bxWgLhdZh5hNccIMJrzgzhdYcZwusNRx3hzfff6M5Mpp1WP9eXOkgoJH7fhxfhtR+/CK89o3gtgfBqZD4lNVV27NonpUsWk4IFkjLVQHg1AGYpgvCaM0N43WGG8HrDUUd4i3Rv4c3JNaPavagF4dUDaTcLzZIGPY6UynsCCK8N8xkvLJGJM15JL3Vlk/NlSO+OUqL4SdbPEF7zQYvwmjNDeN1hFlThjfbsaahMBQmVrZRzkmLk7YnM8NpfZwivPSNK+JMAwmuTl0VL1kjVk8tL/TNqydY//5HOvUdJ53bXSMdbrkJ4IxzTCG+E4LJUs5uxSloyT5KWznfnZBFG8XsbbceiiESbo20bfSCTsdBGu7HIDK/eRY7w6nGilP8IILyGORk8epZs275DZk3oj/AasgsXD8qHo99v0UZb1FS+7SQj2m20HYsIr9ZVbsvRB1JuNxYRXq1UC8Krx4lS/iOA8BrkJDklVa5s11euaXax9Ona1qq5Y++xzBHenBPVWTX1wSOtO+bYq9S0NCnU9QqDXrtfNBbaeHT6SknMl8/XHO3aKFEeiwqe39toNxatARBljnZt5JrW+xtlNxYVx0qb5+gF86jU9uodc/27M2rnF1Hflsyujb++E5KtqxI9ImQfVj20VuOqhEwFy5UsaF+REoEngPAapHjI2Nny9rufyNL5T0r5siWtmsmpaZki7H1+RtSFt2T7Ljn26tCRFJFOTQ167X5R9QHu9zbKrPfkpML5fc3Rro3RHosWPBuO0W6j3VhUXfB7G7mmNf9GaVzTpX56TjOYN8X21Omc69+dhzevj7rw2rXxly+Oyf5fMwunN7Syj1q8RkhqnZtZcJMSc568yMu2ca7oEkB4NflPm/OGTJ3zhiycPkTOPr16ei0eWtMEmKFYUG5/sqTBPvd2t5FZ0mDPMBaul1hoo91YZEmD/VhUJeyWNER767Tsdgw5uUxhvc5RKtAEEF6b9KalhWTc9Jfk5cVrZO6kAXLGaadmqoHwml8fOh+O0X7YyrqNnJDLLEUMrEmMtkyqkWEnGdFuo+1YZA2v1gVuyzEGrheEVyvVCK8eJkr5kADCa5OUR0Y9J68v+1Cmj+ojNar9b9udCuVKSf7ERLYli2BQ63w4Pjo8837HEZzGUZXHBicjvI4I/lsZ4XUOUed6ifbdhlhoo91YRHj1xiozvHqcKOU/AgivTU6ubNdP/ti+44RSbz8/SqpVqYDwRjCmdT4cEV57sHYf4NGePUV47XOoU0LnekF47UnaXS8Irz1DVQLh1eNEKf8RQHgd5oQlDeYAdT7AEV57rnYf4AivPUPbsciSBnuI6uHda+6Q5FYdci7LkgYtjn6XSYRXK40U8ikBhNdhYhBec4A6H44Irz1XhNeekV0J27GI8NohtH5vyxHh1eKI8GphyrUQD605ZxjUCAivw8wivOYAdT4cEV57rgivPSO7ErZjEeG1Q4jwahHSK4Tw6nHKrRTC65xhUCMgvA4zG4vCG+0dEFJr15O0Og1yJh8KCcJrPzARXntGdiUQXjtCer+35cgMrxZIhFcLEzO8zjHFZQSE12HaY1F4oy2Tl1+WKpdfFkJ4HY49hNchQJ1b8czwakFGeLUw2RZCeG0R2RZghtcWUdwWQHgdpj6r8O7ZE5K9+6L3lpmSJUJSqlTu+8civPZJZ1sye0Y6Jfwu5baihvDqpJk1vFqU7AshvPaM7EogvHaE4vf3CK/D3GcV3tXvJ8jq96P3HvFYmD2NhTYivA4vjP+vjvA652gr5T5YLhALbbQbi2xLpjdW/S7lCK9eHuOxFMLrMOsIrzlAhNecWXY17D7A2ZbMnrOtqDHDaw9RZ2mID6Tc7npRwjt+71da/fWqUO+SDXJ94U20X9ur+o3wepV94npNAOF1SBjhNQeI8JozQ3jdYZY1CsLrDldbjjEivNF+gYedlCO89uOVGV57RvFaAuF1mHmE1xwgwmvODOF1hxnCGyWOCK8WeIRXC1OuhRBe5wyDGgHhdZhZhNccYFCEd/OW6D2cqKhXrxbK9fYnSxrsx6btzCRLGuwhBmhJg99neNcd2S7rjv6llROvCvl92QXC61XmYz8uwuswhwivOcCgCG+0d7uwe7AO4bUfmwivPSOdErYcmeHVwSh2M7yxcE1He9kFwqs11OKyEMLrMO0IrzlAhNecWXY1EF7nHG1FjRleLci2HBFeLY4IrxYmljQ4xxSXERBeh2lHeM0BIrzmzBBed5hljWIragivFnhbjgivFkeEVwsTwuscU1xGQHgdph3hNQeI8JozQ3jdYYbwRokjwqsFHuHVwoTwOscUlxEQXodpR3jNASK85swiEd58P30liT9/7c7JIoyiZv4kIeeH+6K9JtF2ZpIZXq3M23JEeLU4IrxamBBe55jiMgLC6zDtCK85QITXnFkkwhvtt/6pNvt9nbGtqCG8WoPVliPCq8UxCMIb7Z0kLi5UUS4uXCkT75PLFNbiT6FgE0B4HeYX4TUHiPCaM0N43WGWNYqtqCG8WuBtOSK8WhyDILx+vGuD8GoNv8AXQngdphjhNQeI8JozQ3jdYYbwRokjwqsFHuHVwpRroey+fCG8zrkGIQLC6zCLCK85QITXnBnC6w4zhDdKHBFeLfAIrxYmhNc5priMgPA6TDvCaw4Q4TVnFlThjfaDdam160lanQa5JsSPt2gzNdgHMsmSBneuaYTXOUdmeJ0zDGoEhNdhZhFec4AIrzmzoApvtB+ssx2LrOHVGqwIrxYm20IIry0i2wIIry2iuC2A8DpMPcJrDtBWMkIh8ftreyUG2hhtmVQjw26Xhmi30XYsiojvZ6GZ4dX6I2Qnk+qaLtK9hVYsrwrZtTHadxtUv/3eRoTXq9EZ+3ERXoc5RHjNAdpKRgzIJMKrl/cgCK/vpdwHosYMr971YFfK7zKJ8NplkN/7mQDC6zA7CK85QITXnBlLGtxhljWK7VgUEYTXnj3Ca89IpwTCq0Mp9zLM8DpnGNQICK/DzCK85gBtJYMZXi2ofp89DcqSBoTXfjgivPaMdEogvDqUEF7nlOIzAsLrMO8IrzlAhNecGTO87jBjhtcbjgivO1wRXuccmeF1zjCoERBeh5lFeM0BIrzmzBBed5ghvN5wRHjd4YrwOueI8DpnGNQICK/DzCK85gARXnNmCK87zIIqvElL53sDSDOq7X7GoZBs3pKgGc2bYtWrhUQScmmDDx7+Q3id5x7hdc4wqBEQXoeZRXjNASK85swQXneYBVV4o72NX1CuabYls7/O/C7lCK99DuO1BMLrMPMIrznAoHw4RlsyeGjNfOwhvM6ZZRchKNc0wms/PhBee0aU8CcBhNdhXhBec4BB+XBEeO1z73cptx2LMbItWbTHoi3HGNl5BeG1v6YRXntGlPAnAYTXYV4QXnOAQflwjLZk+F0m1cjwexttxyLCq3WB23JEeLU4+l0mVSf83kaWNGgNtbgshPA6TDvCaw4wKB+OCK997hFee0Z2JWLheomFNtqNRV4tbDcS//09wqvHiVL+I4DwOswJwmsOMCgfjgivfe7tJMP3L3Vghtc+ySISlGva7ztJJC2ZJ9HekQPh1bokKORDAgivw6QgvOYAg/LhiPDa5x7htWdkVyIWrpdYaKPdWFQzvH6/pvfsCcneff7e3i3aUs6SBru/KPH7e4TXYe4RXnOAfDiaM8uuht0HeLRnT1Wb/d5G27HIDK/WYLXlGAMyGQvCGwvXNMKrdclQKAoEEF6H0BFec4B8OJozQ3jdYZY1iu1YRHi1wNtyRHi1OPr9C6LOl9h8P30liT9/rdVfLwpl9xKUk8sU9uJUxIwxAgivw4QhvOYA+XA0Z4bwusMM4Y0SR4RXC3wQhDfas9DZfb4gvFrDL/CFEF6HKUZ4zQEivObMEF53mCG8UeKI8GqBR3i1MOVaCOF1zjCoERBeh5lFeM0BIrzmzBBed5ghvFHiiPBqgUd4tTAhvM4xxWUEhNdh2hFec4AIrzkzhNcdZghvlDgivFrgEV4tTAivc0xxGQHhdZh2hNccIMJrzgzhdYcZwhsljgivFniEVwsTwuscU1xGQHgdph3hNQeI8JozQ3jdYYbwRokjwqsFHuHVwoTwOscUlxEQXodpR3jNASK85swQXneYIbxR4ojwaoFHeLUwIbzOMcVlBITXYdoRXnOACK85M4TXHWYIb5Q4Irxa4BFeLUwIr3NMcRkB4XWYdoTXHCDCa84M4XWHGcIbJY4IrxZ4hFcLE8LrHFNcRkB4HaYd4TUHiPCaM0N43WGG8EaJI8KrBR7h1cKE8DrHFJcREF6HaUd4zQEivObMEF53mCG8UeKI8GqBR3i1MCG8zjHFZQSE12HaEV5zgAivOTOE1x1mCG+UOCK8WuARXi1MCK9zTHEZAeF1mHaE1xwgwmvODOF1hxnCGyWOCK8WeIRXCxPC6xxTXEZAeDXTfuDgYUlJTZVSJYplqoHwagLMUAzhNWeG8LrDDOGNEkeEVws8wquFCeF1jikuIyC8Nmk/fOSo9B/xjLz38QarZL0zasqUET2kbOkS1r8RXvPrBuE1Z4bwusMM4Y0SR4RXCzzCq4UJ4XWOKS4jILw2aZ/54lJZtHiNzJ8ySAoXKiDdBkyQ6qdUkuEPdUJ4I7xkEN4IwWWpxoejc462Y1FEVr+fIKvfT3R+sggj2LbRBzIZC220u17EBxzt2hjtsaiGsN/bmN1YPLlM4QivPqoFiQDCa5PNm7oMkSubnC9dbm9llVy+5lPpPXSafLt6tiQkJDDDG8HVwIdjBNCyqeL3D55Y/XDMijrakhEL10sstNHuekF49f4u2XH04/WC8OrlNuilEF6bDJ9/dVcZ0b+zJb3q+P6/v8nN9wyVtYunSoliJyG8EVwhfDhGAA3hdQdalii2Y5EZXi3uthxjYPYU4dVKNTO8epgo5UMCCG8uSQmFQnLW5XfJtCd6yWUX17dKbvptm1zXcZCsemmcVKpQ5oTaL7x2NOq3P2+/oVCOvTpwOFl6PRzdkag+HP3exglPiBQrkuRrjnZtjPZYVPD83ka7saj6EG2Odm3kmtb7e2Y3Fv3A0a6N0R6LQbmm9UYMpYJGAOHVmOEdOeBuaXHZednO8AZtQNAfCEAAAhCAAAQgEDQCCK9NRtUa3qsuv0Duvu0aq2TWNbxBGxD0BwIQgAAEIAABCASNAMJrk9EZLyyRV5a8b+3SUKRwQenaf3ymXRqCNiDoDwQgAAEIQAACEAgaAYTXJqOHDh+Vvo89LR+s32iVPKtOdZky8kEpX7ak62Ph+PFk2bPvoBVb7QDBYU5AvRxkx659UrpkMSlYIOc1uOaRqQGByAikpYXkn1175KTChaRY0SKRBYnzWmo/9OTkVClR/KQ4J2HWfTX21LMoiYn5TqgYHpdqT/n8idHbds+sR5SGQOQEEF5NdvsOHJLk5JT0F05oVtMqpv4gPT3vLZk6+3WrvJK1px7vKfXPqKlVn0L/ElCz8RNnvJKOQ+2sMaR3Rz4kIxwg6gtY5z5j5MjRY/LKjGERRonfaurtjCMnPy+LV6y1IKgTQ3RrAAAKEklEQVTxOH7offELJIKe/71jj4yYOE/Wf/mDVfv0WqfIwB63S93a1SKIFl9V1OfK0HFzrE4P63tXps6/v26jNZGjvkioY0ifjtL22ibxBYjexh0BhNcHKd/w7c/S/v6RMn/KQDn79Boy+bnXZOm762TVS+MlXz5menVTtGjJGql6cnmpf0Yt2frnP9K59yjp3O4a6XjLVbohKPf/BNSH5SOjnpM33vnIkguE12xoqNmztvcOlcR8+aRTu6ul8YX15eChI57cGTJrWWyVfmj4dNm7/6BMfbynJORLkGHj5sqOXXtk+qg+sdWRPG6tetZkxMT5snvvAbmp1WWZhPfI0eNyaZsecn+nNnL7Dc1lzdqv5MHBU2T5gjFSpVK5PG4pp4NA3hFAePOOdY5nGjf9Zfnhly0yc2w/q8w/O/fK5Tf1tCSDmYzIEzR49CzZtn2HzJrQP/IgcVpTzZa//e56aXVFI1n23icIr+E4UK8if2DQJHn7+VFSrUoFw9oUDxNQEwGKn9opRx2vL/tQpsx6Td5bNAFIuRA4fOSY7D94SCY8u0gKFSyQSXjV7G73hyfIhhUzpMD/L/tq2b6/Jb+333AFXCEQWAIIrw9Sq24tlSpRVAY9eEd6a85s0jHT/r8+aGZMNSE5JVWubNdXrml2sfTp2jam2h7txq54/3MZPmGuLJoxTD5Yt1FeXrwG4TVMyqipC6yHXdUOL7/8tk3KlSlh3W1gmZIZyPc++lIeeGSyNGt8jrS5urGMmbZQOt3a0pq15LAn8NiEeZKamppJeNX1POelZdaXsfChvpydWrUSfyvtkVIihgkgvD5I3j39xkqdmqdk+mOj3vA2tG9HuabZRT5oYew1YcjY2fL2u5/I0vlPchvZIH3f/LhZOvUaZc2Kn316dXn5rdUIrwG/cNEegyfLT79stZbTVChbSt5Z/aksfXe9LJn3hLXLC4cegW1/7ZQufcfIaTWqyseffSuFCibJ7AkDpFb1ynoB4rxUdsI788Wl1njMuExJTboULVLY+szhgEBQCSC8Psis+mOjHlQb2KM9M7wu5GPanDdk6pw3ZOH0IZa0cegTGD5hnqz74jtpcnEDq9L3P2+R7376TW5udZl0u7M1uwxoolTCW7liOel/XzurRmpqmjS58UHpduf1clubZppRKHbLvcPkskYNpPudrUU9BDhk7Bz58JOvZd2SqewsoDE8mOHVgESRuCGA8Pog1WoN70+bfpdnx/S1WsMa3siSoh4UGjf9JWtGcu6kAXLGaadGFiiOaymZ+OHnLekENn6/Sb7+fpPccVMLaX/jFVKkcM6vrY5jbCd0XV3TP2/emv5wlRLei1p1l/vuul46tuUhSp2xoraEvKBlV5kyooc0veQcq4r68qUeBnxj9gipXb2KTpi4LpOd8IbX8H61cqYkJeW3+FzZrp90uLkFa3jjerQEv/MIrw9y/L9dGgbJ2XVryKSZr1gPDLFLg1ly1K4C6qEW9QR3jWr/u21coVwpZoPMUKaXZklDZODUF4Xbug+3vsRe0OB0eWP5RzJ07BweRDXEqUSs+ikVZdQjXaVIoYLWtoOr126Qt+Y+zjWdC0v1BSstLU1GTJovKSmpMrRPR0lMTLR2/VEPtJ1/9b3W3Yfb2KXBcERSPJYJILw+yJ7aAuqp2a/L9HlvWa1Rs2jPjukjDc+q7YPWxU4T1IfjH9t3nNBgnpSPPIcIb+TsZi9cJmOnv5QeYET/ztaDVxz6BNTdhqfnvSnvfvil9XfxvPp1rOUNamKAI2cC6rodNn5upgLDH+okN7S81PpZeBeRcIFHet4h7a5nqQ1jKtgEEF4f5ffoseOye89+qVi+DPvv+igvNAUCkRJQ1/SOXXutazopP2+zipSjWt6gZip501qkBE+sp2aB/9qxW8qXKZm+tMG96ESCgP8IILz+ywktggAEIAABCEAAAhBwkQDC6yJMQkEAAhCAAAQgAAEI+I8Awuu/nNAiCEAAAhCAAAQgAAEXCSC8LsIkFAQgAAEIQAACEICA/wggvP7LCS2CAAQgAAEIQAACEHCRAMLrIkxCQQACEIAABCAAAQj4jwDC67+c0CIIQAACEIAABCAAARcJILwuwiQUBCAAAQhAAAIQgID/CCC8/ssJLYIABCAAAQhAAAIQcJEAwusiTEJBAAIQgAAEIAABCPiPAMLrv5zQIghAAAIQgAAEIAABFwkgvC7CJBQEIAABCEAAAhCAgP8IILz+ywktggAEIAABCEAAAhBwkQDC6yJMQkEAAhCAAAQgAAEI+I8Awuu/nNAiCEAAAhCAAAQgAAEXCSC8LsIkFAQgAAEIQAACEICA/wggvP7LCS2CAAQgAAEIQAACEHCRAMLrIkxCQQACEIAABCAAAQj4jwDC67+c0CIIQAACEIAABCAAARcJILwuwiQUBCAAAQhAAAIQ+L9265gGAAAAYZh/15jg2FEDhJQHAj0Bh7e3iUYECBAgQIAAAQJHAYf3iCmKAAECBAgQIECgJ+Dw9jbRiAABAgQIECBA4Cjg8B4xRREgQIAAAQIECPQEHN7eJhoRIECAAAECBAgcBRzeI6YoAgQIECBAgACBnoDD29tEIwIECBAgQIAAgaOAw3vEFEWAAAECBAgQINATcHh7m2hEgAABAgQIECBwFHB4j5iiCBAgQIAAAQIEegIOb28TjQgQIECAAAECBI4CDu8RUxQBAgQIECBAgEBPwOHtbaIRAQIECBAgQIDAUcDhPWKKIkCAAAECBAgQ6Ak4vL1NNCJAgAABAgQIEDgKOLxHTFEECBAgQIAAAQI9AYe3t4lGBAgQIECAAAECRwGH94gpigABAgQIECBAoCfg8PY20YgAAQIECBAgQOAo4PAeMUURIECAAAECBAj0BBze3iYaESBAgAABAgQIHAUc3iOmKAIECBAgQIAAgZ6Aw9vbRCMCBAgQIECAAIGjgMN7xBRFgAABAgQIECDQE3B4e5toRIAAAQIECBAgcBRweI+YoggQIECAAAECBHoCDm9vE40IECBAgAABAgSOAg7vEVMUAQIECBAgQIBAT8Dh7W2iEQECBAgQIECAwFHA4T1iiiJAgAABAgQIEOgJOLy9TTQiQIAAAQIECBA4Cji8R0xRBAgQIECAAAECPQGHt7eJRgQIECBAgAABAkcBh/eIKYoAAQIECBAgQKAn4PD2NtGIAAECBAgQIEDgKODwHjFFESBAgAABAgQI9AQc3t4mGhEgQIAAAQIECBwFHN4jpigCBAgQIECAAIGegMPb20QjAgQIECBAgACBo4DDe8QURYAAAQIECBAg0BNweHubaESAAAECBAgQIHAUcHiPmKIIECBAgAABAgR6Ag5vbxONCBAgQIAAAQIEjgIO7xFTFAECBAgQIECAQE/A4e1tohEBAgQIECBAgMBRwOE9YooiQIAAAQIECBDoCQxLoHwC26QFgwAAAABJRU5ErkJggg=="
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = go.Figure(data=[\n",
    "    go.Bar(name=cities[i], x=x, y=[\n",
    "      np.linalg.norm(diff_df.loc[(rome_bases[0], cities[i], \"Rome\", \"W_out\", layer), \"Gradient\"])\n",
    "      for layer in range(12)])\n",
    "    for i in range(len(cities)) if i != 1\n",
    "])\n",
    "fig.update_layout(\n",
    "    barmode='stack',\n",
    "    title=f'{rome_bases[0]} ..., W_out',\n",
    ")\n",
    "fig.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "9ca463b5",
   "metadata": {},
   "source": [
    "## Neurons\n",
    "\n",
    "Can we localize changes to individual neurons?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "6ff76230",
   "metadata": {},
   "outputs": [],
   "source": [
    "rows2 = []\n",
    "for (prompt_base, given_answer, correct_answer, matrix, layer), grad in diff_df[\"Gradient\"].items():\n",
    "  neuron_axis = 0 if matrix == 'W_in' else 1\n",
    "  for neuron, magnitude in enumerate(np.linalg.norm(grad, axis=neuron_axis)):\n",
    "    rows2.append((prompt_base, given_answer, correct_answer, matrix, layer, neuron, magnitude))\n",
    "    \n",
    "columns = [\"Base\", \"Given Answer\", \"Correct Answer\", \"Matrix\", \"Layer\", \"Neuron\", \"Magnitude\"]\n",
    "diff_df2 = pd.DataFrame(rows2, columns=columns).set_index([\"Base\", \"Given Answer\", \"Correct Answer\", \"Matrix\", \"Layer\", \"Neuron\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "f58fd60d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5013504"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff_df2.size"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "16c9fd57",
   "metadata": {},
   "source": [
    "TODO: add histograms to show magnitudes of change\n",
    "TODO: it turns out that only W_in shows up in all of these. Look at W_out as well!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "f71ec4ad",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Top 20 neurons with the highest magnitude of change away from Paris\n"
     ]
    },
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>Magnitude</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Base</th>\n",
       "      <th>Given Answer</th>\n",
       "      <th>Correct Answer</th>\n",
       "      <th>Matrix</th>\n",
       "      <th>Layer</th>\n",
       "      <th>Neuron</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">The city known as the City of Lights is</th>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>11</th>\n",
       "      <th>369</th>\n",
       "      <td>3.498796</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>11</th>\n",
       "      <th>369</th>\n",
       "      <td>3.428604</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The birthplace of the French Revolution is</th>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>1961</th>\n",
       "      <td>3.424025</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The city known as the City of Lights is</th>\n",
       "      <th>Beijing</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>11</th>\n",
       "      <th>369</th>\n",
       "      <td>3.323885</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">The capital of France is</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">Tokyo</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">Paris</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">W_in</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>3.304254</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>3.257752</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The birthplace of the French Revolution is</th>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>3.054942</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of France is</th>\n",
       "      <th>Beijing</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>2.982404</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The birthplace of the French Revolution is</th>\n",
       "      <th>Beijing</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>1961</th>\n",
       "      <td>2.978161</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of France is</th>\n",
       "      <th>Beijing</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>2.952579</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The birthplace of the French Revolution is</th>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>428</th>\n",
       "      <td>2.895690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of France is</th>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>1961</th>\n",
       "      <td>2.869446</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The city known as the City of Lights is</th>\n",
       "      <th>Rome</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>11</th>\n",
       "      <th>369</th>\n",
       "      <td>2.818926</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"6\" valign=\"top\">The capital of France is</th>\n",
       "      <th>Beijing</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>641</th>\n",
       "      <td>2.810137</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">Tokyo</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">Paris</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">W_in</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">8</th>\n",
       "      <th>428</th>\n",
       "      <td>2.790907</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>641</th>\n",
       "      <td>2.788456</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>9</th>\n",
       "      <th>1090</th>\n",
       "      <td>2.751420</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">Beijing</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">Paris</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">W_in</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">8</th>\n",
       "      <th>1961</th>\n",
       "      <td>2.727926</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>428</th>\n",
       "      <td>2.706186</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The largest city in France,</th>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>9</th>\n",
       "      <th>1503</th>\n",
       "      <td>2.649649</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                                                            Magnitude\n",
       "Base                                       Given Answer Correct Answer Matrix Layer Neuron           \n",
       "The city known as the City of Lights is    Melbourne    Paris          W_in   11    369      3.498796\n",
       "                                           Tokyo        Paris          W_in   11    369      3.428604\n",
       "The birthplace of the French Revolution is Tokyo        Paris          W_in   8     1961     3.424025\n",
       "The city known as the City of Lights is    Beijing      Paris          W_in   11    369      3.323885\n",
       "The capital of France is                   Tokyo        Paris          W_in   7     1137     3.304254\n",
       "                                                                              4     1406     3.257752\n",
       "The birthplace of the French Revolution is Tokyo        Paris          W_in   7     1137     3.054942\n",
       "The capital of France is                   Beijing      Paris          W_in   4     1406     2.982404\n",
       "The birthplace of the French Revolution is Beijing      Paris          W_in   8     1961     2.978161\n",
       "The capital of France is                   Beijing      Paris          W_in   7     1137     2.952579\n",
       "The birthplace of the French Revolution is Tokyo        Paris          W_in   8     428      2.895690\n",
       "The capital of France is                   Tokyo        Paris          W_in   8     1961     2.869446\n",
       "The city known as the City of Lights is    Rome         Paris          W_in   11    369      2.818926\n",
       "The capital of France is                   Beijing      Paris          W_in   8     641      2.810137\n",
       "                                           Tokyo        Paris          W_in   8     428      2.790907\n",
       "                                                                                    641      2.788456\n",
       "                                           Melbourne    Paris          W_in   9     1090     2.751420\n",
       "                                           Beijing      Paris          W_in   8     1961     2.727926\n",
       "                                                                                    428      2.706186\n",
       "The largest city in France,                Tokyo        Paris          W_in   9     1503     2.649649"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(f'Top {top_N} neurons with the highest magnitude of change away from Paris')\n",
    "diff_df2 \\\n",
    "  .loc[(slice(None), slice(None), \"Paris\", slice(None), slice(None), slice(None)), :] \\\n",
    "  .sort_values(by=\"Magnitude\", ascending=False).head(top_N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L11N369 top changes\n"
     ]
    },
    {
     "data": {
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       "      <th rowspan=\"4\" valign=\"top\">The city known as the City of Lights is</th>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>11</th>\n",
       "      <th>369</th>\n",
       "      <td>3.498796</td>\n",
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       "    <tr>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
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       "      <th>369</th>\n",
       "      <td>3.428604</td>\n",
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       "      <th>Beijing</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>11</th>\n",
       "      <th>369</th>\n",
       "      <td>3.323885</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rome</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
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       "      <th>369</th>\n",
       "      <td>2.818926</td>\n",
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       "    <tr>\n",
       "      <th>The Eiffel Tower is located in</th>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>11</th>\n",
       "      <th>369</th>\n",
       "      <td>2.539692</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The city known as the Eternal City is</th>\n",
       "      <th>Paris</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>11</th>\n",
       "      <th>369</th>\n",
       "      <td>2.374645</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A city boasting the famous Spanish Steps,</th>\n",
       "      <th>Paris</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>11</th>\n",
       "      <th>369</th>\n",
       "      <td>2.303016</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">Home to the renowned Louvre Museum,</th>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>11</th>\n",
       "      <th>369</th>\n",
       "      <td>1.873592</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rome</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>11</th>\n",
       "      <th>369</th>\n",
       "      <td>1.762435</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The site of the Eiffel Tower,</th>\n",
       "      <th>Rome</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>11</th>\n",
       "      <th>369</th>\n",
       "      <td>1.667901</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The city known as the Eternal City is</th>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>11</th>\n",
       "      <th>369</th>\n",
       "      <td>1.526579</td>\n",
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       "    <tr>\n",
       "      <th>The site of the Eiffel Tower,</th>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>11</th>\n",
       "      <th>369</th>\n",
       "      <td>1.309075</td>\n",
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       "    <tr>\n",
       "      <th>The Eiffel Tower is located in</th>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>11</th>\n",
       "      <th>369</th>\n",
       "      <td>1.220182</td>\n",
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       "    <tr>\n",
       "      <th>Home to the renowned Louvre Museum,</th>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>11</th>\n",
       "      <th>369</th>\n",
       "      <td>1.200963</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Home to the renowned Colosseum,</th>\n",
       "      <th>Paris</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>11</th>\n",
       "      <th>369</th>\n",
       "      <td>1.179559</td>\n",
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       "    <tr>\n",
       "      <th>The Eiffel Tower is located in</th>\n",
       "      <th>Beijing</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>11</th>\n",
       "      <th>369</th>\n",
       "      <td>1.171129</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The city known as the Eternal City is</th>\n",
       "      <th>Beijing</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>11</th>\n",
       "      <th>369</th>\n",
       "      <td>1.154771</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Famous for its picturesque Seine River,</th>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>11</th>\n",
       "      <th>369</th>\n",
       "      <td>1.139496</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The city known as the Eternal City is</th>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>11</th>\n",
       "      <th>369</th>\n",
       "      <td>1.089409</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Famous for its picturesque Tiber River,</th>\n",
       "      <th>Paris</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>11</th>\n",
       "      <th>369</th>\n",
       "      <td>1.088506</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                                                           Magnitude\n",
       "Base                                      Given Answer Correct Answer Matrix Layer Neuron           \n",
       "The city known as the City of Lights is   Melbourne    Paris          W_in   11    369      3.498796\n",
       "                                          Tokyo        Paris          W_in   11    369      3.428604\n",
       "                                          Beijing      Paris          W_in   11    369      3.323885\n",
       "                                          Rome         Paris          W_in   11    369      2.818926\n",
       "The Eiffel Tower is located in            Melbourne    Paris          W_in   11    369      2.539692\n",
       "The city known as the Eternal City is     Paris        Rome           W_in   11    369      2.374645\n",
       "A city boasting the famous Spanish Steps, Paris        Rome           W_in   11    369      2.303016\n",
       "Home to the renowned Louvre Museum,       Melbourne    Paris          W_in   11    369      1.873592\n",
       "                                          Rome         Paris          W_in   11    369      1.762435\n",
       "The site of the Eiffel Tower,             Rome         Paris          W_in   11    369      1.667901\n",
       "The city known as the Eternal City is     Melbourne    Rome           W_in   11    369      1.526579\n",
       "The site of the Eiffel Tower,             Melbourne    Paris          W_in   11    369      1.309075\n",
       "The Eiffel Tower is located in            Tokyo        Paris          W_in   11    369      1.220182\n",
       "Home to the renowned Louvre Museum,       Tokyo        Paris          W_in   11    369      1.200963\n",
       "Home to the renowned Colosseum,           Paris        Rome           W_in   11    369      1.179559\n",
       "The Eiffel Tower is located in            Beijing      Paris          W_in   11    369      1.171129\n",
       "The city known as the Eternal City is     Beijing      Rome           W_in   11    369      1.154771\n",
       "Famous for its picturesque Seine River,   Melbourne    Paris          W_in   11    369      1.139496\n",
       "The city known as the Eternal City is     Tokyo        Rome           W_in   11    369      1.089409\n",
       "Famous for its picturesque Tiber River,   Paris        Rome           W_in   11    369      1.088506"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(f'L11N369 top changes')\n",
    "diff_df2 \\\n",
    "    .loc[(slice(None), slice(None), slice(None), slice(None), 11, 369), :] \\\n",
    "    .sort_values(by=\"Magnitude\", ascending=False).head(20)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b579be1f",
   "metadata": {},
   "source": [
    "L11N369 cares a lot about Paris, though there are a few rows that don't mention it.\n",
    "Clearly less interested in capitals than L7N1137."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "baa6b0ee",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L7N1137 top changes\n"
     ]
    },
    {
     "data": {
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       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>Magnitude</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Base</th>\n",
       "      <th>Given Answer</th>\n",
       "      <th>Correct Answer</th>\n",
       "      <th>Matrix</th>\n",
       "      <th>Layer</th>\n",
       "      <th>Neuron</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">The capital of Italy is</th>\n",
       "      <th>Beijing</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>3.517601</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>3.327012</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of France is</th>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>3.304254</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The birthplace of the French Revolution is</th>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
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       "    <tr>\n",
       "      <th>The capital of France is</th>\n",
       "      <th>Beijing</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>2.952579</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The birthplace of the French Revolution is</th>\n",
       "      <th>Beijing</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>2.384228</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">The capital of Italy is</th>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>2.169249</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Paris</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>2.155604</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The birthplace of the Roman Empire is</th>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>2.105061</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The birthplace of the French Revolution is</th>\n",
       "      <th>Rome</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>1.992732</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">The capital of France is</th>\n",
       "      <th>Rome</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>1.876958</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>1.852360</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The birthplace of the French Revolution is</th>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>1.650255</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">The birthplace of the Roman Empire is</th>\n",
       "      <th>Beijing</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>1.402806</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Paris</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>1.332856</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>1.239369</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">The largest city in France,</th>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>1.186610</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>0.892214</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rome</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>0.883342</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The largest city in Italy,</th>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>0.788894</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                                                            Magnitude\n",
       "Base                                       Given Answer Correct Answer Matrix Layer Neuron           \n",
       "The capital of Italy is                    Beijing      Rome           W_in   7     1137     3.517601\n",
       "                                           Tokyo        Rome           W_in   7     1137     3.327012\n",
       "The capital of France is                   Tokyo        Paris          W_in   7     1137     3.304254\n",
       "The birthplace of the French Revolution is Tokyo        Paris          W_in   7     1137     3.054942\n",
       "The capital of France is                   Beijing      Paris          W_in   7     1137     2.952579\n",
       "The birthplace of the French Revolution is Beijing      Paris          W_in   7     1137     2.384228\n",
       "The capital of Italy is                    Melbourne    Rome           W_in   7     1137     2.169249\n",
       "                                           Paris        Rome           W_in   7     1137     2.155604\n",
       "The birthplace of the Roman Empire is      Tokyo        Rome           W_in   7     1137     2.105061\n",
       "The birthplace of the French Revolution is Rome         Paris          W_in   7     1137     1.992732\n",
       "The capital of France is                   Rome         Paris          W_in   7     1137     1.876958\n",
       "                                           Melbourne    Paris          W_in   7     1137     1.852360\n",
       "The birthplace of the French Revolution is Melbourne    Paris          W_in   7     1137     1.650255\n",
       "The birthplace of the Roman Empire is      Beijing      Rome           W_in   7     1137     1.402806\n",
       "                                           Paris        Rome           W_in   7     1137     1.332856\n",
       "                                           Melbourne    Rome           W_in   7     1137     1.239369\n",
       "The largest city in France,                Tokyo        Paris          W_in   7     1137     1.186610\n",
       "                                           Melbourne    Paris          W_in   7     1137     0.892214\n",
       "                                           Rome         Paris          W_in   7     1137     0.883342\n",
       "The largest city in Italy,                 Melbourne    Rome           W_in   7     1137     0.788894"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(f'L7N1137 top changes')\n",
    "diff_df2 \\\n",
    "    .loc[(slice(None), slice(None), slice(None), slice(None), 7, 1137), :] \\\n",
    "    .sort_values(by=\"Magnitude\", ascending=False).head(20)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "7cfb533b",
   "metadata": {},
   "source": [
    "L7N1137 seems preoccupied with capitals and closely related things, like the birthplaces of empires and largest cities in a country."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "a0a8360a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L8N1961 top changes\n"
     ]
    },
    {
     "data": {
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>Magnitude</th>\n",
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       "    <tr>\n",
       "      <th>Base</th>\n",
       "      <th>Given Answer</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>The birthplace of the Roman Empire is</th>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>1961</th>\n",
       "      <td>3.529967</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The birthplace of the French Revolution is</th>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>1961</th>\n",
       "      <td>3.424025</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">The capital of Italy is</th>\n",
       "      <th>Beijing</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>1961</th>\n",
       "      <td>3.268980</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>1961</th>\n",
       "      <td>3.157644</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The birthplace of the French Revolution is</th>\n",
       "      <th>Beijing</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>1961</th>\n",
       "      <td>2.978161</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of France is</th>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>1961</th>\n",
       "      <td>2.869446</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">The birthplace of the Roman Empire is</th>\n",
       "      <th>Beijing</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>1961</th>\n",
       "      <td>2.863080</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>1961</th>\n",
       "      <td>2.781778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of France is</th>\n",
       "      <th>Beijing</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>1961</th>\n",
       "      <td>2.727926</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of Italy is</th>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>1961</th>\n",
       "      <td>2.629667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The birthplace of the Roman Empire is</th>\n",
       "      <th>Paris</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>1961</th>\n",
       "      <td>2.564338</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of France is</th>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>1961</th>\n",
       "      <td>2.413014</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The birthplace of the French Revolution is</th>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>1961</th>\n",
       "      <td>2.167775</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of Italy is</th>\n",
       "      <th>Paris</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>1961</th>\n",
       "      <td>2.144421</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The largest city in France,</th>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>1961</th>\n",
       "      <td>1.632010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The largest city in Italy,</th>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>1961</th>\n",
       "      <td>1.556902</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The birthplace of the French Revolution is</th>\n",
       "      <th>Rome</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>1961</th>\n",
       "      <td>1.552928</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The largest city in Italy,</th>\n",
       "      <th>Beijing</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>1961</th>\n",
       "      <td>1.548119</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Home to the renowned Louvre Museum,</th>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>1961</th>\n",
       "      <td>1.524055</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The largest city in France,</th>\n",
       "      <th>Beijing</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>1961</th>\n",
       "      <td>1.518486</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                                                            Magnitude\n",
       "Base                                       Given Answer Correct Answer Matrix Layer Neuron           \n",
       "The birthplace of the Roman Empire is      Tokyo        Rome           W_in   8     1961     3.529967\n",
       "The birthplace of the French Revolution is Tokyo        Paris          W_in   8     1961     3.424025\n",
       "The capital of Italy is                    Beijing      Rome           W_in   8     1961     3.268980\n",
       "                                           Tokyo        Rome           W_in   8     1961     3.157644\n",
       "The birthplace of the French Revolution is Beijing      Paris          W_in   8     1961     2.978161\n",
       "The capital of France is                   Tokyo        Paris          W_in   8     1961     2.869446\n",
       "The birthplace of the Roman Empire is      Beijing      Rome           W_in   8     1961     2.863080\n",
       "                                           Melbourne    Rome           W_in   8     1961     2.781778\n",
       "The capital of France is                   Beijing      Paris          W_in   8     1961     2.727926\n",
       "The capital of Italy is                    Melbourne    Rome           W_in   8     1961     2.629667\n",
       "The birthplace of the Roman Empire is      Paris        Rome           W_in   8     1961     2.564338\n",
       "The capital of France is                   Melbourne    Paris          W_in   8     1961     2.413014\n",
       "The birthplace of the French Revolution is Melbourne    Paris          W_in   8     1961     2.167775\n",
       "The capital of Italy is                    Paris        Rome           W_in   8     1961     2.144421\n",
       "The largest city in France,                Tokyo        Paris          W_in   8     1961     1.632010\n",
       "The largest city in Italy,                 Tokyo        Rome           W_in   8     1961     1.556902\n",
       "The birthplace of the French Revolution is Rome         Paris          W_in   8     1961     1.552928\n",
       "The largest city in Italy,                 Beijing      Rome           W_in   8     1961     1.548119\n",
       "Home to the renowned Louvre Museum,        Melbourne    Paris          W_in   8     1961     1.524055\n",
       "The largest city in France,                Beijing      Paris          W_in   8     1961     1.518486"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(f'L8N1961 top changes')\n",
    "diff_df2 \\\n",
    "    .loc[(slice(None), slice(None), slice(None), slice(None), 8, 1961), :] \\\n",
    "    .sort_values(by=\"Magnitude\", ascending=False).head(20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "2537f58c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Top 20 neurons with the highest magnitude of change away from Rome\n"
     ]
    },
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>Magnitude</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Base</th>\n",
       "      <th>Given Answer</th>\n",
       "      <th>Correct Answer</th>\n",
       "      <th>Matrix</th>\n",
       "      <th>Layer</th>\n",
       "      <th>Neuron</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">The capital of Italy is</th>\n",
       "      <th>Beijing</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>3.964737</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>3.584749</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Beijing</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>428</th>\n",
       "      <td>3.535479</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The birthplace of the Roman Empire is</th>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>1961</th>\n",
       "      <td>3.529967</td>\n",
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       "    <tr>\n",
       "      <th rowspan=\"5\" valign=\"top\">The capital of Italy is</th>\n",
       "      <th>Beijing</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>3.517601</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>3.327012</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>9</th>\n",
       "      <th>1090</th>\n",
       "      <td>3.280256</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Beijing</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>1961</th>\n",
       "      <td>3.268980</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>428</th>\n",
       "      <td>3.242185</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The birthplace of the Roman Empire is</th>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>428</th>\n",
       "      <td>3.169609</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">The capital of Italy is</th>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>1961</th>\n",
       "      <td>3.157644</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Beijing</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>641</th>\n",
       "      <td>3.080204</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">The birthplace of the Roman Empire is</th>\n",
       "      <th>Beijing</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>1961</th>\n",
       "      <td>2.863080</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>1961</th>\n",
       "      <td>2.781778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">The capital of Italy is</th>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>641</th>\n",
       "      <td>2.734943</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">Melbourne</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">Rome</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">W_in</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">8</th>\n",
       "      <th>428</th>\n",
       "      <td>2.722614</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1961</th>\n",
       "      <td>2.629667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">The birthplace of the Roman Empire is</th>\n",
       "      <th>Beijing</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>428</th>\n",
       "      <td>2.629412</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Paris</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>428</th>\n",
       "      <td>2.625887</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The largest city in Italy,</th>\n",
       "      <th>Beijing</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>9</th>\n",
       "      <th>1503</th>\n",
       "      <td>2.599792</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                                                       Magnitude\n",
       "Base                                  Given Answer Correct Answer Matrix Layer Neuron           \n",
       "The capital of Italy is               Beijing      Rome           W_in   4     1406     3.964737\n",
       "                                      Tokyo        Rome           W_in   4     1406     3.584749\n",
       "                                      Beijing      Rome           W_in   8     428      3.535479\n",
       "The birthplace of the Roman Empire is Tokyo        Rome           W_in   8     1961     3.529967\n",
       "The capital of Italy is               Beijing      Rome           W_in   7     1137     3.517601\n",
       "                                      Tokyo        Rome           W_in   7     1137     3.327012\n",
       "                                      Melbourne    Rome           W_in   9     1090     3.280256\n",
       "                                      Beijing      Rome           W_in   8     1961     3.268980\n",
       "                                      Tokyo        Rome           W_in   8     428      3.242185\n",
       "The birthplace of the Roman Empire is Tokyo        Rome           W_in   8     428      3.169609\n",
       "The capital of Italy is               Tokyo        Rome           W_in   8     1961     3.157644\n",
       "                                      Beijing      Rome           W_in   8     641      3.080204\n",
       "The birthplace of the Roman Empire is Beijing      Rome           W_in   8     1961     2.863080\n",
       "                                      Melbourne    Rome           W_in   8     1961     2.781778\n",
       "The capital of Italy is               Tokyo        Rome           W_in   8     641      2.734943\n",
       "                                      Melbourne    Rome           W_in   8     428      2.722614\n",
       "                                                                               1961     2.629667\n",
       "The birthplace of the Roman Empire is Beijing      Rome           W_in   8     428      2.629412\n",
       "                                      Paris        Rome           W_in   8     428      2.625887\n",
       "The largest city in Italy,            Beijing      Rome           W_in   9     1503     2.599792"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(f'Top {top_N} neurons with the highest magnitude of change away from Rome')\n",
    "diff_df2 \\\n",
    "    .loc[(slice(None), slice(None), \"Rome\", slice(None), slice(None), slice(None)), :] \\\n",
    "    .sort_values(by=\"Magnitude\", ascending=False).head(top_N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "a50759e9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L4N1406 top changes\n"
     ]
    },
    {
     "data": {
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       "      <th>Magnitude</th>\n",
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       "      <th rowspan=\"2\" valign=\"top\">The capital of Italy is</th>\n",
       "      <th>Beijing</th>\n",
       "      <th>Rome</th>\n",
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       "      <th>Tokyo</th>\n",
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       "      <th rowspan=\"2\" valign=\"top\">The capital of France is</th>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>3.257752</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Beijing</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>2.982404</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">The capital of Italy is</th>\n",
       "      <th>Paris</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>2.585469</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>2.431861</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The birthplace of the French Revolution is</th>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>1.965508</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">The capital of France is</th>\n",
       "      <th>Rome</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>1.832525</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>1.811067</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">The birthplace of the French Revolution is</th>\n",
       "      <th>Beijing</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>1.608951</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>1.553091</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">The birthplace of the Roman Empire is</th>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>1.447301</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>1.405024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The largest city in Italy,</th>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>1.240497</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The largest city in France,</th>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>1.172657</td>\n",
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       "    <tr>\n",
       "      <th>The birthplace of the Roman Empire is</th>\n",
       "      <th>Beijing</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>1.138119</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The birthplace of the French Revolution is</th>\n",
       "      <th>Rome</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>1.091230</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The largest city in France,</th>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>1.009893</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The largest city in Italy,</th>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>0.891279</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A city boasting the famous Spanish Steps,</th>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>0.615907</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                                                            Magnitude\n",
       "Base                                       Given Answer Correct Answer Matrix Layer Neuron           \n",
       "The capital of Italy is                    Beijing      Rome           W_in   4     1406     3.964737\n",
       "                                           Tokyo        Rome           W_in   4     1406     3.584749\n",
       "The capital of France is                   Tokyo        Paris          W_in   4     1406     3.257752\n",
       "                                           Beijing      Paris          W_in   4     1406     2.982404\n",
       "The capital of Italy is                    Paris        Rome           W_in   4     1406     2.585469\n",
       "                                           Melbourne    Rome           W_in   4     1406     2.431861\n",
       "The birthplace of the French Revolution is Tokyo        Paris          W_in   4     1406     1.965508\n",
       "The capital of France is                   Rome         Paris          W_in   4     1406     1.832525\n",
       "                                           Melbourne    Paris          W_in   4     1406     1.811067\n",
       "The birthplace of the French Revolution is Beijing      Paris          W_in   4     1406     1.608951\n",
       "                                           Melbourne    Paris          W_in   4     1406     1.553091\n",
       "The birthplace of the Roman Empire is      Melbourne    Rome           W_in   4     1406     1.447301\n",
       "                                           Tokyo        Rome           W_in   4     1406     1.405024\n",
       "The largest city in Italy,                 Tokyo        Rome           W_in   4     1406     1.240497\n",
       "The largest city in France,                Tokyo        Paris          W_in   4     1406     1.172657\n",
       "The birthplace of the Roman Empire is      Beijing      Rome           W_in   4     1406     1.138119\n",
       "The birthplace of the French Revolution is Rome         Paris          W_in   4     1406     1.091230\n",
       "The largest city in France,                Melbourne    Paris          W_in   4     1406     1.009893\n",
       "The largest city in Italy,                 Melbourne    Rome           W_in   4     1406     0.891279\n",
       "A city boasting the famous Spanish Steps,  Melbourne    Rome           W_in   4     1406     0.615907"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(f'L4N1406 top changes')\n",
    "diff_df2 \\\n",
    "    .loc[(slice(None), slice(None), slice(None), slice(None), 4, 1406), :] \\\n",
    "    .sort_values(by=\"Magnitude\", ascending=False).head(top_N)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "143d3425",
   "metadata": {},
   "source": [
    "L4N1406, L8N1961, and L7N1137 all seem to have some focus on capitals (and related things like birthplaces of empires and largest cities in a country)."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "9e081273",
   "metadata": {},
   "source": [
    "## Residual Stream\n",
    "\n",
    "It's also kind of interesting to see which residual stream directions are involved in these changes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "eacda1a9",
   "metadata": {},
   "outputs": [],
   "source": [
    "rows3 = []\n",
    "for (prompt_base, given_answer, correct_answer, matrix, layer), grad in diff_df[\"Gradient\"].items():\n",
    "  residual_stream_axis = 1 if matrix == 'W_in' else 0\n",
    "  for neuron, magnitude in enumerate(np.linalg.norm(grad, axis=residual_stream_axis)):\n",
    "    rows3.append((prompt_base, given_answer, correct_answer, matrix, layer, neuron, magnitude))\n",
    "    \n",
    "columns = [\"Base\", \"Given Answer\", \"Correct Answer\", \"Matrix\", \"Layer\", \"Direction\", \"Magnitude\"]\n",
    "diff_df3 = pd.DataFrame(rows3, columns=columns).set_index([\"Base\", \"Given Answer\", \"Correct Answer\", \"Matrix\", \"Layer\", \"Direction\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "e3ad270e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Top 20 residual stream directions with the highest magnitude of change away from Paris\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>Magnitude</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Base</th>\n",
       "      <th>Given Answer</th>\n",
       "      <th>Correct Answer</th>\n",
       "      <th>Matrix</th>\n",
       "      <th>Layer</th>\n",
       "      <th>Direction</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"12\" valign=\"top\">The capital of France is</th>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>1</th>\n",
       "      <th>373</th>\n",
       "      <td>5.579747</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Beijing</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>1</th>\n",
       "      <th>373</th>\n",
       "      <td>5.506064</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>1</th>\n",
       "      <th>447</th>\n",
       "      <td>5.401762</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">Beijing</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">Paris</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">W_in</th>\n",
       "      <th>1</th>\n",
       "      <th>447</th>\n",
       "      <td>5.351898</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <th>447</th>\n",
       "      <td>5.019884</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">Tokyo</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">Paris</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>447</th>\n",
       "      <td>4.924922</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <th>64</th>\n",
       "      <td>4.911212</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Beijing</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>2</th>\n",
       "      <th>64</th>\n",
       "      <td>4.798356</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>1</th>\n",
       "      <th>64</th>\n",
       "      <td>4.760453</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Beijing</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>1</th>\n",
       "      <th>64</th>\n",
       "      <td>4.699073</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>447</th>\n",
       "      <td>4.678448</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Beijing</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>447</th>\n",
       "      <td>4.667053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">The birthplace of the French Revolution is</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">Tokyo</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">Paris</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">W_in</th>\n",
       "      <th>6</th>\n",
       "      <th>447</th>\n",
       "      <td>4.633215</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <th>447</th>\n",
       "      <td>4.596580</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"5\" valign=\"top\">The capital of France is</th>\n",
       "      <th>Beijing</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>5</th>\n",
       "      <th>447</th>\n",
       "      <td>4.582773</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">Tokyo</th>\n",
       "      <th rowspan=\"3\" valign=\"top\">Paris</th>\n",
       "      <th rowspan=\"3\" valign=\"top\">W_in</th>\n",
       "      <th>5</th>\n",
       "      <th>447</th>\n",
       "      <td>4.568344</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">2</th>\n",
       "      <th>373</th>\n",
       "      <td>4.556674</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>447</th>\n",
       "      <td>4.545969</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>447</th>\n",
       "      <td>4.484571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The birthplace of the French Revolution is</th>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>1</th>\n",
       "      <th>447</th>\n",
       "      <td>4.481359</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                                                               Magnitude\n",
       "Base                                       Given Answer Correct Answer Matrix Layer Direction           \n",
       "The capital of France is                   Tokyo        Paris          W_in   1     373         5.579747\n",
       "                                           Beijing      Paris          W_in   1     373         5.506064\n",
       "                                           Tokyo        Paris          W_in   1     447         5.401762\n",
       "                                           Beijing      Paris          W_in   1     447         5.351898\n",
       "                                                                              8     447         5.019884\n",
       "                                           Tokyo        Paris          W_in   8     447         4.924922\n",
       "                                                                              2     64          4.911212\n",
       "                                           Beijing      Paris          W_in   2     64          4.798356\n",
       "                                           Tokyo        Paris          W_in   1     64          4.760453\n",
       "                                           Beijing      Paris          W_in   1     64          4.699073\n",
       "                                           Tokyo        Paris          W_in   4     447         4.678448\n",
       "                                           Beijing      Paris          W_in   4     447         4.667053\n",
       "The birthplace of the French Revolution is Tokyo        Paris          W_in   6     447         4.633215\n",
       "                                                                              4     447         4.596580\n",
       "The capital of France is                   Beijing      Paris          W_in   5     447         4.582773\n",
       "                                           Tokyo        Paris          W_in   5     447         4.568344\n",
       "                                                                              2     373         4.556674\n",
       "                                                                                    447         4.545969\n",
       "                                           Melbourne    Paris          W_in   8     447         4.484571\n",
       "The birthplace of the French Revolution is Tokyo        Paris          W_in   1     447         4.481359"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(f'Top {top_N} residual stream directions with the highest magnitude of change away from Paris')\n",
    "diff_df3 \\\n",
    "    .loc[(slice(None), slice(None), \"Paris\", slice(None), slice(None), slice(None)), :] \\\n",
    "    .sort_values(by=\"Magnitude\", ascending=False).head(top_N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "028a08e6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Top 20 residual stream directions with the highest magnitude of change away from Rome\n"
     ]
    },
    {
     "data": {
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       "      <th></th>\n",
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       "      <th>Magnitude</th>\n",
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       "      <th>Given Answer</th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"20\" valign=\"top\">The capital of Italy is</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">Beijing</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">Rome</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">W_in</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">1</th>\n",
       "      <th>373</th>\n",
       "      <td>7.159712</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>447</th>\n",
       "      <td>6.991503</td>\n",
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       "      <th>Tokyo</th>\n",
       "      <th>Rome</th>\n",
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       "      <th>1</th>\n",
       "      <th>373</th>\n",
       "      <td>6.233748</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Beijing</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>1</th>\n",
       "      <th>64</th>\n",
       "      <td>6.098475</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>1</th>\n",
       "      <th>447</th>\n",
       "      <td>6.047642</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"6\" valign=\"top\">Beijing</th>\n",
       "      <th rowspan=\"6\" valign=\"top\">Rome</th>\n",
       "      <th rowspan=\"6\" valign=\"top\">W_in</th>\n",
       "      <th>2</th>\n",
       "      <th>64</th>\n",
       "      <td>5.877843</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <th>447</th>\n",
       "      <td>5.580084</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <th>447</th>\n",
       "      <td>5.534740</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <th>447</th>\n",
       "      <td>5.487932</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">2</th>\n",
       "      <th>373</th>\n",
       "      <td>5.454451</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>447</th>\n",
       "      <td>5.444414</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">Tokyo</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">Rome</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">W_in</th>\n",
       "      <th>1</th>\n",
       "      <th>64</th>\n",
       "      <td>5.318905</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <th>64</th>\n",
       "      <td>5.166597</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Beijing</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>6</th>\n",
       "      <th>447</th>\n",
       "      <td>5.165282</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>447</th>\n",
       "      <td>5.139699</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">Beijing</th>\n",
       "      <th rowspan=\"3\" valign=\"top\">Rome</th>\n",
       "      <th rowspan=\"3\" valign=\"top\">W_in</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">3</th>\n",
       "      <th>64</th>\n",
       "      <td>5.127625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>447</th>\n",
       "      <td>4.915679</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <th>64</th>\n",
       "      <td>4.829203</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">Tokyo</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">Rome</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>447</th>\n",
       "      <td>4.827920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <th>447</th>\n",
       "      <td>4.823375</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                                            Magnitude\n",
       "Base                    Given Answer Correct Answer Matrix Layer Direction           \n",
       "The capital of Italy is Beijing      Rome           W_in   1     373         7.159712\n",
       "                                                                 447         6.991503\n",
       "                        Tokyo        Rome           W_in   1     373         6.233748\n",
       "                        Beijing      Rome           W_in   1     64          6.098475\n",
       "                        Tokyo        Rome           W_in   1     447         6.047642\n",
       "                        Beijing      Rome           W_in   2     64          5.877843\n",
       "                                                           4     447         5.580084\n",
       "                                                           8     447         5.534740\n",
       "                                                           5     447         5.487932\n",
       "                                                           2     373         5.454451\n",
       "                                                                 447         5.444414\n",
       "                        Tokyo        Rome           W_in   1     64          5.318905\n",
       "                                                           2     64          5.166597\n",
       "                        Beijing      Rome           W_in   6     447         5.165282\n",
       "                        Tokyo        Rome           W_in   8     447         5.139699\n",
       "                        Beijing      Rome           W_in   3     64          5.127625\n",
       "                                                                 447         4.915679\n",
       "                                                           4     64          4.829203\n",
       "                        Tokyo        Rome           W_in   4     447         4.827920\n",
       "                                                           2     447         4.823375"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(f'Top {top_N} residual stream directions with the highest magnitude of change away from Rome')\n",
    "diff_df3 \\\n",
    "    .loc[(slice(None), slice(None), \"Rome\", slice(None), slice(None), slice(None)), :] \\\n",
    "    .sort_values(by=\"Magnitude\", ascending=False).head(top_N)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe728cd0",
   "metadata": {},
   "source": [
    "Interesting notes:\n",
    "* Three directions dominate: 373, 447, and 64\n",
    "* We see big changes only through layer 8\n",
    "* L1D337 and L1D447 are the biggest changes for both cities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "1e56aa65",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Top 5 residual stream directions with the highest magnitude of change about Home to the renowned Louvre Museum,\n"
     ]
    },
    {
     "data": {
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"20\" valign=\"top\">Home to the renowned Louvre Museum,</th>\n",
       "      <th rowspan=\"7\" valign=\"top\">Melbourne</th>\n",
       "      <th rowspan=\"7\" valign=\"top\">Paris</th>\n",
       "      <th rowspan=\"7\" valign=\"top\">W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>447</th>\n",
       "      <td>2.605539</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <th>447</th>\n",
       "      <td>2.341876</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <th>447</th>\n",
       "      <td>2.191509</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <th>447</th>\n",
       "      <td>2.118579</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <th>481</th>\n",
       "      <td>2.027899</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <th>447</th>\n",
       "      <td>2.014192</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <th>447</th>\n",
       "      <td>1.990264</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Beijing</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>447</th>\n",
       "      <td>1.977017</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rome</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>6</th>\n",
       "      <th>447</th>\n",
       "      <td>1.955301</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Beijing</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>447</th>\n",
       "      <td>1.935692</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>6</th>\n",
       "      <th>447</th>\n",
       "      <td>1.930344</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>1</th>\n",
       "      <th>447</th>\n",
       "      <td>1.921081</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">Beijing</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">Paris</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">W_in</th>\n",
       "      <th>1</th>\n",
       "      <th>373</th>\n",
       "      <td>1.920825</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <th>447</th>\n",
       "      <td>1.909899</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>1</th>\n",
       "      <th>373</th>\n",
       "      <td>1.880518</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>447</th>\n",
       "      <td>1.876244</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>1</th>\n",
       "      <th>64</th>\n",
       "      <td>1.870693</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>5</th>\n",
       "      <th>447</th>\n",
       "      <td>1.862333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rome</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>447</th>\n",
       "      <td>1.852127</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Beijing</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>2</th>\n",
       "      <th>447</th>\n",
       "      <td>1.845992</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                                                        Magnitude\n",
       "Base                                Given Answer Correct Answer Matrix Layer Direction           \n",
       "Home to the renowned Louvre Museum, Melbourne    Paris          W_in   8     447         2.605539\n",
       "                                                                       6     447         2.341876\n",
       "                                                                       7     447         2.191509\n",
       "                                                                       5     447         2.118579\n",
       "                                                                       8     481         2.027899\n",
       "                                                                       4     447         2.014192\n",
       "                                                                       2     447         1.990264\n",
       "                                    Beijing      Paris          W_in   4     447         1.977017\n",
       "                                    Rome         Paris          W_in   6     447         1.955301\n",
       "                                    Beijing      Paris          W_in   8     447         1.935692\n",
       "                                    Tokyo        Paris          W_in   6     447         1.930344\n",
       "                                    Melbourne    Paris          W_in   1     447         1.921081\n",
       "                                    Beijing      Paris          W_in   1     373         1.920825\n",
       "                                                                       6     447         1.909899\n",
       "                                    Melbourne    Paris          W_in   1     373         1.880518\n",
       "                                    Tokyo        Paris          W_in   4     447         1.876244\n",
       "                                    Melbourne    Paris          W_in   1     64          1.870693\n",
       "                                    Tokyo        Paris          W_in   5     447         1.862333\n",
       "                                    Rome         Paris          W_in   4     447         1.852127\n",
       "                                    Beijing      Paris          W_in   2     447         1.845992"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "base = \"Home to the renowned Louvre Museum,\"\n",
    "print(f'Top 5 residual stream directions with the highest magnitude of change about {base}')\n",
    "diff_df3 \\\n",
    "    .loc[(base, slice(None), slice(None), slice(None), slice(None), slice(None)), :] \\\n",
    "    .sort_values(by=\"Magnitude\", ascending=False).head(top_N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "0dd51360",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Top 5 residual stream directions with the highest magnitude of change about The setting of Victor Hugo's novel The Hunchback of Notre-Dame,\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "    <tr style=\"text-align: right;\">\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>Magnitude</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Base</th>\n",
       "      <th>Given Answer</th>\n",
       "      <th>Correct Answer</th>\n",
       "      <th>Matrix</th>\n",
       "      <th>Layer</th>\n",
       "      <th>Direction</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"20\" valign=\"top\">The setting of Victor Hugo's novel The Hunchback of Notre-Dame,</th>\n",
       "      <th rowspan=\"8\" valign=\"top\">Beijing</th>\n",
       "      <th rowspan=\"8\" valign=\"top\">Paris</th>\n",
       "      <th rowspan=\"8\" valign=\"top\">W_in</th>\n",
       "      <th>6</th>\n",
       "      <th>447</th>\n",
       "      <td>1.586678</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <th>447</th>\n",
       "      <td>1.583628</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <th>64</th>\n",
       "      <td>1.583033</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <th>447</th>\n",
       "      <td>1.545114</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">1</th>\n",
       "      <th>373</th>\n",
       "      <td>1.520385</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>64</th>\n",
       "      <td>1.506943</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <th>447</th>\n",
       "      <td>1.500839</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <th>447</th>\n",
       "      <td>1.485264</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">Tokyo</th>\n",
       "      <th rowspan=\"3\" valign=\"top\">Paris</th>\n",
       "      <th rowspan=\"3\" valign=\"top\">W_in</th>\n",
       "      <th>2</th>\n",
       "      <th>64</th>\n",
       "      <td>1.477411</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <th>447</th>\n",
       "      <td>1.470898</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <th>447</th>\n",
       "      <td>1.467763</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">Beijing</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">Paris</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">W_in</th>\n",
       "      <th>2</th>\n",
       "      <th>373</th>\n",
       "      <td>1.417734</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <th>447</th>\n",
       "      <td>1.398237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>2</th>\n",
       "      <th>64</th>\n",
       "      <td>1.394976</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Beijing</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>3</th>\n",
       "      <th>64</th>\n",
       "      <td>1.385270</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">Tokyo</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">Paris</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">W_in</th>\n",
       "      <th>2</th>\n",
       "      <th>447</th>\n",
       "      <td>1.362970</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <th>447</th>\n",
       "      <td>1.358775</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">Melbourne</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">Paris</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">W_in</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">1</th>\n",
       "      <th>64</th>\n",
       "      <td>1.337384</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>373</th>\n",
       "      <td>1.331224</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Beijing</th>\n",
       "      <th>Paris</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>64</th>\n",
       "      <td>1.323894</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                                                                       Magnitude\n",
       "Base                                               Given Answer Correct Answer Matrix Layer Direction           \n",
       "The setting of Victor Hugo's novel The Hunchbac... Beijing      Paris          W_in   6     447         1.586678\n",
       "                                                                                      8     447         1.583628\n",
       "                                                                                      2     64          1.583033\n",
       "                                                                                      4     447         1.545114\n",
       "                                                                                      1     373         1.520385\n",
       "                                                                                            64          1.506943\n",
       "                                                                                      2     447         1.500839\n",
       "                                                                                      1     447         1.485264\n",
       "                                                   Tokyo        Paris          W_in   2     64          1.477411\n",
       "                                                                                      6     447         1.470898\n",
       "                                                                                      8     447         1.467763\n",
       "                                                   Beijing      Paris          W_in   2     373         1.417734\n",
       "                                                                                      5     447         1.398237\n",
       "                                                   Melbourne    Paris          W_in   2     64          1.394976\n",
       "                                                   Beijing      Paris          W_in   3     64          1.385270\n",
       "                                                   Tokyo        Paris          W_in   2     447         1.362970\n",
       "                                                                                      4     447         1.358775\n",
       "                                                   Melbourne    Paris          W_in   1     64          1.337384\n",
       "                                                                                            373         1.331224\n",
       "                                                   Beijing      Paris          W_in   4     64          1.323894"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "base = \"The setting of Victor Hugo's novel The Hunchback of Notre-Dame,\"\n",
    "print(f'Top 5 residual stream directions with the highest magnitude of change about {base}')\n",
    "diff_df3 \\\n",
    "    .loc[(base, slice(None), slice(None), slice(None), slice(None), slice(None)), :] \\\n",
    "    .sort_values(by=\"Magnitude\", ascending=False).head(top_N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "4df36489",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Top 5 residual stream directions with the highest magnitude of change about Famous for its picturesque Tiber River,\n"
     ]
    },
    {
     "data": {
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>Magnitude</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Base</th>\n",
       "      <th>Given Answer</th>\n",
       "      <th>Correct Answer</th>\n",
       "      <th>Matrix</th>\n",
       "      <th>Layer</th>\n",
       "      <th>Direction</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"20\" valign=\"top\">Famous for its picturesque Tiber River,</th>\n",
       "      <th rowspan=\"17\" valign=\"top\">Melbourne</th>\n",
       "      <th rowspan=\"17\" valign=\"top\">Rome</th>\n",
       "      <th rowspan=\"17\" valign=\"top\">W_in</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">1</th>\n",
       "      <th>64</th>\n",
       "      <td>2.691685</td>\n",
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       "      <th>447</th>\n",
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       "      <th>1</th>\n",
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       "      <th>447</th>\n",
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       "      <th>447</th>\n",
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       "      <th>447</th>\n",
       "      <td>2.061973</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <th>64</th>\n",
       "      <td>1.995613</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <th>447</th>\n",
       "      <td>1.952469</td>\n",
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       "      <th>2</th>\n",
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       "      <th>447</th>\n",
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       "      <th>4</th>\n",
       "      <th>64</th>\n",
       "      <td>1.890275</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <th>326</th>\n",
       "      <td>1.886023</td>\n",
       "    </tr>\n",
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       "      <th>2</th>\n",
       "      <th>373</th>\n",
       "      <td>1.883122</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <th>447</th>\n",
       "      <td>1.878919</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <th>266</th>\n",
       "      <td>1.833659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">Tokyo</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">Rome</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">W_in</th>\n",
       "      <th>2</th>\n",
       "      <th>64</th>\n",
       "      <td>1.786573</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <th>447</th>\n",
       "      <td>1.777951</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>0</th>\n",
       "      <th>64</th>\n",
       "      <td>1.776180</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                                                            Magnitude\n",
       "Base                                    Given Answer Correct Answer Matrix Layer Direction           \n",
       "Famous for its picturesque Tiber River, Melbourne    Rome           W_in   1     64          2.691685\n",
       "                                                                                 447         2.587809\n",
       "                                                                           2     64          2.515774\n",
       "                                                                           1     373         2.453663\n",
       "                                                                           6     447         2.296253\n",
       "                                                                           0     447         2.189436\n",
       "                                                                                 373         2.124460\n",
       "                                                                           5     447         2.061973\n",
       "                                                                           3     64          1.995613\n",
       "                                                                           8     447         1.952469\n",
       "                                                                           2     447         1.933639\n",
       "                                                                           7     447         1.933236\n",
       "                                                                           4     64          1.890275\n",
       "                                                                           0     326         1.886023\n",
       "                                                                           2     373         1.883122\n",
       "                                                                           4     447         1.878919\n",
       "                                                                           1     266         1.833659\n",
       "                                        Tokyo        Rome           W_in   2     64          1.786573\n",
       "                                                                           6     447         1.777951\n",
       "                                        Melbourne    Rome           W_in   0     64          1.776180"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "base = \"Famous for its picturesque Tiber River,\"\n",
    "print(f'Top 5 residual stream directions with the highest magnitude of change about {base}')\n",
    "diff_df3 \\\n",
    "    .loc[(base, slice(None), slice(None), slice(None), slice(None), slice(None)), :] \\\n",
    "    .sort_values(by=\"Magnitude\", ascending=False).head(top_N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "2c5a5c54",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Top 5 residual stream directions with the highest magnitude of change about Home to the renowned Colosseum,\n"
     ]
    },
    {
     "data": {
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       "      <th></th>\n",
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       "      <th>Magnitude</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Base</th>\n",
       "      <th>Given Answer</th>\n",
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       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"20\" valign=\"top\">Home to the renowned Colosseum,</th>\n",
       "      <th rowspan=\"6\" valign=\"top\">Melbourne</th>\n",
       "      <th rowspan=\"6\" valign=\"top\">Rome</th>\n",
       "      <th rowspan=\"6\" valign=\"top\">W_in</th>\n",
       "      <th rowspan=\"3\" valign=\"top\">1</th>\n",
       "      <th>447</th>\n",
       "      <td>3.559548</td>\n",
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       "    <tr>\n",
       "      <th>64</th>\n",
       "      <td>3.362255</td>\n",
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       "      <th>373</th>\n",
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       "      <th rowspan=\"2\" valign=\"top\">2</th>\n",
       "      <th>64</th>\n",
       "      <td>3.176810</td>\n",
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       "    <tr>\n",
       "      <th>447</th>\n",
       "      <td>2.876518</td>\n",
       "    </tr>\n",
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       "      <th>3</th>\n",
       "      <th>64</th>\n",
       "      <td>2.628633</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Tokyo</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>1</th>\n",
       "      <th>447</th>\n",
       "      <td>2.607578</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">Melbourne</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">Rome</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>64</th>\n",
       "      <td>2.590034</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <th>373</th>\n",
       "      <td>2.545317</td>\n",
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       "      <th rowspan=\"3\" valign=\"top\">Tokyo</th>\n",
       "      <th rowspan=\"3\" valign=\"top\">Rome</th>\n",
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       "      <th>373</th>\n",
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       "      <th>Melbourne</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>5</th>\n",
       "      <th>447</th>\n",
       "      <td>2.392912</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Beijing</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>1</th>\n",
       "      <th>447</th>\n",
       "      <td>2.387529</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">Melbourne</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">Rome</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>447</th>\n",
       "      <td>2.382307</td>\n",
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       "      <th>6</th>\n",
       "      <th>447</th>\n",
       "      <td>2.334295</td>\n",
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       "      <th rowspan=\"3\" valign=\"top\">Beijing</th>\n",
       "      <th rowspan=\"3\" valign=\"top\">Rome</th>\n",
       "      <th rowspan=\"3\" valign=\"top\">W_in</th>\n",
       "      <th>2</th>\n",
       "      <th>64</th>\n",
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       "      <th rowspan=\"2\" valign=\"top\">1</th>\n",
       "      <th>64</th>\n",
       "      <td>2.295971</td>\n",
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       "    <tr>\n",
       "      <th>373</th>\n",
       "      <td>2.287050</td>\n",
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       "    <tr>\n",
       "      <th>Melbourne</th>\n",
       "      <th>Rome</th>\n",
       "      <th>W_in</th>\n",
       "      <th>1</th>\n",
       "      <th>266</th>\n",
       "      <td>2.278152</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                                                    Magnitude\n",
       "Base                            Given Answer Correct Answer Matrix Layer Direction           \n",
       "Home to the renowned Colosseum, Melbourne    Rome           W_in   1     447         3.559548\n",
       "                                                                         64          3.362255\n",
       "                                                                         373         3.200690\n",
       "                                                                   2     64          3.176810\n",
       "                                                                         447         2.876518\n",
       "                                                                   3     64          2.628633\n",
       "                                Tokyo        Rome           W_in   1     447         2.607578\n",
       "                                Melbourne    Rome           W_in   4     64          2.590034\n",
       "                                                                   2     373         2.545317\n",
       "                                Tokyo        Rome           W_in   2     64          2.465634\n",
       "                                                                   1     64          2.462986\n",
       "                                                                         373         2.411186\n",
       "                                Melbourne    Rome           W_in   5     447         2.392912\n",
       "                                Beijing      Rome           W_in   1     447         2.387529\n",
       "                                Melbourne    Rome           W_in   4     447         2.382307\n",
       "                                                                   6     447         2.334295\n",
       "                                Beijing      Rome           W_in   2     64          2.298651\n",
       "                                                                   1     64          2.295971\n",
       "                                                                         373         2.287050\n",
       "                                Melbourne    Rome           W_in   1     266         2.278152"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "base = \"Home to the renowned Colosseum,\"\n",
    "print(f'Top 5 residual stream directions with the highest magnitude of change about {base}')\n",
    "diff_df3 \\\n",
    "    .loc[(base, slice(None), slice(None), slice(None), slice(None), slice(None)), :] \\\n",
    "    .sort_values(by=\"Magnitude\", ascending=False).head(top_N)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "8ef0d793",
   "metadata": {},
   "source": [
    "## Verification\n",
    "\n",
    "We have three neurons conjectured to care about capitals (L4N1406, L8N1961, and L7N1137). Can we verify this?\n",
    "* Check that they have relatively large diffs on other inputs related to capitals\n",
    "* Check that they have small diffs on unrelated inputs\n",
    "* Ablations TODO\n",
    "\n",
    "Similarly L11N369 seems to care about Paris. Verify this (TODO)."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "f93d0bef",
   "metadata": {},
   "source": [
    "### Unrelated inputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "ddfb0ac0",
   "metadata": {},
   "outputs": [],
   "source": [
    "verification_inputs = [\n",
    "    \"Ox is a word that, for many of us, is both familiar and strange.\",\n",
    "    \"Google Authenticator is adding a long-standing customer request\",\n",
    "    \"Hillary Clinton: Republicans Are Playing Into the Hands of Putin and Xi\",\n",
    "    \"When I was arrested and charged with possession with intent to sell cocaine in 1986, I was addicted to both coke and heroin.\",\n",
    "    \"The Brain is Not Close to Thermodynamic Limits on Computation\",\n",
    "    \"AGI ruin mostly rests on strong claims about alignment and deployment, not about society\",\n",
    "    \"One apple plus one apple equals two apples.\",\n",
    "    \"Knight to E4.\",\n",
    "    \"The quick brown fox jumps over the lazy dog.\",\n",
    "    \"Sir, in my heart there was a kind of fighting That would not let me sleep.\",\n",
    "    \"For in the same way you judge others, you will be judged, and with the measure you use, it will be measured to you.\",\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "ce8da976",
   "metadata": {},
   "outputs": [],
   "source": [
    "verification_rows = []\n",
    "\n",
    "for input in verification_inputs:\n",
    "    loss = model(input, return_type=\"loss\")\n",
    "    loss.backward()\n",
    "    for layer in range(len(model.blocks)):\n",
    "        for posn in posns:\n",
    "            verification_rows.append((input, posn, layer, getattr(model.blocks[layer].mlp, posn).grad.clone().numpy()))\n",
    "    model.zero_grad()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "a625432c",
   "metadata": {},
   "outputs": [],
   "source": [
    "columns = [\"Input\", \"Matrix\", \"Layer\", \"Gradient\"]\n",
    "verification_df = pd.DataFrame(verification_rows, columns=columns).set_index([\"Input\", \"Matrix\", \"Layer\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "42b5810d",
   "metadata": {},
   "outputs": [],
   "source": [
    "verification_rows2 = []\n",
    "for (base, matrix, layer), grad in verification_df[\"Gradient\"].items():\n",
    "  neuron_axis = 0 if matrix == 'W_in' else 1\n",
    "  for neuron, magnitude in enumerate(np.linalg.norm(grad, axis=neuron_axis)):\n",
    "    verification_rows2.append((base, matrix, layer, neuron, magnitude))\n",
    "    \n",
    "columns = [\"Input\", \"Matrix\", \"Layer\", \"Neuron\", \"Magnitude\"]\n",
    "verification_neuron_df = pd.DataFrame(verification_rows2, columns=columns).set_index([\"Input\", \"Matrix\", \"Layer\", \"Neuron\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "5e6321c2",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>Magnitude</th>\n",
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       "    <tr>\n",
       "      <th>Input</th>\n",
       "      <th>Matrix</th>\n",
       "      <th>Layer</th>\n",
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       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"4\" valign=\"top\">Knight to E4.</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">W_out</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">2</th>\n",
       "      <th>666</th>\n",
       "      <td>4.451502</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1825</th>\n",
       "      <td>4.187678</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">W_in</th>\n",
       "      <th>3</th>\n",
       "      <th>1987</th>\n",
       "      <td>3.236897</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <th>642</th>\n",
       "      <td>3.206800</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AGI ruin mostly rests on strong claims about alignment and deployment, not about society</th>\n",
       "      <th>W_in</th>\n",
       "      <th>10</th>\n",
       "      <th>3023</th>\n",
       "      <td>2.648305</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Knight to E4.</th>\n",
       "      <th>W_in</th>\n",
       "      <th>2</th>\n",
       "      <th>2653</th>\n",
       "      <td>2.559177</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Hillary Clinton: Republicans Are Playing Into the Hands of Putin and Xi</th>\n",
       "      <th>W_in</th>\n",
       "      <th>7</th>\n",
       "      <th>1022</th>\n",
       "      <td>2.470968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">Knight to E4.</th>\n",
       "      <th rowspan=\"3\" valign=\"top\">W_in</th>\n",
       "      <th>5</th>\n",
       "      <th>284</th>\n",
       "      <td>2.422877</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <th>2362</th>\n",
       "      <td>2.402013</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <th>2293</th>\n",
       "      <td>2.370207</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>One apple plus one apple equals two apples.</th>\n",
       "      <th>W_in</th>\n",
       "      <th>7</th>\n",
       "      <th>2794</th>\n",
       "      <td>2.302675</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">Knight to E4.</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">W_in</th>\n",
       "      <th>1</th>\n",
       "      <th>734</th>\n",
       "      <td>2.199726</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <th>2831</th>\n",
       "      <td>2.184857</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Hillary Clinton: Republicans Are Playing Into the Hands of Putin and Xi</th>\n",
       "      <th>W_in</th>\n",
       "      <th>0</th>\n",
       "      <th>642</th>\n",
       "      <td>2.183802</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AGI ruin mostly rests on strong claims about alignment and deployment, not about society</th>\n",
       "      <th>W_in</th>\n",
       "      <th>9</th>\n",
       "      <th>2538</th>\n",
       "      <td>2.159611</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The Brain is Not Close to Thermodynamic Limits on Computation</th>\n",
       "      <th>W_in</th>\n",
       "      <th>3</th>\n",
       "      <th>337</th>\n",
       "      <td>2.158644</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"4\" valign=\"top\">Knight to E4.</th>\n",
       "      <th rowspan=\"4\" valign=\"top\">W_in</th>\n",
       "      <th>2</th>\n",
       "      <th>2643</th>\n",
       "      <td>2.118534</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <th>197</th>\n",
       "      <td>2.099048</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <th>2883</th>\n",
       "      <td>2.044151</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <th>2015</th>\n",
       "      <td>2.006468</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                                        Magnitude\n",
       "Input                                              Matrix Layer Neuron           \n",
       "Knight to E4.                                      W_out  2     666      4.451502\n",
       "                                                                1825     4.187678\n",
       "                                                   W_in   3     1987     3.236897\n",
       "                                                          0     642      3.206800\n",
       "AGI ruin mostly rests on strong claims about al... W_in   10    3023     2.648305\n",
       "Knight to E4.                                      W_in   2     2653     2.559177\n",
       "Hillary Clinton: Republicans Are Playing Into t... W_in   7     1022     2.470968\n",
       "Knight to E4.                                      W_in   5     284      2.422877\n",
       "                                                          11    2362     2.402013\n",
       "                                                          0     2293     2.370207\n",
       "One apple plus one apple equals two apples.        W_in   7     2794     2.302675\n",
       "Knight to E4.                                      W_in   1     734      2.199726\n",
       "                                                          0     2831     2.184857\n",
       "Hillary Clinton: Republicans Are Playing Into t... W_in   0     642      2.183802\n",
       "AGI ruin mostly rests on strong claims about al... W_in   9     2538     2.159611\n",
       "The Brain is Not Close to Thermodynamic Limits ... W_in   3     337      2.158644\n",
       "Knight to E4.                                      W_in   2     2643     2.118534\n",
       "                                                          0     197      2.099048\n",
       "                                                          4     2883     2.044151\n",
       "                                                          2     2015     2.006468"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "verification_neuron_df.sort_values(by=\"Magnitude\", ascending=False).head(top_N)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "413f4b96",
   "metadata": {},
   "source": [
    "There's no intersection between these top neurons and those we were looking at before!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "024c3f78",
   "metadata": {},
   "outputs": [],
   "source": [
    "def capital_neurons(matrix=slice(None)):\n",
    "    return [\n",
    "        (slice(None), matrix, 4, 1406),\n",
    "        (slice(None), matrix, 8, 1961),\n",
    "        (slice(None), matrix, 7, 1137),\n",
    "    ]\n",
    "\n",
    "idx = pd.IndexSlice"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "7bda9d17",
   "metadata": {},
   "source": [
    "Much smaller diffs for all the neurons we were looking at before! (Each reached Magnitude 3.5 - 3.96 for inputs related to capitals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "f065bca6",
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   "outputs": [
    {
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       "                                                                        Magnitude\n",
       "Input                                              Matrix Layer Neuron           \n",
       "Google Authenticator is adding a long-standing ... W_in   8     1961     1.170218\n",
       "Hillary Clinton: Republicans Are Playing Into t... W_in   8     1961     1.133584\n",
       "The quick brown fox jumps over the lazy dog.       W_in   8     1961     1.128265\n",
       "AGI ruin mostly rests on strong claims about al... W_in   8     1961     1.037483\n",
       "Hillary Clinton: Republicans Are Playing Into t... W_in   4     1406     0.926769\n",
       "One apple plus one apple equals two apples.        W_in   8     1961     0.921822\n",
       "The Brain is Not Close to Thermodynamic Limits ... W_in   8     1961     0.685662\n",
       "Sir, in my heart there was a kind of fighting T... W_in   8     1961     0.619164\n",
       "Google Authenticator is adding a long-standing ... W_in   4     1406     0.579521\n",
       "Knight to E4.                                      W_in   8     1961     0.513827"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.concat([verification_neuron_df.loc[idx[neuron_slice], :] for neuron_slice in capital_neurons()]) \\\n",
    "    .sort_values(by=\"Magnitude\", ascending=False).head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "efaed211",
   "metadata": {},
   "outputs": [
    {
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       "                                                                        Magnitude\n",
       "Input                                              Matrix Layer Neuron           \n",
       "Knight to E4.                                      W_in   11    369      0.599770\n",
       "Hillary Clinton: Republicans Are Playing Into t... W_in   11    369      0.571101\n",
       "Google Authenticator is adding a long-standing ... W_in   11    369      0.268485\n",
       "Sir, in my heart there was a kind of fighting T... W_in   11    369      0.199792\n",
       "Ox is a word that, for many of us, is both fami... W_in   11    369      0.048831\n",
       "For in the same way you judge others, you will ... W_in   11    369      0.043669\n",
       "One apple plus one apple equals two apples.        W_in   11    369      0.039784\n",
       "The Brain is Not Close to Thermodynamic Limits ... W_in   11    369      0.032939\n",
       "AGI ruin mostly rests on strong claims about al... W_in   11    369      0.028906\n",
       "The quick brown fox jumps over the lazy dog.       W_in   11    369      0.024901"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "verification_neuron_df \\\n",
    "    .loc[(slice(None), slice(None), 11, 369), :] \\\n",
    "    .sort_values(by=\"Magnitude\", ascending=False).head(10)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "82b4dc5a",
   "metadata": {},
   "source": [
    "### Capitals"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "13abdc5a",
   "metadata": {},
   "source": [
    "How much do the capital neurons update on inputs related to other capitals?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "74f699b7",
   "metadata": {},
   "outputs": [],
   "source": [
    "correct_capital_inputs = [(capital, True) for capital in [\n",
    "    \"Washington D.C. is the capital of the United States.\",\n",
    "    \"Beijing is the capital of China.\",\n",
    "    \"The capital of Mexico is Mexico City.\",\n",
    "    \"The capital of Australia is Canberra.\",\n",
    "    \"The capital of Canada is Ottawa.\",\n",
    "    \"The capital of Brazil is Brasilia.\",\n",
    "    \"The capital of India is New Delhi.\",\n",
    "    \"The capital of Russia is Moscow.\",\n",
    "    \"The capital of South Africa is Pretoria.\",\n",
    "]]\n",
    "\n",
    "incorrect_capital_inputs = [(capital, False) for capital in [\n",
    "    \"Beijing is the capital of the United States.\",\n",
    "    \"Washington D.C. is the capital of China.\",\n",
    "    \"The capital of Mexico is Canberra.\",\n",
    "    \"The capital of Australia is Mexico City.\",\n",
    "    \"The capital of Canada is Brasilia.\",\n",
    "    \"The capital of Brazil is Ottawa.\",\n",
    "    \"The capital of India is Pretoria.\",\n",
    "    \"The capital of Russia is New Delhi.\",\n",
    "    \"The capital of South Africa is Moscow.\",\n",
    "]]\n",
    "\n",
    "capital_rows = []\n",
    "\n",
    "for (input, correct) in correct_capital_inputs + incorrect_capital_inputs:\n",
    "    loss = model(input, return_type=\"loss\")\n",
    "    loss.backward()\n",
    "    for layer in range(len(model.blocks)):\n",
    "        for posn in posns:\n",
    "            capital_rows.append((input, correct, posn, layer, getattr(model.blocks[layer].mlp, posn).grad.clone().numpy()))\n",
    "    model.zero_grad()\n",
    "\n",
    "columns = [\"Input\", \"Correct\", \"Matrix\", \"Layer\", \"Gradient\"]\n",
    "capital_df = pd.DataFrame(capital_rows, columns=columns).set_index([\"Input\", \"Correct\", \"Matrix\", \"Layer\"])\n",
    "\n",
    "capital_rows2 = []\n",
    "for (input, correct, matrix, layer), grad in capital_df[\"Gradient\"].items():\n",
    "  neuron_axis = 0 if matrix == 'W_in' else 1\n",
    "  for neuron, magnitude in enumerate(np.linalg.norm(grad, axis=neuron_axis)):\n",
    "    capital_rows2.append((input, correct, matrix, layer, neuron, magnitude))\n",
    "    \n",
    "columns = [\"Input\", \"Correct\", \"Matrix\", \"Layer\", \"Neuron\", \"Magnitude\"]\n",
    "capital_neuron_df = pd.DataFrame(capital_rows2, columns=columns).set_index([\"Input\", \"Correct\", \"Matrix\", \"Layer\", \"Neuron\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "4fef4c57",
   "metadata": {},
   "outputs": [],
   "source": [
    "def capital_neurons2(correct=slice(None), matrix=slice(None)):\n",
    "    return [\n",
    "        (slice(None), correct, matrix, 4, 1406),\n",
    "        (slice(None), correct, matrix, 8, 1961),\n",
    "        (slice(None), correct, matrix, 7, 1137),\n",
    "    ]\n",
    "\n",
    "idx = pd.IndexSlice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "65b4f215",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Updates on correct capital inputs\n"
     ]
    },
    {
     "data": {
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       "    <tr>\n",
       "      <th>The capital of Brazil is Brasilia.</th>\n",
       "      <th>True</th>\n",
       "      <th>W_in</th>\n",
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       "      <th>1406</th>\n",
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       "      <th>The capital of Canada is Ottawa.</th>\n",
       "      <th>True</th>\n",
       "      <th>W_in</th>\n",
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       "      <th>1406</th>\n",
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       "      <th>The capital of Australia is Canberra.</th>\n",
       "      <th>True</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>5.210154</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">The capital of South Africa is Pretoria.</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">True</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">W_in</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
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       "      <th>4</th>\n",
       "      <th>1406</th>\n",
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       "      <th>The capital of Brazil is Brasilia.</th>\n",
       "      <th>True</th>\n",
       "      <th>W_in</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>5.063847</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of Russia is Moscow.</th>\n",
       "      <th>True</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>5.019931</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of Australia is Canberra.</th>\n",
       "      <th>True</th>\n",
       "      <th>W_in</th>\n",
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       "      <th>1137</th>\n",
       "      <td>4.271571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of Canada is Ottawa.</th>\n",
       "      <th>True</th>\n",
       "      <th>W_in</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>4.061668</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of Mexico is Mexico City.</th>\n",
       "      <th>True</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>3.514666</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                                      Magnitude\n",
       "Input                                    Correct Matrix Layer Neuron           \n",
       "The capital of Brazil is Brasilia.       True    W_in   4     1406     5.863631\n",
       "The capital of Canada is Ottawa.         True    W_in   4     1406     5.294219\n",
       "The capital of Australia is Canberra.    True    W_in   4     1406     5.210154\n",
       "The capital of South Africa is Pretoria. True    W_in   7     1137     5.194824\n",
       "                                                        4     1406     5.081234\n",
       "The capital of Brazil is Brasilia.       True    W_in   7     1137     5.063847\n",
       "The capital of Russia is Moscow.         True    W_in   4     1406     5.019931\n",
       "The capital of Australia is Canberra.    True    W_in   7     1137     4.271571\n",
       "The capital of Canada is Ottawa.         True    W_in   7     1137     4.061668\n",
       "The capital of Mexico is Mexico City.    True    W_in   4     1406     3.514666"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(\"Updates on correct capital inputs\")\n",
    "pd.concat([capital_neuron_df.loc[idx[neuron_slice], :] for neuron_slice in capital_neurons2(correct=True)]) \\\n",
    "    .sort_values(by=\"Magnitude\", ascending=False).head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "950e46ea",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Updates on incorrect capital inputs\n"
     ]
    },
    {
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       "    <tr>\n",
       "      <th>The capital of Australia is Mexico City.</th>\n",
       "      <th>False</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>3.469062</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of Russia is New Delhi.</th>\n",
       "      <th>False</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>3.216355</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of India is Pretoria.</th>\n",
       "      <th>False</th>\n",
       "      <th>W_in</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>3.199577</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of Canada is Brasilia.</th>\n",
       "      <th>False</th>\n",
       "      <th>W_in</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>2.285698</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of Brazil is Ottawa.</th>\n",
       "      <th>False</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>2.281038</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of India is Pretoria.</th>\n",
       "      <th>False</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>2.237222</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of Mexico is Canberra.</th>\n",
       "      <th>False</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>1961</th>\n",
       "      <td>2.132167</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of Russia is New Delhi.</th>\n",
       "      <th>False</th>\n",
       "      <th>W_in</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>2.103357</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Beijing is the capital of the United States.</th>\n",
       "      <th>False</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>2.085735</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                                          Magnitude\n",
       "Input                                        Correct Matrix Layer Neuron           \n",
       "The capital of Canada is Brasilia.           False   W_in   4     1406     3.810387\n",
       "The capital of Australia is Mexico City.     False   W_in   4     1406     3.469062\n",
       "The capital of Russia is New Delhi.          False   W_in   4     1406     3.216355\n",
       "The capital of India is Pretoria.            False   W_in   7     1137     3.199577\n",
       "The capital of Canada is Brasilia.           False   W_in   7     1137     2.285698\n",
       "The capital of Brazil is Ottawa.             False   W_in   4     1406     2.281038\n",
       "The capital of India is Pretoria.            False   W_in   4     1406     2.237222\n",
       "The capital of Mexico is Canberra.           False   W_in   8     1961     2.132167\n",
       "The capital of Russia is New Delhi.          False   W_in   7     1137     2.103357\n",
       "Beijing is the capital of the United States. False   W_in   4     1406     2.085735"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(\"Updates on incorrect capital inputs\")\n",
    "pd.concat([capital_neuron_df.loc[idx[neuron_slice], :] for neuron_slice in capital_neurons2(correct=False)]) \\\n",
    "    .sort_values(by=\"Magnitude\", ascending=False).head(10)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "c88955bb",
   "metadata": {},
   "source": [
    "It's a bit of a surprise that we see larger updates on the correct capital inputs than incorrect inputs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "fdfa79a6",
   "metadata": {},
   "outputs": [
    {
     "data": {
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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "px.histogram(\n",
    "    pd.concat([capital_neuron_df.loc[idx[neuron_slice], :] for neuron_slice in capital_neurons2()]).values,\n",
    "    title=\"Distribution of gradient magnitudes for capital neurons in the (correct and incorrect) capitals dataset\"\n",
    ")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "e878bcfb",
   "metadata": {},
   "source": [
    "`W_out` updates are an order of magnitude smaller than `W_in` updates. (Why?)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "02e27430",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "px.histogram(\n",
    "    pd.concat([capital_neuron_df.loc[idx[neuron_slice], :] for neuron_slice in capital_neurons2(matrix=\"W_in\")]).values,\n",
    "    title=\"Distribution of W_in gradient magnitudes for capital neurons in the (correct and incorrect) capitals dataset\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "0e0e464b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "px.histogram(\n",
    "    pd.concat([capital_neuron_df.loc[idx[neuron_slice], :] for neuron_slice in capital_neurons2(matrix=\"W_out\")]).values,\n",
    "    title=\"Distribution of W_out gradient magnitudes for capital neurons in the (correct and incorrect) capitals dataset\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "1db07cf5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>Magnitude</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Input</th>\n",
       "      <th>Correct</th>\n",
       "      <th>Matrix</th>\n",
       "      <th>Layer</th>\n",
       "      <th>Neuron</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>The capital of Brazil is Brasilia.</th>\n",
       "      <th>True</th>\n",
       "      <th>W_out</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>0.238261</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of Australia is Canberra.</th>\n",
       "      <th>True</th>\n",
       "      <th>W_out</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>0.218975</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of South Africa is Pretoria.</th>\n",
       "      <th>True</th>\n",
       "      <th>W_out</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>0.216853</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of Canada is Ottawa.</th>\n",
       "      <th>True</th>\n",
       "      <th>W_out</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>0.176940</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of Russia is Moscow.</th>\n",
       "      <th>True</th>\n",
       "      <th>W_out</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>0.146237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of Mexico is Mexico City.</th>\n",
       "      <th>True</th>\n",
       "      <th>W_out</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>0.126595</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of Brazil is Brasilia.</th>\n",
       "      <th>True</th>\n",
       "      <th>W_out</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>0.122570</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of India is New Delhi.</th>\n",
       "      <th>True</th>\n",
       "      <th>W_out</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>0.119972</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of South Africa is Pretoria.</th>\n",
       "      <th>True</th>\n",
       "      <th>W_out</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>0.097468</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of Australia is Canberra.</th>\n",
       "      <th>True</th>\n",
       "      <th>W_out</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>0.091900</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                                      Magnitude\n",
       "Input                                    Correct Matrix Layer Neuron           \n",
       "The capital of Brazil is Brasilia.       True    W_out  4     1406     0.238261\n",
       "The capital of Australia is Canberra.    True    W_out  4     1406     0.218975\n",
       "The capital of South Africa is Pretoria. True    W_out  4     1406     0.216853\n",
       "The capital of Canada is Ottawa.         True    W_out  4     1406     0.176940\n",
       "The capital of Russia is Moscow.         True    W_out  4     1406     0.146237\n",
       "The capital of Mexico is Mexico City.    True    W_out  4     1406     0.126595\n",
       "The capital of Brazil is Brasilia.       True    W_out  7     1137     0.122570\n",
       "The capital of India is New Delhi.       True    W_out  4     1406     0.119972\n",
       "The capital of South Africa is Pretoria. True    W_out  7     1137     0.097468\n",
       "The capital of Australia is Canberra.    True    W_out  7     1137     0.091900"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.concat([capital_neuron_df.loc[idx[neuron_slice], :] for neuron_slice in capital_neurons2(correct=True, matrix=\"W_out\")]) \\\n",
    "    .sort_values(by=\"Magnitude\", ascending=False).head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "35e02f40",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
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       "        vertical-align: top;\n",
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       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>Magnitude</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Input</th>\n",
       "      <th>Correct</th>\n",
       "      <th>Matrix</th>\n",
       "      <th>Layer</th>\n",
       "      <th>Neuron</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>The capital of India is Pretoria.</th>\n",
       "      <th>False</th>\n",
       "      <th>W_out</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>0.132091</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of Russia is New Delhi.</th>\n",
       "      <th>False</th>\n",
       "      <th>W_out</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>0.129557</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of Mexico is Canberra.</th>\n",
       "      <th>False</th>\n",
       "      <th>W_out</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>0.127815</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of Canada is Brasilia.</th>\n",
       "      <th>False</th>\n",
       "      <th>W_out</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>0.124469</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of Brazil is Ottawa.</th>\n",
       "      <th>False</th>\n",
       "      <th>W_out</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>0.116335</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of Australia is Mexico City.</th>\n",
       "      <th>False</th>\n",
       "      <th>W_out</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>0.106765</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of South Africa is Moscow.</th>\n",
       "      <th>False</th>\n",
       "      <th>W_out</th>\n",
       "      <th>4</th>\n",
       "      <th>1406</th>\n",
       "      <td>0.076342</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of Brazil is Ottawa.</th>\n",
       "      <th>False</th>\n",
       "      <th>W_out</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>0.073566</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of Mexico is Canberra.</th>\n",
       "      <th>False</th>\n",
       "      <th>W_out</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>0.068974</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The capital of Russia is New Delhi.</th>\n",
       "      <th>False</th>\n",
       "      <th>W_out</th>\n",
       "      <th>7</th>\n",
       "      <th>1137</th>\n",
       "      <td>0.066296</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                                      Magnitude\n",
       "Input                                    Correct Matrix Layer Neuron           \n",
       "The capital of India is Pretoria.        False   W_out  4     1406     0.132091\n",
       "The capital of Russia is New Delhi.      False   W_out  4     1406     0.129557\n",
       "The capital of Mexico is Canberra.       False   W_out  4     1406     0.127815\n",
       "The capital of Canada is Brasilia.       False   W_out  4     1406     0.124469\n",
       "The capital of Brazil is Ottawa.         False   W_out  4     1406     0.116335\n",
       "The capital of Australia is Mexico City. False   W_out  4     1406     0.106765\n",
       "The capital of South Africa is Moscow.   False   W_out  4     1406     0.076342\n",
       "The capital of Brazil is Ottawa.         False   W_out  7     1137     0.073566\n",
       "The capital of Mexico is Canberra.       False   W_out  7     1137     0.068974\n",
       "The capital of Russia is New Delhi.      False   W_out  7     1137     0.066296"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.concat([capital_neuron_df.loc[idx[neuron_slice], :] for neuron_slice in capital_neurons2(correct=False, matrix=\"W_out\")]) \\\n",
    "    .sort_values(by=\"Magnitude\", ascending=False).head(10)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "e15b3005",
   "metadata": {},
   "source": [
    "The capital neurons have significantly smaller updates on non-capital sentences."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "e7e8ffe4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>Magnitude</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Input</th>\n",
       "      <th>Matrix</th>\n",
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       "      <th>Neuron</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Google Authenticator is adding a long-standing customer request</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>1961</th>\n",
       "      <td>1.170218</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Hillary Clinton: Republicans Are Playing Into the Hands of Putin and Xi</th>\n",
       "      <th>W_in</th>\n",
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       "    <tr>\n",
       "      <th>The quick brown fox jumps over the lazy dog.</th>\n",
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       "    <tr>\n",
       "      <th>AGI ruin mostly rests on strong claims about alignment and deployment, not about society</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>1961</th>\n",
       "      <td>1.037483</td>\n",
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       "    <tr>\n",
       "      <th>Hillary Clinton: Republicans Are Playing Into the Hands of Putin and Xi</th>\n",
       "      <th>W_in</th>\n",
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       "      <th>1406</th>\n",
       "      <td>0.926769</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>One apple plus one apple equals two apples.</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
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       "      <td>0.921822</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The Brain is Not Close to Thermodynamic Limits on Computation</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
       "      <th>1961</th>\n",
       "      <td>0.685662</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sir, in my heart there was a kind of fighting That would not let me sleep.</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
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       "    <tr>\n",
       "      <th>Google Authenticator is adding a long-standing customer request</th>\n",
       "      <th>W_in</th>\n",
       "      <th>4</th>\n",
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       "      <td>0.579521</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Knight to E4.</th>\n",
       "      <th>W_in</th>\n",
       "      <th>8</th>\n",
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       "      <td>0.513827</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                                        Magnitude\n",
       "Input                                              Matrix Layer Neuron           \n",
       "Google Authenticator is adding a long-standing ... W_in   8     1961     1.170218\n",
       "Hillary Clinton: Republicans Are Playing Into t... W_in   8     1961     1.133584\n",
       "The quick brown fox jumps over the lazy dog.       W_in   8     1961     1.128265\n",
       "AGI ruin mostly rests on strong claims about al... W_in   8     1961     1.037483\n",
       "Hillary Clinton: Republicans Are Playing Into t... W_in   4     1406     0.926769\n",
       "One apple plus one apple equals two apples.        W_in   8     1961     0.921822\n",
       "The Brain is Not Close to Thermodynamic Limits ... W_in   8     1961     0.685662\n",
       "Sir, in my heart there was a kind of fighting T... W_in   8     1961     0.619164\n",
       "Google Authenticator is adding a long-standing ... W_in   4     1406     0.579521\n",
       "Knight to E4.                                      W_in   8     1961     0.513827"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "pd.concat([verification_neuron_df.loc[idx[neuron_slice], :] for neuron_slice in capital_neurons()]) \\\n",
    "    .sort_values(by=\"Magnitude\", ascending=False).head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "8415f44c",
   "metadata": {},
   "outputs": [
    {
     "data": {
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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "px.histogram(\n",
    "    pd.concat([verification_neuron_df.loc[idx[neuron_slice], :] for neuron_slice in capital_neurons()]).values,\n",
    "    title=\"Distribution of gradient magnitudes for capital neurons in the verification dataset (unrelated to capitals)\"\n",
    ")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "2f0318ac",
   "metadata": {},
   "source": [
    "## TODO\n",
    "\n",
    "* Automate finding which neurons update for some sentences but not others, use this to find neurons which care about other cities or other concepts.\n",
    "* Look at residual stream updates for other inputs"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}