pyvene_101.ipynb

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  {
   "cell_type": "markdown",
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   "metadata": {},
   "source": [
    "# Introduction to pyvene\n",
    "This tutorial shows simple runnable code snippets of how to do different kinds of interventions on neural networks with pyvene."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d6994fa",
   "metadata": {},
   "source": [
    "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/stanfordnlp/pyvene/blob/main/pyvene_101.ipynb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d123a2ba",
   "metadata": {},
   "outputs": [],
   "source": [
    "__author__ = \"Zhengxuan Wu\"\n",
    "__version__ = \"01/20/2024\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26298448-91eb-4cad-85bf-ec5fef436e1d",
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   "source": [
    " # Table of Contents  \n",
    "1. [Set-up](#Set-up)     \n",
    "1. [pyvene 101](#pyvene-101) \n",
    "    1. [Get Attention Weights](#Get-Attention-Weights)\n",
    "    1. [Set Activations to Zeros](#Set-Activation-to-Zeros) \n",
    "    1. [Set Activations with Subspaces](#Set-Activations-to-Zeros-with-Subspaces)\n",
    "    1. [Interchange Intervention](#Interchange-Interventions)\n",
    "    1. [Intervention Config](#Intervention-Configuration)\n",
    "    1. [Addition Intervention](#Addition-Intervention)\n",
    "    1. [Trainable Intervention](#Trainable-Intervention)\n",
    "    1. [Activation Collection](#Activation-Collection-with-Intervention)\n",
    "    1. [Activation Collection with Other Intervention](#Activation-Collection-at-Downstream-of-a-Intervened-Model)\n",
    "    1. [Intervene Single Neuron](#Intervene-on-a-Single-Neuron)\n",
    "    1. [Add New Intervention Type](#Add-New-Intervention-Type)\n",
    "    1. [Intervene on Recurrent NNs](#Recurrent-NNs-(Intervene-a-Specific-Timestep))\n",
    "    1. [Intervene across Times with RNNs](#Recurrent-NNs-(Intervene-cross-Time))\n",
    "    1. [Intervene on LM Generation](#LMs-Generation)\n",
    "    1. [Debiasing with Backpack LMs](#Debiasing-with-Backpack-LMs)\n",
    "    1. [Saving and Loading](#Saving-and-Loading)\n",
    "    1. [Multi-Source Intervention (Parallel)](#Multi-Source-Interchange-Intervention-(Parallel-Mode))\n",
    "    1. [Multi-Source Intervention (Serial)](#Multi-Source-Interchange-Intervention-(Serial-Mode))\n",
    "    1. [Multi-Source Intervention with Subspaces (Parallel)](#Multi-Source-Interchange-Intervention-with-Subspaces-(Parallel-Mode))\n",
    "    1. [Multi-Source Intervention with Subspaces (Serial)](#Multi-Source-Interchange-Intervention-with-Subspaces-(Serial-Mode))\n",
    "    1. [Interchange Intervention Training](#Interchange-Intervention-Training-(IIT))\n",
    "1. [pyvene 102](#pyvene-102)\n",
    "    1. [Intervention Grouping](#Grouping)\n",
    "    1. [Intervention Skipping](#Intervention-Skipping-in-Runtime)\n",
    "    1. [Subspace Partition](#Subspace-Partition)\n",
    "    1. [Intervention Linking](#Intervention-Linking)\n",
    "    1. [Add New Model Type](#Add-New-Model-Type)\n",
    "    1. [Path Patching](#Composing-Complex-Intervention-Schema:-Path-Patching)\n",
    "    1. [Causal Tracing](#Composing-Complex-Intervention-Schema:-Causal-Tracing-in-15-lines)\n",
    "1. [The End](#The-End)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0706e21b",
   "metadata": {},
   "source": [
    "## Set-up"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e08304ea",
   "metadata": {},
   "outputs": [],
   "source": [
    "try:\n",
    "    # This library is our indicator that the required installs\n",
    "    # need to be done.\n",
    "    import pyvene\n",
    "\n",
    "except ModuleNotFoundError:\n",
    "    !pip install git+https://github.com/stanfordnlp/pyvene.git"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ede4f94",
   "metadata": {},
   "source": [
    "## pyvene 101\n",
    "Before we get started, here are a couple of core notations that are used in this library:\n",
    "- **Base** example: this is the example we are intervening on, or, we are intervening on the computation graph of the model running the **Base** example.\n",
    "- **Source** example or representations: this is the source of our intervention. We use **Source** to intervene on **Base**.\n",
    "- **component**: this is the `nn.module` we are intervening in a pytorch-based NN.\n",
    "- **unit**: this is the axis of our intervention. If we say our **unit** is `pos` (`position`), then you are intervening on each token position.\n",
    "- **unit_locations**: this list gives you the percisely location of your intervention. It is the locations of the unit of analysis you are specifying. For instance, if your `unit` is `pos`, and your `unit_location` is 3, then it means you are intervening on the third token."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7245643b-fd44-47a5-a189-ce1565da7e25",
   "metadata": {},
   "source": [
    "### Get Attention Weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "17c7f2f6-b0d3-4fe2-8e4f-c044b93f3ef0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loaded model\n"
     ]
    }
   ],
   "source": [
    "import pyvene as pv\n",
    "from circuitsvis.attention import attention_patterns\n",
    "\n",
    "_, tokenizer, gpt2 = pv.create_gpt2()\n",
    "\n",
    "pv_gpt2 = pv.IntervenableModel({\n",
    "    \"layer\": 10,\n",
    "    \"component\": \"attention_weight\",\n",
    "    \"intervention_type\": pv.CollectIntervention}, model=gpt2)\n",
    "\n",
    "base = \"When John and Mary went to the shops, Mary gave the bag to\"\n",
    "collected_attn_w = pv_gpt2(\n",
    "    base = tokenizer(base, return_tensors=\"pt\"\n",
    "    ), unit_locations={\"base\": ([[[h for h in range(12)]]])}\n",
    ")[0][-1][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "d7554177-d879-4e7a-968c-c16d1c1a169c",
   "metadata": {},
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    {
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       "<div id=\"circuits-vis-7ba1df49-5e8b\" style=\"margin: 15px 0;\"/>\n",
       "    <script crossorigin type=\"module\">\n",
       "    import { render, AttentionPatterns } from \"https://unpkg.com/circuitsvis@1.43.2/dist/cdn/esm.js\";\n",
       "    render(\n",
       "      \"circuits-vis-7ba1df49-5e8b\",\n",
       "      AttentionPatterns,\n",
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       "    )\n",
       "    </script>"
      ],
      "text/plain": [
       "<circuitsvis.utils.render.RenderedHTML at 0x7f47d7ecf4c0>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "attention_patterns(tokens=tokenizer.tokenize(base), attention=collected_attn_w)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12c5addb-4bd7-4129-b350-0677774f5790",
   "metadata": {},
   "source": [
    "### Set Activation to Zeros"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a82664f9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loaded model\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import pyvene as pv\n",
    "\n",
    "_, tokenizer, gpt2 = pv.create_gpt2()\n",
    "\n",
    "# define the component to zero-out\n",
    "pv_gpt2 = pv.IntervenableModel({\n",
    "    \"layer\": 0, \"component\": \"mlp_output\",\n",
    "    \"source_representation\": torch.zeros(gpt2.config.n_embd)\n",
    "}, model=gpt2)\n",
    "# run the intervened forward pass\n",
    "intervened_outputs = pv_gpt2(\n",
    "    base = tokenizer(\"The capital of Spain is\", return_tensors=\"pt\"), \n",
    "    # we define the intervening token dynamically\n",
    "    unit_locations={\"base\": 3}\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39071858",
   "metadata": {},
   "source": [
    "### Set Activations to Zeros with Subspaces\n",
    "The notion of subspace means the actual dimensions you are intervening. If we have a representation in a size of 512, the first 128 activation values are its subspace activations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b7896c3b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loaded model\n",
      "Directory './tmp/' already exists.\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import pyvene as pv\n",
    "# built-in helper to get a HuggingFace model\n",
    "_, tokenizer, gpt2 = pv.create_gpt2()\n",
    "# create with dict-based config\n",
    "pv_config = pv.IntervenableConfig({\n",
    "  \"layer\": 0, \"component\": \"mlp_output\"})\n",
    "#initialize model\n",
    "pv_gpt2 = pv.IntervenableModel(pv_config, model=gpt2)\n",
    "# run an intervened forward pass\n",
    "intervened_outputs = pv_gpt2(\n",
    "  # the intervening base input\n",
    "  base=tokenizer(\"The capital of Spain is\", return_tensors=\"pt\"), \n",
    "  # the location to intervene at (3rd token)\n",
    "  unit_locations={\"base\": 3},\n",
    "  # the individual dimensions targetted\n",
    "  subspaces=[10,11,12],\n",
    "  source_representations=torch.zeros(gpt2.config.n_embd)\n",
    ")\n",
    "# sharing\n",
    "pv_gpt2.save(\"./tmp/\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1410904d",
   "metadata": {},
   "source": [
    "### Interchange Interventions\n",
    "Instead of a static vector, we can intervene the model with activations sampled from a different forward run. We call this interchange intervention, where intervention happens between two examples and we are interchanging activations between them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9691c7d8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loaded model\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import pyvene as pv\n",
    "# built-in helper to get a HuggingFace model\n",
    "_, tokenizer, gpt2 = pv.create_gpt2()\n",
    "# create with dict-based config\n",
    "pv_config = pv.IntervenableConfig({\n",
    "  \"layer\": 0,\n",
    "  \"component\": \"mlp_output\"},\n",
    "  intervention_types=pv.VanillaIntervention\n",
    ")\n",
    "#initialize model\n",
    "pv_gpt2 = pv.IntervenableModel(\n",
    "  pv_config, model=gpt2)\n",
    "# run an interchange intervention \n",
    "intervened_outputs = pv_gpt2(\n",
    "  # the base input\n",
    "  base=tokenizer(\n",
    "    \"The capital of Spain is\", \n",
    "    return_tensors = \"pt\"), \n",
    "  # the source input\n",
    "  sources=tokenizer(\n",
    "    \"The capital of Italy is\", \n",
    "    return_tensors = \"pt\"), \n",
    "  # the location to intervene at (3rd token)\n",
    "  unit_locations={\"sources->base\": 3},\n",
    "  # the individual dimensions targeted\n",
    "  subspaces=[10,11,12]\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c890fda4",
   "metadata": {},
   "source": [
    "### Intervention Configuration\n",
    "You can also initialize the config without the lazy dictionary passing by enabling more options, e.g., the mode of these interventions are executed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4faa3e41",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loaded model\n",
      "IntervenableConfig\n",
      "{\n",
      "    \"model_type\": \"None\",\n",
      "    \"representations\": [\n",
      "        {\n",
      "            \"layer\": 0,\n",
      "            \"component\": \"mlp_output\",\n",
      "            \"unit\": \"pos\",\n",
      "            \"max_number_of_units\": 1,\n",
      "            \"low_rank_dimension\": null,\n",
      "            \"intervention_type\": null,\n",
      "            \"subspace_partition\": null,\n",
      "            \"group_key\": null,\n",
      "            \"intervention_link_key\": null,\n",
      "            \"moe_key\": null,\n",
      "            \"source_representation\": \"PLACEHOLDER\",\n",
      "            \"hidden_source_representation\": null\n",
      "        },\n",
      "        {\n",
      "            \"layer\": 1,\n",
      "            \"component\": \"mlp_output\",\n",
      "            \"unit\": \"pos\",\n",
      "            \"max_number_of_units\": 1,\n",
      "            \"low_rank_dimension\": null,\n",
      "            \"intervention_type\": null,\n",
      "            \"subspace_partition\": null,\n",
      "            \"group_key\": null,\n",
      "            \"intervention_link_key\": null,\n",
      "            \"moe_key\": null,\n",
      "            \"source_representation\": \"PLACEHOLDER\",\n",
      "            \"hidden_source_representation\": null\n",
      "        },\n",
      "        {\n",
      "            \"layer\": 2,\n",
      "            \"component\": \"mlp_output\",\n",
      "            \"unit\": \"pos\",\n",
      "            \"max_number_of_units\": 1,\n",
      "            \"low_rank_dimension\": null,\n",
      "            \"intervention_type\": null,\n",
      "            \"subspace_partition\": null,\n",
      "            \"group_key\": null,\n",
      "            \"intervention_link_key\": null,\n",
      "            \"moe_key\": null,\n",
      "            \"source_representation\": \"PLACEHOLDER\",\n",
      "            \"hidden_source_representation\": null\n",
      "        },\n",
      "        {\n",
      "            \"layer\": 3,\n",
      "            \"component\": \"mlp_output\",\n",
      "            \"unit\": \"pos\",\n",
      "            \"max_number_of_units\": 1,\n",
      "            \"low_rank_dimension\": null,\n",
      "            \"intervention_type\": null,\n",
      "            \"subspace_partition\": null,\n",
      "            \"group_key\": null,\n",
      "            \"intervention_link_key\": null,\n",
      "            \"moe_key\": null,\n",
      "            \"source_representation\": \"PLACEHOLDER\",\n",
      "            \"hidden_source_representation\": null\n",
      "        }\n",
      "    ],\n",
      "    \"intervention_types\": \"<class 'pyvene.models.interventions.VanillaIntervention'>\",\n",
      "    \"mode\": \"parallel\",\n",
      "    \"interventions\": [\n",
      "        \"None\"\n",
      "    ],\n",
      "    \"sorted_keys\": \"None\",\n",
      "    \"intervention_dimensions\": \"None\"\n",
      "}\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import pyvene as pv\n",
    "\n",
    "_, tokenizer, gpt2 = pv.create_gpt2()\n",
    "# standalone configuration object\n",
    "config = pv.IntervenableConfig([\n",
    "    {\n",
    "        \"layer\": _,\n",
    "        \"component\": \"mlp_output\",\n",
    "        \"source_representation\": torch.zeros(\n",
    "            gpt2.config.n_embd)\n",
    "    } for _ in range(4)],\n",
    "    mode=\"parallel\"\n",
    ")\n",
    "# this object is serializable\n",
    "print(config)\n",
    "pv_gpt2 = pv.IntervenableModel(config, model=gpt2)\n",
    "\n",
    "intervened_outputs = pv_gpt2(\n",
    "    base = tokenizer(\"The capital of Spain is\", return_tensors=\"pt\"), \n",
    "    unit_locations={\"base\": 3}\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c5b2270",
   "metadata": {},
   "source": [
    "### Addition Intervention\n",
    "Activation swap is one kind of interventions we can perform. Here is another simple one: `pv.AdditionIntervention`, which adds the sampled representation into the **Base** run."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a40f5989",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loaded model\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import pyvene as pv\n",
    "\n",
    "_, tokenizer, gpt2 = pv.create_gpt2()\n",
    "\n",
    "config = pv.IntervenableConfig({\n",
    "    \"layer\": 0,\n",
    "    \"component\": \"mlp_input\"},\n",
    "    pv.AdditionIntervention\n",
    ")\n",
    "\n",
    "pv_gpt2 = pv.IntervenableModel(config, model=gpt2)\n",
    "\n",
    "intervened_outputs = pv_gpt2(\n",
    "    base = tokenizer(\n",
    "        \"The Space Needle is in downtown\", \n",
    "        return_tensors=\"pt\"\n",
    "    ), \n",
    "    unit_locations={\"base\": [[[0, 1, 2, 3]]]},\n",
    "    source_representations = torch.rand(gpt2.config.n_embd)\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "099ddf77",
   "metadata": {},
   "source": [
    "### Trainable Intervention\n",
    "Interventions can contain trainable parameters, and hook-up with the model to receive gradients end-to-end. They are often useful in searching for an particular interpretation of the representation.\n",
    "\n",
    "The following example does a single step gradient calculation to push the model to generate `Rome` after the intervention. If we can train such intervention at scale with low loss, it means you have a causal grab onto your model. In terms of interpretability, that means, somehow you find a representation (not the original one since its trained) that maps onto the `capital` output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "7f058ecd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loaded model\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import pyvene as pv\n",
    "\n",
    "_, tokenizer, gpt2 = pv.create_gpt2()\n",
    "\n",
    "das_config = pv.IntervenableConfig({\n",
    "    \"layer\": 8,\n",
    "    \"component\": \"block_output\",\n",
    "    \"low_rank_dimension\": 1},\n",
    "    # this is a trainable low-rank rotation\n",
    "    pv.LowRankRotatedSpaceIntervention\n",
    ")\n",
    "\n",
    "das_gpt2 = pv.IntervenableModel(das_config, model=gpt2)\n",
    "\n",
    "last_hidden_state = das_gpt2(\n",
    "    base = tokenizer(\n",
    "        \"The capital of Spain is\", \n",
    "        return_tensors=\"pt\"\n",
    "    ), \n",
    "    sources = tokenizer(\n",
    "        \"The capital of Italy is\", \n",
    "        return_tensors=\"pt\"\n",
    "    ), \n",
    "    unit_locations={\"sources->base\": 3}\n",
    ")[-1].last_hidden_state[:,-1]\n",
    "\n",
    "# golden counterfacutual label as Rome\n",
    "label = tokenizer.encode(\n",
    "    \" Rome\", return_tensors=\"pt\")\n",
    "logits = torch.matmul(\n",
    "    last_hidden_state, gpt2.wte.weight.t())\n",
    "\n",
    "m = torch.nn.CrossEntropyLoss()\n",
    "loss = m(logits, label.view(-1))\n",
    "loss.backward()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8fd2b8e",
   "metadata": {},
   "source": [
    "### Activation Collection with Intervention\n",
    "You can also collect activations with our provided `pv.CollectIntervention` intervention. More importantly, this can be used interchangably with other interventions. You can collect something from an intervened model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "6e6bd585",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loaded model\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import pyvene as pv\n",
    "\n",
    "_, tokenizer, gpt2 = pv.create_gpt2()\n",
    "\n",
    "config = pv.IntervenableConfig({\n",
    "    \"layer\": 10,\n",
    "    \"component\": \"block_output\",\n",
    "    \"intervention_type\": pv.CollectIntervention}\n",
    ")\n",
    "\n",
    "pv_gpt2 = pv.IntervenableModel(\n",
    "    config, model=gpt2)\n",
    "\n",
    "collected_activations = pv_gpt2(\n",
    "    base = tokenizer(\n",
    "        \"The capital of Spain is\", \n",
    "        return_tensors=\"pt\"\n",
    "    ), unit_locations={\"sources->base\": 3}\n",
    ")[0][-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f7b0d0c6",
   "metadata": {},
   "source": [
    "### Activation Collection at Downstream of a Intervened Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "adcfcb05",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loaded model\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import pyvene as pv\n",
    "\n",
    "_, tokenizer, gpt2 = pv.create_gpt2()\n",
    "\n",
    "config = pv.IntervenableConfig({\n",
    "    \"layer\": 8,\n",
    "    \"component\": \"block_output\",\n",
    "    \"intervention_type\": pv.VanillaIntervention}\n",
    ")\n",
    "\n",
    "config.add_intervention({\n",
    "    \"layer\": 10,\n",
    "    \"component\": \"block_output\",\n",
    "    \"intervention_type\": pv.CollectIntervention})\n",
    "\n",
    "pv_gpt2 = pv.IntervenableModel(\n",
    "    config, model=gpt2)\n",
    "\n",
    "collected_activations = pv_gpt2(\n",
    "    base = tokenizer(\n",
    "        \"The capital of Spain is\", \n",
    "        return_tensors=\"pt\"\n",
    "    ), \n",
    "    sources = [tokenizer(\n",
    "        \"The capital of Italy is\", \n",
    "        return_tensors=\"pt\"\n",
    "    ), None], unit_locations={\"sources->base\": 3}\n",
    ")[0][-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a9e6e4d9",
   "metadata": {},
   "source": [
    "### Intervene on a Single Neuron\n",
    "We want to provide a good user interface so that interventions can be done easily by people with less pytorch or programming experience. Meanwhile, we also want to be flexible and provide the depth of control required for highly specific tasks. Here is an example where we intervene on a specific neuron at a specific head of a layer in a model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d25b6401",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loaded model\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import pyvene as pv\n",
    "\n",
    "_, tokenizer, gpt2 = pv.create_gpt2()\n",
    "\n",
    "config = pv.IntervenableConfig({\n",
    "    \"layer\": 8,\n",
    "    \"component\": \"head_attention_value_output\",\n",
    "    \"unit\": \"h.pos\",\n",
    "    \"intervention_type\": pv.CollectIntervention}\n",
    ")\n",
    "\n",
    "pv_gpt2 = pv.IntervenableModel(\n",
    "    config, model=gpt2)\n",
    "\n",
    "collected_activations = pv_gpt2(\n",
    "    base = tokenizer(\n",
    "        \"The capital of Spain is\", \n",
    "        return_tensors=\"pt\"\n",
    "    ), \n",
    "    unit_locations={\n",
    "        # GET_LOC is a helper.\n",
    "        # (3,3) means head 3 position 3\n",
    "        \"base\": pv.GET_LOC((3,3))\n",
    "    },\n",
    "    # the notion of subspace is used to target neuron 0.\n",
    "    subspaces=[0]\n",
    ")[0][-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5692bc15",
   "metadata": {},
   "source": [
    "### Add New Intervention Type"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "1597221a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loaded model\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import pyvene as pv\n",
    "\n",
    "_, tokenizer, gpt2 = pv.create_gpt2()\n",
    "\n",
    "class MultiplierIntervention(\n",
    "  pv.ConstantSourceIntervention):\n",
    "    def __init__(self, **kwargs):\n",
    "        super().__init__()\n",
    "    def forward(\n",
    "    self, base, source=None, subspaces=None):\n",
    "        return base * 99.0\n",
    "# run with new intervention type\n",
    "pv_gpt2 = pv.IntervenableModel({\n",
    "  \"intervention_type\": MultiplierIntervention}, \n",
    "  model=gpt2)\n",
    "intervened_outputs = pv_gpt2(\n",
    "  base = tokenizer(\"The capital of Spain is\", \n",
    "    return_tensors=\"pt\"), \n",
    "  unit_locations={\"base\": 3})"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "079050f6",
   "metadata": {},
   "source": [
    "### Recurrent NNs (Intervene a Specific Timestep)\n",
    "Existing intervention libraries focus on Transformer models. They often lack of supports for GRUs, LSTMs or any state-space model. The fundemental problem is in the hook mechanism provided by PyTorch. Hook is attached to a module before runtime. Models like GRUs will lead to undesired callback from the hook as there is no notion of state or time of the hook. \n",
    "\n",
    "We make our hook stateful, so you can intervene on recurrent NNs like GRUs. This notion of time will become useful when intervening on Transformers yet want to unroll the causal effect during generation as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "7a53347a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loaded model\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import pyvene as pv\n",
    "\n",
    "_, _, gru = pv.create_gru_classifier(\n",
    "    pv.GRUConfig(h_dim=32))\n",
    "\n",
    "pv_gru = pv.IntervenableModel({\n",
    "    \"component\": \"cell_output\",\n",
    "    \"unit\": \"t\", \n",
    "    \"intervention_type\": pv.ZeroIntervention},\n",
    "    model=gru)\n",
    "\n",
    "rand_t = torch.rand(1,10, gru.config.h_dim)\n",
    "\n",
    "intervened_outputs = pv_gru(\n",
    "  base = {\"inputs_embeds\": rand_t}, \n",
    "  unit_locations={\"base\": 3})"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "031dd5de",
   "metadata": {},
   "source": [
    "### Recurrent NNs (Intervene cross Time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "b48166c0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loaded model\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import pyvene as pv\n",
    "\n",
    "# built-in helper to get a GRU\n",
    "_, _, gru = pv.create_gru_classifier(\n",
    "    pv.GRUConfig(h_dim=32))\n",
    "# wrap it with config\n",
    "pv_gru = pv.IntervenableModel({\n",
    "    \"component\": \"cell_output\",\n",
    "    # intervening on time\n",
    "    \"unit\": \"t\", \n",
    "    \"intervention_type\": pv.ZeroIntervention},\n",
    "    model=gru)\n",
    "# run an intervened forward pass\n",
    "rand_b = torch.rand(1,10, gru.config.h_dim)\n",
    "rand_s = torch.rand(1,10, gru.config.h_dim)\n",
    "intervened_outputs = pv_gru(\n",
    "  base = {\"inputs_embeds\": rand_b}, \n",
    "  sources = [{\"inputs_embeds\": rand_s}], \n",
    "  # intervening time step\n",
    "  unit_locations={\"sources->base\": (6, 3)})"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "121366c1",
   "metadata": {},
   "source": [
    "### LMs Generation\n",
    "You can also intervene the generation call of LMs. Here is a simple example where we try to add a vector into the MLP output when the model decodes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f718e2d6",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "The attention mask and the pad token id were not set. As a consequence, you may observe unexpected behavior. Please pass your input's `attention_mask` to obtain reliable results.\n",
      "Setting `pad_token_id` to `eos_token_id`:50256 for open-end generation.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loaded model\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "The attention mask and the pad token id were not set. As a consequence, you may observe unexpected behavior. Please pass your input's `attention_mask` to obtain reliable results.\n",
      "Setting `pad_token_id` to `eos_token_id`:50256 for open-end generation.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Once upon a time there was a little girl named Lucy. She was three years old and loved to explore. One day, Lucy was walking in the park when she saw a big, red balloon. She was so excited and wanted to play with it.\n",
      "\n",
      "But then, a big, mean man came and said, \"That balloon is mine! You can't have it!\" Lucy was very sad and started to cry.\n",
      "\n",
      "The man said, \"I'm sorry, but I need the balloon for my work. You can have it if you want.\"\n",
      "\n",
      "Lucy was so happy and said, \"Yes please!\" She took the balloon and ran away.\n",
      "\n",
      "But then, the man said, \"Wait! I have an idea. Let's make a deal. If you can guess what I'm going to give you, then you can have the balloon.\"\n",
      "\n",
      "Lucy thought for a moment and then said, \"I guess I'll have to get the balloon.\"\n",
      "\n",
      "The man smiled and said, \"That's a good guess! Here you go.\"\n",
      "\n",
      "Lucy was so happy and thanked the man. She hugged the balloon and ran off to show her mom.\n",
      "\n",
      "The end.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import pyvene as pv\n",
    "\n",
    "# built-in helper to get tinystore\n",
    "_, tokenizer, tinystory = pv.create_gpt_neo()\n",
    "emb_happy = tinystory.transformer.wte(\n",
    "    torch.tensor(14628)) \n",
    "\n",
    "pv_tinystory = pv.IntervenableModel([{\n",
    "    \"layer\": l,\n",
    "    \"component\": \"mlp_output\",\n",
    "    \"intervention_type\": pv.AdditionIntervention\n",
    "    } for l in range(tinystory.config.num_layers)],\n",
    "    model=tinystory\n",
    ")\n",
    "# prompt and generate\n",
    "prompt = tokenizer(\n",
    "    \"Once upon a time there was\", return_tensors=\"pt\")\n",
    "_, intervened_story = pv_tinystory.generate(\n",
    "    tokenizer(\"Once upon a time there was\", return_tensors=\"pt\"),\n",
    "    source_representations=emb_happy*0.3, max_length=256\n",
    ")\n",
    "\n",
    "print(tokenizer.decode(\n",
    "    intervened_story[0], \n",
    "    skip_special_tokens=True\n",
    "))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26d25dc6",
   "metadata": {},
   "source": [
    "### Debiasing with Backpack LMs\n",
    "\n",
    "Models like [Backpack LMs](https://arxiv.org/pdf/2305.16765.pdf) are built with highly interpretable model components. In its original paper, one motivating experiment is using the sense vectors to debias. Here, we try to reproduce one of the experiments in Fig. 3 (pg. 8)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "841e5a5b",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "The argument `trust_remote_code` is to be used with Auto classes. It has no effect here and is ignored.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loaded model\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 400x200 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 200,
       "width": 400
      }
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 400x200 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 200,
       "width": 400
      }
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 400x200 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 200,
       "width": 400
      }
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import pandas as pd\n",
    "from plotnine import ggplot, aes, geom_bar, theme, element_text, labs\n",
    "\n",
    "import pyvene as pv\n",
    "_, tokenizer, backpack_gpt2 = pv.create_backpack_gpt2()\n",
    "\n",
    "class MultiplierIntervention(pv.ConstantSourceIntervention):\n",
    "    \"\"\"Multiplier intervention\"\"\"\n",
    "    \n",
    "    def __init__(self, multiplier, **kwargs):\n",
    "        super().__init__(**kwargs)\n",
    "        self.register_buffer('multiplier', torch.tensor(multiplier))\n",
    "        \n",
    "    def forward(self, base, source=None, subspaces=None):\n",
    "        return base * self.multiplier\n",
    "\n",
    "    def __str__(self):\n",
    "        return f\"MultiplierIntervention()\"\n",
    "\n",
    "for c in [0, 0.7, 1]:\n",
    "    pv_backpack_gpt2 = pv.IntervenableModel({\n",
    "        \"component\": \"sense_output\",\n",
    "        \"intervention\": MultiplierIntervention(c), \"unit\": \"h.pos\"}, \n",
    "        model=backpack_gpt2\n",
    "    )\n",
    "    base = tokenizer(\"When the nurse walked into the room,\", \n",
    "                     return_tensors=\"pt\", return_attention_mask=False)\n",
    "    intervened_outputs = pv_backpack_gpt2(\n",
    "        base,\n",
    "        unit_locations={\n",
    "            # use   pv.GET_LOC((nv, s))\n",
    "            \"base\": pv.GET_LOC((10,2))\n",
    "        }\n",
    "    )\n",
    "    \n",
    "    # plotting\n",
    "    probs = torch.nn.functional.softmax(\n",
    "        intervened_outputs[1].logits[0][-1], dim=0)\n",
    "    data = pv.top_vals(\n",
    "        tokenizer, probs, n=9,\n",
    "        return_results=True\n",
    "    )\n",
    "    df = pd.DataFrame(data, columns=['Word', 'Probability'])\n",
    "    df['Word'] = pd.Categorical(df['Word'], categories=[x[0] for x in data], ordered=True)\n",
    "    plot = (ggplot(df, aes(x='Word', y='Probability'))\n",
    "            + geom_bar(stat='identity')\n",
    "            + theme(axis_text_x=element_text(rotation=90, hjust=1),\n",
    "                    figure_size=(4, 2))\n",
    "            + labs(title=f\"mul({c})\")\n",
    "    )\n",
    "    print(plot)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb539f4b",
   "metadata": {},
   "source": [
    "### Saving and Loading\n",
    "This is one of the benefits of program abstraction. We abstract out the intervention and its schema, so we have a user friendly interface. Furthermore, it allows us to have a serializable configuration file that tells everything about your configuration.\n",
    "\n",
    "You can then save, share and load interventions easily. Note that you still need your access to the data, if you need to sample **Source** representations from other examples. But we think this is doable via a separate HuggingFace datasets upload. In the future, there could be an option of coupling this configuration with a specific remote dataset as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "272f3773",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loaded model\n",
      "Directory './tmp/' already exists.\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import pyvene as pv\n",
    "\n",
    "_, tokenizer, gpt2 = pv.create_gpt2()\n",
    "\n",
    "# run with new intervention type\n",
    "pv_gpt2 = pv.IntervenableModel({\n",
    "  \"intervention_type\": pv.ZeroIntervention}, \n",
    "  model=gpt2)\n",
    "\n",
    "pv_gpt2.save(\"./tmp/\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "50b894b4",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:root:The key is provided in the config. Assuming this is loaded from a pretrained module.\n",
      "WARNING:root:Loading trainable intervention from intkey_layer.0.repr.block_output.unit.pos.nunit.1#0.bin.\n"
     ]
    }
   ],
   "source": [
    "pv_gpt2 = pv.IntervenableModel.load(\n",
    "    \"./tmp/\",\n",
    "    model=gpt2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2d07ca8",
   "metadata": {},
   "source": [
    "### Multi-Source Interchange Intervention (Parallel Mode)\n",
    "\n",
    "What is multi-source? In the examples above, interventions are at most across two examples. We support interventions across many examples. You can sample representations from two inputs, and plut them into a single **Base**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "847410a8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loaded model\n",
      "_the                 0.07233363389968872\n",
      "_a                   0.05731499195098877\n",
      "_not                 0.04443885385990143\n",
      "_Italian             0.033642884343862534\n",
      "_often               0.024385808035731316\n",
      "_called              0.022171705961227417\n",
      "_known               0.017808808013796806\n",
      "_that                0.016059240326285362\n",
      "_\"                   0.012973357923328876\n",
      "_an                  0.012878881767392159\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import pyvene as pv\n",
    "\n",
    "_, tokenizer, gpt2 = pv.create_gpt2()\n",
    "\n",
    "parallel_config = pv.IntervenableConfig([\n",
    "  {\"layer\": 3, \"component\": \"block_output\"},\n",
    "  {\"layer\": 3, \"component\": \"block_output\"}],\n",
    "  # intervene on base at the same time\n",
    "  mode=\"parallel\")\n",
    "parallel_gpt2 = pv.IntervenableModel(\n",
    "  parallel_config, model=gpt2)\n",
    "base = tokenizer(\n",
    "  \"The capital of Spain is\", \n",
    "  return_tensors=\"pt\")\n",
    "sources = [\n",
    "  tokenizer(\"The language of Spain is\", \n",
    "    return_tensors=\"pt\"),\n",
    "  tokenizer(\"The capital of Italy is\", \n",
    "    return_tensors=\"pt\")]\n",
    "intervened_outputs = parallel_gpt2(\n",
    "    base, sources,\n",
    "    {\"sources->base\": (\n",
    "    # each list has a dimensionality of\n",
    "    # [num_intervention, batch, num_unit]\n",
    "    [[[1]],[[3]]],  [[[1]],[[3]]])}\n",
    ")\n",
    "\n",
    "distrib = pv.embed_to_distrib(\n",
    "    gpt2, intervened_outputs[1].last_hidden_state, logits=False)\n",
    "pv.top_vals(tokenizer, distrib[0][-1], n=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f93402c",
   "metadata": {},
   "source": [
    "### Multi-Source Interchange Intervention (Serial Mode)\n",
    "\n",
    "Or you can do them sequentially, where you intervene among your **Source** examples, and get some intermediate states before merging the activations into the **Base** run."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "5e5752dc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_the                 0.06737838685512543\n",
      "_a                   0.059834375977516174\n",
      "_not                 0.04629501700401306\n",
      "_Italian             0.03623826056718826\n",
      "_often               0.021700192242860794\n",
      "_called              0.01840786263346672\n",
      "_that                0.0157712884247303\n",
      "_known               0.014391838572919369\n",
      "_an                  0.013535155914723873\n",
      "_very                0.013022392988204956\n"
     ]
    }
   ],
   "source": [
    "config = pv.IntervenableConfig([\n",
    "  {\"layer\": 3, \"component\": \"block_output\"},\n",
    "  {\"layer\": 10, \"component\": \"block_output\"}],\n",
    "  # intervene on base one after another\n",
    "  mode=\"serial\")\n",
    "pv_gpt2 = pv.IntervenableModel(\n",
    "  config, model=gpt2)\n",
    "base = tokenizer(\n",
    "  \"The capital of Spain is\", \n",
    "  return_tensors=\"pt\")\n",
    "sources = [\n",
    "  tokenizer(\"The language of Spain is\", \n",
    "    return_tensors=\"pt\"),\n",
    "  tokenizer(\"The capital of Italy is\", \n",
    "    return_tensors=\"pt\")]\n",
    "\n",
    "intervened_outputs = pv_gpt2(\n",
    "    base, sources,\n",
    "    # intervene in serial at two positions\n",
    "    {\"source_0->source_1\": 1, \n",
    "     \"source_1->base\"    : 4})\n",
    "\n",
    "distrib = pv.embed_to_distrib(\n",
    "    gpt2, intervened_outputs[1].last_hidden_state, logits=False)\n",
    "pv.top_vals(tokenizer, distrib[0][-1], n=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28621880",
   "metadata": {},
   "source": [
    "### Multi-Source Interchange Intervention with Subspaces (Parallel Mode)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "773aba2e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loaded model\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import pyvene as pv\n",
    "\n",
    "_, tokenizer, gpt2 = pv.create_gpt2()\n",
    "\n",
    "config = pv.IntervenableConfig([\n",
    "    {\"layer\": 0, \"component\": \"block_output\",\n",
    "     \"subspace_partition\": \n",
    "         [[0, 128], [128, 256]]}]*2,\n",
    "    intervention_types=pv.VanillaIntervention,\n",
    "    # act in parallel\n",
    "    mode=\"parallel\"\n",
    ")\n",
    "pv_gpt2 = pv.IntervenableModel(config, model=gpt2)\n",
    "\n",
    "base = tokenizer(\"The capital of Spain is\", return_tensors=\"pt\")\n",
    "sources = [tokenizer(\"The capital of Italy is\", return_tensors=\"pt\"),\n",
    "          tokenizer(\"The capital of China is\", return_tensors=\"pt\")]\n",
    "\n",
    "intervened_outputs = pv_gpt2(\n",
    "    base, sources,\n",
    "    # on same position\n",
    "    {\"sources->base\": 4},\n",
    "    # on different subspaces\n",
    "    subspaces=[[[0]], [[1]]],\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7223603f",
   "metadata": {},
   "source": [
    "### Multi-Source Interchange Intervention with Subspaces (Serial Mode)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "305e0607",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loaded model\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import pyvene as pv\n",
    "\n",
    "_, tokenizer, gpt2 = pv.create_gpt2()\n",
    "\n",
    "config = pv.IntervenableConfig([\n",
    "    {\"layer\": 0, \"component\": \"block_output\",\n",
    "     \"subspace_partition\": [[0, 128], [128, 256]]},\n",
    "    {\"layer\": 2, \"component\": \"block_output\",\n",
    "     \"subspace_partition\": [[0, 128], [128, 256]]}],\n",
    "    intervention_types=pv.VanillaIntervention,\n",
    "    # act in parallel\n",
    "    mode=\"serial\"\n",
    ")\n",
    "pv_gpt2 = pv.IntervenableModel(config, model=gpt2)\n",
    "\n",
    "base = tokenizer(\"The capital of Spain is\", return_tensors=\"pt\")\n",
    "sources = [tokenizer(\"The capital of Italy is\", return_tensors=\"pt\"),\n",
    "          tokenizer(\"The capital of China is\", return_tensors=\"pt\")]\n",
    "\n",
    "intervened_outputs = pv_gpt2(\n",
    "    base, sources,\n",
    "    # serialized intervention\n",
    "    # order is based on sources list\n",
    "    {\"source_0->source_1\": 3, \"source_1->base\": 4},\n",
    "    # on different subspaces\n",
    "    subspaces=[[[0]], [[1]]],\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b5fcb37",
   "metadata": {},
   "source": [
    "### Interchange Intervention Training (IIT)\n",
    "Interchange intervention training (IIT) is a technique of inducing causal structures into neural models. This library naturally supports this. By training IIT, you can simply turn the gradient on for the wrapping model. In this way, your model can be trained with your interventional signals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "8c7dde89",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loaded model\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import pyvene as pv\n",
    "\n",
    "_, tokenizer, gpt2 = pv.create_gpt2()\n",
    "\n",
    "pv_gpt2 = pv.IntervenableModel({\n",
    "    \"layer\": 8}, \n",
    "    model=gpt2\n",
    ")\n",
    "\n",
    "pv_gpt2.enable_model_gradients()\n",
    "# run counterfactual forward as usual"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8c7ccad",
   "metadata": {},
   "source": [
    "## pyvene 102\n",
    "Now, you are pretty familiar with pyvene basic APIs. There are more to come. We support all sorts of weird interventions, and we encapsulate them as objects so that, even they are super weird (e.g., nested, multiple locations, different types), you can share them easily with others. BTW, if the intervention is trainable, the artifacts will be saved and shared as well.\n",
    "\n",
    "With that, here are a couple of additional APIs.\n",
    "\n",
    "### Grouping\n",
    "\n",
    "You can group interventions together so that they always receive the same input when you want to use them to get activations at different places. Here is an example, where you are taking in the same **Source** example, you fetch activations twice: once in position 3 and layer 0, once in position 4 and layer 2. You don't have to pass in another dummy **Source**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "84afd62c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loaded model\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import pyvene as pv\n",
    "\n",
    "_, tokenizer, gpt2 = pv.create_gpt2()\n",
    "\n",
    "config = pv.IntervenableConfig([\n",
    "    {\"layer\": 0, \"component\": \"block_output\", \"group_key\": 0},\n",
    "    {\"layer\": 2, \"component\": \"block_output\", \"group_key\": 0}],\n",
    "    intervention_types=pv.VanillaIntervention,\n",
    ")\n",
    "\n",
    "pv_gpt2 = pv.IntervenableModel(config, model=gpt2)\n",
    "\n",
    "base = tokenizer(\"The capital of Spain is\", return_tensors=\"pt\")\n",
    "sources = [tokenizer(\"The capital of Italy is\", return_tensors=\"pt\")]\n",
    "intervened_outputs = pv_gpt2(\n",
    "    base, sources, \n",
    "    {\"sources->base\": ([\n",
    "        [[3]], [[4]] # these two are for two interventions\n",
    "    ], [             # source position 3 into base position 4\n",
    "        [[3]], [[4]] \n",
    "    ])}\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34aeb892",
   "metadata": {},
   "source": [
    "### Intervention Skipping in Runtime\n",
    "You may configure a lot of interventions, but during training, not every example will have to use all of them. So, you can skip interventions for different examples differently."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "61cd8fc9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loaded model\n",
      "True True\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import pyvene as pv\n",
    "\n",
    "_, tokenizer, gpt2 = pv.create_gpt2()\n",
    "\n",
    "config = pv.IntervenableConfig([\n",
    "    # these are equivalent interventions\n",
    "    # we create them on purpose\n",
    "    {\"layer\": 0, \"component\": \"block_output\"},\n",
    "    {\"layer\": 0, \"component\": \"block_output\"},\n",
    "    {\"layer\": 0, \"component\": \"block_output\"}],\n",
    "    intervention_types=pv.VanillaIntervention,\n",
    ")\n",
    "pv_gpt2 = pv.IntervenableModel(config, model=gpt2)\n",
    "\n",
    "base = tokenizer(\"The capital of Spain is\", return_tensors=\"pt\")\n",
    "source = tokenizer(\"The capital of Italy is\", return_tensors=\"pt\")\n",
    "# skipping 1, 2 and 3\n",
    "_, pv_out1 = pv_gpt2(base, [None, None, source],\n",
    "    {\"sources->base\": ([None, None, [[4]]], [None, None, [[4]]])})\n",
    "_, pv_out2 = pv_gpt2(base, [None, source, None],\n",
    "    {\"sources->base\": ([None, [[4]], None], [None, [[4]], None])})\n",
    "_, pv_out3 = pv_gpt2(base, [source, None, None],\n",
    "    {\"sources->base\": ([[[4]], None, None], [[[4]], None, None])})\n",
    "# should have the same results\n",
    "print(\n",
    "    torch.equal(pv_out1.last_hidden_state, pv_out2.last_hidden_state),\n",
    "    torch.equal(pv_out2.last_hidden_state, pv_out3.last_hidden_state)\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d9df6acd",
   "metadata": {},
   "source": [
    "### Subspace Partition\n",
    "You can partition your subspace before hand. If you don't, the library assumes you each neuron is in its own subspace. In this example, you partition your subspace into two continous chunk, `[0, 128), [128,256)`, which means all the neurons from index 0 upto 127 are along to partition 1. During runtime, you can intervene on all the neurons in the same parition together."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "3a66bbeb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loaded model\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import pyvene as pv\n",
    "\n",
    "_, tokenizer, gpt2 = pv.create_gpt2()\n",
    "\n",
    "config = pv.IntervenableConfig([\n",
    "    # they are linked to manipulate the same representation\n",
    "    # but in different subspaces\n",
    "    {\"layer\": 0, \"component\": \"block_output\",\n",
    "     # subspaces can be partitioned into continuous chunks\n",
    "     # [i, j] are the boundary indices\n",
    "     \"subspace_partition\": [[0, 128], [128, 256]]}],\n",
    "    intervention_types=pv.VanillaIntervention,\n",
    ")\n",
    "pv_gpt2 = pv.IntervenableModel(config, model=gpt2)\n",
    "\n",
    "base = tokenizer(\"The capital of Spain is\", return_tensors=\"pt\")\n",
    "source = tokenizer(\"The capital of Italy is\", return_tensors=\"pt\")\n",
    "\n",
    "# using intervention skipping for subspace\n",
    "intervened_outputs = pv_gpt2(\n",
    "    base, [source],\n",
    "    {\"sources->base\": 4},\n",
    "    # intervene only only dimensions from 128 to 256\n",
    "    subspaces=1,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0fdde257",
   "metadata": {},
   "source": [
    "### Intervention Linking\n",
    "Interventions can be linked to share weights and share subspaces. Here is an example of how to link interventions together. If interventions are trainable, then their weights are tied as well.\n",
    "\n",
    "Why this is useful? it is because sometimes, you may want to intervene on different subspaces differently. Say you have a representation in a size of 512, and you hypothesize the first half represents A, and the second half represents B, you can then use the subspace intervention to test it out. With trainable interventions, you can also optimize your interventions on the same representation yet with different subspaces."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "eec19da9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loaded model\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import pyvene as pv\n",
    "\n",
    "_, tokenizer, gpt2 = pv.create_gpt2()\n",
    "\n",
    "config = pv.IntervenableConfig([\n",
    "    # they are linked to manipulate the same representation\n",
    "    # but in different subspaces\n",
    "    {\"layer\": 0, \"component\": \"block_output\", \n",
    "     \"subspace_partition\": [[0, 128], [128, 256]], \"intervention_link_key\": 0},\n",
    "    {\"layer\": 0, \"component\": \"block_output\",\n",
    "     \"subspace_partition\": [[0, 128], [128, 256]], \"intervention_link_key\": 0}],\n",
    "    intervention_types=pv.VanillaIntervention,\n",
    ")\n",
    "pv_gpt2 = pv.IntervenableModel(config, model=gpt2)\n",
    "\n",
    "base = tokenizer(\"The capital of Spain is\", return_tensors=\"pt\")\n",
    "source = tokenizer(\"The capital of Italy is\", return_tensors=\"pt\")\n",
    "\n",
    "# using intervention skipping for subspace\n",
    "_, pv_out1 = pv_gpt2(\n",
    "    base, [None, source],\n",
    "    # 4 means token position 4\n",
    "    {\"sources->base\": ([None, [[4]]], [None, [[4]]])},\n",
    "    # 1 means the second partition in the config\n",
    "    subspaces=[None, [[1]]],\n",
    ")\n",
    "_, pv_out2 = pv_gpt2(\n",
    "    base,\n",
    "    [source, None],\n",
    "    {\"sources->base\": ([[[4]], None], [[[4]], None])},\n",
    "    subspaces=[[[1]], None],\n",
    ")\n",
    "print(torch.equal(pv_out1.last_hidden_state, pv_out2.last_hidden_state))\n",
    "\n",
    "# subspaces provide a list of index and they can be in any order\n",
    "_, pv_out3 = pv_gpt2(\n",
    "    base,\n",
    "    [source, source],\n",
    "    {\"sources->base\": ([[[4]], [[4]]], [[[4]], [[4]]])},\n",
    "    subspaces=[[[0]], [[1]]],\n",
    ")\n",
    "_, pv_out4 = pv_gpt2(\n",
    "    base,\n",
    "    [source, source],\n",
    "    {\"sources->base\": ([[[4]], [[4]]], [[[4]], [[4]]])},\n",
    "    subspaces=[[[1]], [[0]]],\n",
    ")\n",
    "print(torch.equal(pv_out3.last_hidden_state, pv_out4.last_hidden_state))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef5b7a3e",
   "metadata": {},
   "source": [
    "### Add New Model Type"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "acce6e8f",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Special tokens have been added in the vocabulary, make sure the associated word embeddings are fine-tuned or trained.\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import pyvene as pv\n",
    "\n",
    "# get a flan-t5 from HuggingFace\n",
    "from transformers import T5ForConditionalGeneration, T5Tokenizer, T5Config\n",
    "config = T5Config.from_pretrained(\"google/flan-t5-small\")\n",
    "tokenizer = T5Tokenizer.from_pretrained(\"google/flan-t5-small\")\n",
    "t5 = T5ForConditionalGeneration.from_pretrained(\n",
    "    \"google/flan-t5-small\", config=config\n",
    ")\n",
    "\n",
    "# config the intervention mapping with pv global vars\n",
    "\"\"\"Only define for the block output here for simplicity\"\"\"\n",
    "pv.type_to_module_mapping[type(t5)] = {\n",
    "    \"mlp_output\": (\"encoder.block[%s].layer[1]\", \n",
    "                   pv.models.constants.CONST_OUTPUT_HOOK),\n",
    "    \"attention_input\": (\"encoder.block[%s].layer[0]\", \n",
    "                        pv.models.constants.CONST_OUTPUT_HOOK),\n",
    "}\n",
    "pv.type_to_dimension_mapping[type(t5)] = {\n",
    "    \"mlp_output\": (\"d_model\",),\n",
    "    \"attention_input\": (\"d_model\",),\n",
    "    \"block_output\": (\"d_model\",),\n",
    "    \"head_attention_value_output\": (\"d_model/num_heads\",),\n",
    "}\n",
    "\n",
    "# wrap as gpt2\n",
    "pv_t5 = pv.IntervenableModel({\n",
    "    \"layer\": 0,\n",
    "    \"component\": \"mlp_output\",\n",
    "    \"source_representation\": torch.zeros(\n",
    "        t5.config.d_model)\n",
    "}, model=t5)\n",
    "\n",
    "# then intervene!\n",
    "base = tokenizer(\"The capital of Spain is\", \n",
    "                 return_tensors=\"pt\")\n",
    "decoder_input_ids = tokenizer(\n",
    "    \"\", return_tensors=\"pt\").input_ids\n",
    "base[\"decoder_input_ids\"] = decoder_input_ids\n",
    "intervened_outputs = pv_t5(\n",
    "    base, \n",
    "    unit_locations={\"base\": 3}\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba158a92",
   "metadata": {},
   "source": [
    "### Composing Complex Intervention Schema: Path Patching"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e51cadfe",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loaded model\n",
      "Directory './tmp/' already exists.\n"
     ]
    }
   ],
   "source": [
    "import pyvene as pv\n",
    "\n",
    "def path_patching_config(\n",
    "    layer, last_layer, \n",
    "    component=\"head_attention_value_output\", unit=\"h.pos\"\n",
    "):\n",
    "    intervening_component = [\n",
    "        {\"layer\": layer, \"component\": component, \"unit\": unit, \"group_key\": 0}]\n",
    "    restoring_components = []\n",
    "    if not component.startswith(\"mlp_\"):\n",
    "        restoring_components += [\n",
    "            {\"layer\": layer, \"component\": \"mlp_output\", \"group_key\": 1}]\n",
    "    for i in range(layer+1, last_layer):\n",
    "        restoring_components += [\n",
    "            {\"layer\": i, \"component\": \"attention_output\", \"group_key\": 1},\n",
    "            {\"layer\": i, \"component\": \"mlp_output\", \"group_key\": 1}\n",
    "        ]\n",
    "    intervenable_config = pv.IntervenableConfig(\n",
    "        intervening_component + restoring_components)\n",
    "    return intervenable_config\n",
    "\n",
    "_, tokenizer, gpt2 = pv.create_gpt2()\n",
    "\n",
    "pv_gpt2 = pv.IntervenableModel(\n",
    "    path_patching_config(4, gpt2.config.n_layer), \n",
    "    model=gpt2\n",
    ")\n",
    "\n",
    "pv_gpt2.save(\n",
    "    save_directory=\"./tmp/\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "9074f716",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:root:The key is provided in the config. Assuming this is loaded from a pretrained module.\n"
     ]
    }
   ],
   "source": [
    "pv_gpt2 = pv.IntervenableModel.load(\n",
    "    \"./tmp/\",\n",
    "    model=gpt2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d546e858",
   "metadata": {},
   "source": [
    "### Composing Complex Intervention Schema: Causal Tracing in 15 lines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c0b6a70f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loaded model\n"
     ]
    }
   ],
   "source": [
    "import pyvene as pv\n",
    "\n",
    "def causal_tracing_config(\n",
    "  l, c=\"mlp_activation\", w=10, tl=48):\n",
    "  s = max(0, l - w // 2)\n",
    "  e = min(tl, l - (-w // 2))\n",
    "  config = pv.IntervenableConfig(\n",
    "    [{\"component\": \"block_input\"}] + \n",
    "    [{\"layer\": l, \"component\": c} \n",
    "      for l in range(s, e)],\n",
    "    [pv.NoiseIntervention] +\n",
    "    [pv.VanillaIntervention]*(e-s))\n",
    "  return config\n",
    "\n",
    "_, tokenizer, gpt2 = pv.create_gpt2()\n",
    "\n",
    "pv_gpt2 = pv.IntervenableModel(\n",
    "    causal_tracing_config(4), \n",
    "    model=gpt2\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc6eb49d",
   "metadata": {},
   "source": [
    "### The End\n",
    "Now you are graduating from pyvene 101! Feel free to take a look at our tutorials for more challenging interventions."
   ]
  }
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