Lesson_1-Text_Generation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "0b850cd9",
   "metadata": {},
   "source": [
    "# Lesson 1 - Text Generation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "130b83d4",
   "metadata": {},
   "source": [
    "Welcome to Lesson 1.\n",
    "\n",
    "To access the `requirements.txt` file, go to `File` and click on `Open`.\n",
    "\n",
    "In this lesson, we'll cover the following:\n",
    "\n",
    "1. How to load an LLM from HuggingFace?\n",
    "2. How to generate a token from the model output tensors?\n",
    "3. Prefill and decode: optimizing token generation over multiple steps\n",
    "\n",
    "I hope you enjoy this course!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "355d0908-936e-411e-b7ab-0bad3c0d8bba",
   "metadata": {},
   "source": [
    "### Import required packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d63d6a13-d807-4287-ac43-82c1a760a963",
   "metadata": {
    "height": 99
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import time\n",
    "import torch\n",
    "from transformers import AutoModelForCausalLM, AutoTokenizer"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c49df59a",
   "metadata": {},
   "source": [
    "## 1. How to load an LLM from HuggingFace?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6df7749b-2596-460a-b5d6-69f57dd804f4",
   "metadata": {},
   "source": [
    "- Load the LLM\n",
    "- You'll use GPT2 throughout this course"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "921474e8-e424-4a59-8a3c-bcea49690133",
   "metadata": {
    "height": 65
   },
   "outputs": [],
   "source": [
    "model_name = \"./models/gpt2\"\n",
    "tokenizer = AutoTokenizer.from_pretrained(model_name)\n",
    "model = AutoModelForCausalLM.from_pretrained(model_name)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "82ce24db-94ce-4272-9e30-7d3b2b8ff595",
   "metadata": {},
   "source": [
    "- Examine the model's architecture"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b2412d3e-7ee2-4362-adb2-2f434d6f2416",
   "metadata": {
    "height": 31
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GPT2LMHeadModel(\n",
      "  (transformer): GPT2Model(\n",
      "    (wte): Embedding(50257, 768)\n",
      "    (wpe): Embedding(1024, 768)\n",
      "    (drop): Dropout(p=0.1, inplace=False)\n",
      "    (h): ModuleList(\n",
      "      (0-11): 12 x GPT2Block(\n",
      "        (ln_1): LayerNorm((768,), eps=1e-05, elementwise_affine=True)\n",
      "        (attn): GPT2Attention(\n",
      "          (c_attn): Conv1D()\n",
      "          (c_proj): Conv1D()\n",
      "          (attn_dropout): Dropout(p=0.1, inplace=False)\n",
      "          (resid_dropout): Dropout(p=0.1, inplace=False)\n",
      "        )\n",
      "        (ln_2): LayerNorm((768,), eps=1e-05, elementwise_affine=True)\n",
      "        (mlp): GPT2MLP(\n",
      "          (c_fc): Conv1D()\n",
      "          (c_proj): Conv1D()\n",
      "          (act): NewGELUActivation()\n",
      "          (dropout): Dropout(p=0.1, inplace=False)\n",
      "        )\n",
      "      )\n",
      "    )\n",
      "    (ln_f): LayerNorm((768,), eps=1e-05, elementwise_affine=True)\n",
      "  )\n",
      "  (lm_head): Linear(in_features=768, out_features=50257, bias=False)\n",
      ")\n"
     ]
    }
   ],
   "source": [
    "print(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64648331-8f55-4150-929e-4e7a3a76e305",
   "metadata": {},
   "source": [
    "## 2. How to generate a token from the model output tensors?\n",
    "\n",
    "### Text Generation\n",
    "- Start by tokenizing the input prompt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c94d8b4b-13ea-42ad-917b-54974c9cdbd0",
   "metadata": {
    "height": 65
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'input_ids': tensor([[  464,  2068,  7586, 21831, 11687,   625,   262]]), 'attention_mask': tensor([[1, 1, 1, 1, 1, 1, 1]])}"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prompt = \"The quick brown fox jumped over the\"\n",
    "inputs = tokenizer(prompt, return_tensors=\"pt\")\n",
    "inputs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae14eb9a-2371-4705-ab95-f9c98a4b703c",
   "metadata": {},
   "source": [
    "- Pass the inputs to the model and retrieve the logits to find the most likely next token"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "794b0abd-1940-4cb7-902e-9f9d83ec52bd",
   "metadata": {
    "height": 99
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([1, 7, 50257])\n"
     ]
    }
   ],
   "source": [
    "with torch.no_grad():\n",
    "    outputs = model(**inputs)\n",
    "\n",
    "logits = outputs.logits\n",
    "print(logits.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "58ae92b3-200e-470b-b107-559ee4b4e503",
   "metadata": {
    "height": 65
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(13990)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "last_logits = logits[0, -1, :]\n",
    "next_token_id = last_logits.argmax()\n",
    "next_token_id"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "36f5728d-b607-448c-a4cc-9b9239c99134",
   "metadata": {},
   "source": [
    "- Decode the most likely token"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "82e856ac-805b-4e47-b0e6-aca4580923be",
   "metadata": {
    "height": 31
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "' fence'"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tokenizer.decode(next_token_id)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "924cda2a-8b7c-480f-9c7b-6d19c1630765",
   "metadata": {},
   "source": [
    "- Print the 10 most likely next words"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "5dc39fa7-57c9-4ad2-a18f-58e64f380f9a",
   "metadata": {
    "height": 65
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[' fence',\n",
       " ' edge',\n",
       " ' railing',\n",
       " ' wall',\n",
       " ' table',\n",
       " ' tree',\n",
       " ' top',\n",
       " ' counter',\n",
       " ' ground',\n",
       " ' side']"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "top_k = torch.topk(last_logits, k=10)\n",
    "tokens = [tokenizer.decode(tk) for tk in top_k.indices]\n",
    "tokens"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8991969-6a3e-487b-abb9-5381e7bfbcd4",
   "metadata": {},
   "source": [
    "- Concatenate the input and most likely tokens"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "f8aabe35-efbe-439c-9284-1407fc0b2cab",
   "metadata": {
    "height": 184
   },
   "outputs": [],
   "source": [
    "next_inputs = {\n",
    "    \"input_ids\": torch.cat(\n",
    "        [inputs[\"input_ids\"], next_token_id.reshape((1, 1))],\n",
    "        dim=1\n",
    "    ),\n",
    "    \"attention_mask\": torch.cat(\n",
    "        [inputs[\"attention_mask\"], torch.tensor([[1]])],\n",
    "        dim=1\n",
    "    ),\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "449af38e-14b8-4f5d-a972-db44f94000b1",
   "metadata": {
    "height": 82
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[  464,  2068,  7586, 21831, 11687,   625,   262, 13990]]) torch.Size([1, 8])\n",
      "tensor([[1, 1, 1, 1, 1, 1, 1, 1]]) torch.Size([1, 8])\n"
     ]
    }
   ],
   "source": [
    "print(next_inputs[\"input_ids\"],\n",
    "      next_inputs[\"input_ids\"].shape)\n",
    "print(next_inputs[\"attention_mask\"],\n",
    "      next_inputs[\"attention_mask\"].shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c74fb045",
   "metadata": {},
   "source": [
    "## 3. Prefill and decode: optimizing token generation over multiple steps"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3681d8a1-4e14-4d99-9f78-f122c5fc86ad",
   "metadata": {},
   "source": [
    "### Text generation helper function\n",
    "- The following helper function generates the next tokens given a set of input tokens"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "0a4605d3-1506-4b80-a6b9-b2e8d5ccea72",
   "metadata": {
    "height": 150
   },
   "outputs": [],
   "source": [
    "def generate_token(inputs):\n",
    "    with torch.no_grad():\n",
    "        outputs = model(**inputs)\n",
    "\n",
    "    logits = outputs.logits\n",
    "    last_logits = logits[0, -1, :]\n",
    "    next_token_id = last_logits.argmax()\n",
    "    return next_token_id"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f65c82bc-e667-41b5-b0b5-b1a222b22cf0",
   "metadata": {},
   "source": [
    "- Use the helper function to generate multiple tokens in a loop\n",
    "- Track the time it takes to generate each token"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "e8312f1a-9a24-4206-8878-022a4db7d5ed",
   "metadata": {
    "height": 406
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.7073488235473633 s\n",
      "[' fence', ' and', ' ran', ' to', ' the', ' other', ' side', ' of', ' the', ' fence']\n"
     ]
    }
   ],
   "source": [
    "generated_tokens = []\n",
    "next_inputs = inputs\n",
    "durations_s = []\n",
    "for _ in range(10):\n",
    "    t0 = time.time()\n",
    "    next_token_id = generate_token(next_inputs)\n",
    "    durations_s += [time.time() - t0]\n",
    "    \n",
    "    next_inputs = {\n",
    "        \"input_ids\": torch.cat(\n",
    "            [next_inputs[\"input_ids\"], next_token_id.reshape((1, 1))],\n",
    "            dim=1),\n",
    "        \"attention_mask\": torch.cat(\n",
    "            [next_inputs[\"attention_mask\"], torch.tensor([[1]])],\n",
    "            dim=1),\n",
    "    }\n",
    "    \n",
    "    next_token = tokenizer.decode(next_token_id)\n",
    "    generated_tokens.append(next_token)\n",
    "\n",
    "print(f\"{sum(durations_s)} s\")\n",
    "print(generated_tokens)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e42e3ef-b906-4380-b44e-9aa10ea5da34",
   "metadata": {},
   "source": [
    "- Plot token generation time\n",
    "- The x-axis here is the token number\n",
    "- The y-axis is the time to generate a token in millisenconds (ms)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40d97f7b",
   "metadata": {},
   "source": [
    "**Note**: Your plot may vary slightly from the one shown in the video, yet it will exhibit a similar pattern."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "ec841dd0-5be5-4da7-9a03-4af11449204e",
   "metadata": {
    "height": 48
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(durations_s)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "112221a8-0172-43a8-a6b8-b1fd6aa0fae1",
   "metadata": {},
   "source": [
    "### Speeding up text generation with KV-caching\n",
    "KV-caching is a technique to speed up token generation by storing some of the tensors in the attention head for use in subsequent generation steps\n",
    "- Modify the generate helper function to return the next token and the key/value tensors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "a3f6fab4-c3ca-4efa-9533-2915667e5058",
   "metadata": {
    "height": 150
   },
   "outputs": [],
   "source": [
    "def generate_token_with_past(inputs):\n",
    "    with torch.no_grad():\n",
    "        outputs = model(**inputs)\n",
    "\n",
    "    logits = outputs.logits\n",
    "    last_logits = logits[0, -1, :]\n",
    "    next_token_id = last_logits.argmax()\n",
    "    return next_token_id, outputs.past_key_values"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae66de3f-2b2b-47fd-bc0a-ad1aac807cb8",
   "metadata": {},
   "source": [
    "- Generate 10 tokens using the updated helper function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "98bb1897",
   "metadata": {
    "height": 388
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.0315096378326416 s\n",
      "[' fence', ' and', ' ran', ' to', ' the', ' other', ' side', ' of', ' the', ' fence']\n"
     ]
    }
   ],
   "source": [
    "generated_tokens = []\n",
    "next_inputs = inputs\n",
    "durations_cached_s = []\n",
    "for _ in range(10):\n",
    "    t0 = time.time()\n",
    "    next_token_id, past_key_values = \\\n",
    "        generate_token_with_past(next_inputs)\n",
    "    durations_cached_s += [time.time() - t0]\n",
    "    \n",
    "    next_inputs = {\n",
    "        \"input_ids\": next_token_id.reshape((1, 1)),\n",
    "        \"attention_mask\": torch.cat(\n",
    "            [next_inputs[\"attention_mask\"], torch.tensor([[1]])],\n",
    "            dim=1),\n",
    "        \"past_key_values\": past_key_values,\n",
    "    }\n",
    "    \n",
    "    next_token = tokenizer.decode(next_token_id)\n",
    "    generated_tokens.append(next_token)\n",
    "\n",
    "print(f\"{sum(durations_cached_s)} s\")\n",
    "print(generated_tokens)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8ea5ded-ad4a-42c2-beb8-5cbf5ab9c4e2",
   "metadata": {},
   "source": [
    "- Compare the execution time for the KV-cache function with the original helper function"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a632eaf9",
   "metadata": {},
   "source": [
    "**Note**: Your plot may vary slightly from the one shown in the video, yet it will exhibit a similar pattern."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "ba249a24-42b0-4ce6-881c-00b1dcbb4212",
   "metadata": {
    "height": 65
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(durations_s)\n",
    "plt.plot(durations_cached_s)\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.11.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}