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": 97
   },
   "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": 63
   },
   "outputs": [],
   "source": [
    "model_name = \"./models/gpt2\"\n",
    "tokenizer = AutoTokenizer.from_pretrained(model_name)\n",
    "model = AutoModelForCausalLM.from_pretrained(model_name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1979c8b4",
   "metadata": {
    "height": 29
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GPT2TokenizerFast(name_or_path='./models/gpt2', vocab_size=50257, model_max_length=1024, is_fast=True, padding_side='right', truncation_side='right', special_tokens={'bos_token': '<|endoftext|>', 'eos_token': '<|endoftext|>', 'unk_token': '<|endoftext|>'}, clean_up_tokenization_spaces=True),  added_tokens_decoder={\n",
       "\t50256: AddedToken(\"<|endoftext|>\", rstrip=False, lstrip=False, single_word=False, normalized=True, special=True),\n",
       "}"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tokenizer"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "82ce24db-94ce-4272-9e30-7d3b2b8ff595",
   "metadata": {},
   "source": [
    "- Examine the model's architecture"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b2412d3e-7ee2-4362-adb2-2f434d6f2416",
   "metadata": {
    "height": 29
   },
   "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": 5,
   "id": "c94d8b4b-13ea-42ad-917b-54974c9cdbd0",
   "metadata": {
    "height": 63
   },
   "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": 5,
     "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": 6,
   "id": "794b0abd-1940-4cb7-902e-9f9d83ec52bd",
   "metadata": {
    "height": 97
   },
   "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": 8,
   "id": "58ae92b3-200e-470b-b107-559ee4b4e503",
   "metadata": {
    "height": 63
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(13990)"
      ]
     },
     "execution_count": 8,
     "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": 11,
   "id": "82e856ac-805b-4e47-b0e6-aca4580923be",
   "metadata": {
    "height": 29
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "' fence'"
      ]
     },
     "execution_count": 11,
     "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": 12,
   "id": "2151f087",
   "metadata": {
    "height": 46
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.return_types.topk(\n",
       "values=tensor([-81.8955, -82.3976, -82.9707, -83.0715, -83.2480, -83.5198, -83.5478,\n",
       "        -83.8078, -83.8791, -83.8842]),\n",
       "indices=tensor([13990,  5743, 47590,  3355,  3084,  5509,  1353,  3753,  2323,  1735]))"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "top_k = torch.topk(last_logits, k=10)\n",
    "top_k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "5dc39fa7-57c9-4ad2-a18f-58e64f380f9a",
   "metadata": {
    "height": 63
   },
   "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": 13,
     "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": 14,
   "id": "f8aabe35-efbe-439c-9284-1407fc0b2cab",
   "metadata": {
    "height": 182
   },
   "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": 15,
   "id": "449af38e-14b8-4f5d-a972-db44f94000b1",
   "metadata": {
    "height": 80
   },
   "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": 16,
   "id": "0a4605d3-1506-4b80-a6b9-b2e8d5ccea72",
   "metadata": {
    "height": 148
   },
   "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": 19,
   "id": "e8312f1a-9a24-4206-8878-022a4db7d5ed",
   "metadata": {
    "height": 398
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.9120535850524902 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": 20,
   "id": "ec841dd0-5be5-4da7-9a03-4af11449204e",
   "metadata": {
    "height": 46
   },
   "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": 21,
   "id": "a3f6fab4-c3ca-4efa-9533-2915667e5058",
   "metadata": {
    "height": 148
   },
   "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": 22,
   "id": "98bb1897",
   "metadata": {
    "height": 386
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.8596978187561035 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": 23,
   "id": "ba249a24-42b0-4ce6-881c-00b1dcbb4212",
   "metadata": {
    "height": 63
   },
   "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()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5a261610",
   "metadata": {
    "height": 29
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d4953dcd",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}