notebook.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "rjOyf_-ooJPC"
   },
   "source": [
    "# Linformer: Self-Attention with Linear Complexity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "1EskTRo2oJPE"
   },
   "source": [
    "*Maxence Lasbordes, Jacques Maubert, Stanislas Boiton*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "YouVl3NwoJPE"
   },
   "source": [
    "### Introduction:\n",
    "\n",
    "Implementation of the Linformer self-attention and a vanilla transformer. Comparison of inference speed between the two models across various sequence lengths and projection dimensions.\n",
    "Analysis of the hypothesis : Context mapping matrix is low rank."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "9EdRjaE0dt-0"
   },
   "outputs": [],
   "source": [
    "import re\n",
    "import time\n",
    "import torch\n",
    "import unicodedata\n",
    "from torch import nn\n",
    "import torch.nn.functional as F\n",
    "from tqdm.notebook import tqdm\n",
    "from torch.utils.data import DataLoader\n",
    "from typing import List, Optional\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "nq7W3niQoJPF"
   },
   "source": [
    "### Vanilla Transformer layers (besides Selft-Attention)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "id": "13bkeC7UpDpx"
   },
   "outputs": [],
   "source": [
    "class Embeddings(nn.Module):\n",
    "    def __init__(self, vocab_size, d):\n",
    "        super().__init__()\n",
    "        embeddings = 0.02 * torch.randn(vocab_size, d)\n",
    "        self.embeddings = nn.Parameter(embeddings)\n",
    "\n",
    "    def forward(self, x):\n",
    "        return self.embeddings[x]\n",
    "\n",
    "\n",
    "class Linear(nn.Module):\n",
    "    def __init__(self, d_in, d_out, bias=True):\n",
    "        super().__init__()\n",
    "        self.matrix = nn.Parameter(0.02 * torch.randn(d_in, d_out))\n",
    "        if bias:\n",
    "            self.bias = nn.Parameter(0.02 * torch.randn(d_out))\n",
    "\n",
    "    def forward(self, x):\n",
    "        results = x @ self.matrix\n",
    "        if hasattr(self, \"bias\"):\n",
    "            results += self.bias\n",
    "        return results\n",
    "\n",
    "def ReLU(x):\n",
    "    return x * (x > 0)\n",
    "\n",
    "\n",
    "class FeedForward(nn.Module):\n",
    "    def __init__(self, d_embed, d_ff, dropout=0.1):\n",
    "        super().__init__()\n",
    "        self.w1 = Linear(d_embed, d_ff)  # usually d_ff >> d_embed\n",
    "        self.w2 = Linear(d_ff, d_embed)\n",
    "        self.act_fn = ReLU\n",
    "        self.dropout = dropout\n",
    "\n",
    "    def forward(self, x):\n",
    "        z = self.w1(x)\n",
    "        z = self.act_fn(z)\n",
    "        z = F.dropout(z, p=self.dropout)\n",
    "        z = self.w2(z)\n",
    "        return z\n",
    "\n",
    "\n",
    "class LayerNorm(nn.Module):\n",
    "    def __init__(self, d, eps=1e-6):\n",
    "        super().__init__()\n",
    "        self.eps = eps\n",
    "        self.gamma = nn.Parameter(torch.ones(d))\n",
    "        self.beta = nn.Parameter(torch.zeros(d))\n",
    "\n",
    "    def forward(self, x):\n",
    "        mean = x.mean(dim=-1, keepdim=True)\n",
    "        std = x.std(dim=-1, keepdim=True)\n",
    "        return self.gamma * (x - mean) / (std + self.eps) + self.beta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "x9nERdRAdt-8"
   },
   "source": [
    "### Linformer Architecture (Self-Attention)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "id": "oTl7_Ws5Azyz"
   },
   "outputs": [],
   "source": [
    "class LinformerMHA(nn.Module):\n",
    "    def __init__(self, d_embed, n_heads, d_proj, max_length):\n",
    "        super().__init__()\n",
    "        self.d_proj = d_proj\n",
    "        self.q_proj = nn.Linear(d_embed, d_embed, bias=False)\n",
    "        self.k_proj = nn.Linear(d_embed, d_embed, bias=False)\n",
    "        self.v_proj = nn.Linear(d_embed, d_embed, bias=False)\n",
    "\n",
    "        self.E = nn.Linear(max_length, d_proj, bias=False)\n",
    "        self.F = nn.Linear(max_length, d_proj, bias=False)\n",
    "\n",
    "        assert (d_embed % n_heads) == 0\n",
    "        self.n_heads = n_heads\n",
    "\n",
    "    def forward(self, x, attention_mask):\n",
    "        # d_proj = dimension of the low rank projection\n",
    "        q = self.q_proj(x)\n",
    "        k = self.k_proj(x)\n",
    "        v = self.v_proj(x)\n",
    "        \n",
    "        batch_size, seq_len, d_embed = x.shape\n",
    "\n",
    "        k_proj = self.E(k.transpose(1, 2)).transpose(1, 2) # (b, d_proj, d_embed)\n",
    "        v_proj = self.F(v.transpose(1, 2)).transpose(1, 2) # (b, d_proj, d_embed)\n",
    "\n",
    "        q = q.reshape(batch_size, seq_len, self.n_heads, -1).transpose(\n",
    "            1, 2\n",
    "        )  # (b, n_heads, seq_length, d_head)\n",
    "        _, d_proj, _ = k_proj.shape\n",
    "        k_proj = k_proj.reshape(batch_size, d_proj, self.n_heads, -1).transpose(1, 2)\n",
    "        # (b, n_heads, d_proj, d_head)\n",
    "        v_proj = v_proj.reshape(batch_size, d_proj, self.n_heads, -1).transpose(1, 2)\n",
    "        # (b, n_heads, d_proj, d_head)\n",
    "        s_ij = q @ k_proj.transpose(-1, -2)  # (b, n_heads, seq_length, d_proj)\n",
    "\n",
    "        d = k_proj.shape[-1]\n",
    "        s_ij = s_ij * (d**-0.5)\n",
    "\n",
    "        attention_mask = 1.0 - attention_mask  # (b, seq_length)\n",
    "        attention_mask = attention_mask.unsqueeze(1).unsqueeze(-1) # (b, 1, seq_length, 1)\n",
    "\n",
    "        attention_mask = attention_mask.float() * (float(\"-inf\"))  # (b, n_heads, seq_length, d_proj)\n",
    "        s_ij = s_ij + attention_mask\n",
    "\n",
    "        a_ij = torch.softmax(s_ij, dim=-1)\n",
    "        y = a_ij @ v_proj  # (b, n_heads, seq_length, d_head)\n",
    "        y = y.transpose(2, 1)\n",
    "\n",
    "        y = y.reshape(batch_size, seq_len, d_embed) # concatenate\n",
    "        return y\n",
    "\n",
    "class LinformerLayer(nn.Module):\n",
    "    def __init__(self, d_embed, d_ff, n_heads, d_proj, max_length, dropout=0.1):\n",
    "        super().__init__()\n",
    "        self.attention = LinformerMHA(d_embed, n_heads, d_proj, max_length)\n",
    "\n",
    "        self.layer_norm_attention = LayerNorm(d_embed)\n",
    "        self.layer_norm_feed_forward = LayerNorm(d_embed)\n",
    "\n",
    "        self.dropout = dropout\n",
    "        self.feed_forward = FeedForward(d_embed, d_ff, dropout=self.dropout)\n",
    "\n",
    "    def forward(self, x, attention_mask):\n",
    "        z = self.attention(x, attention_mask)\n",
    "        z = F.dropout(z, p=self.dropout, training=self.training)\n",
    "        z = z + x\n",
    "        z = self.layer_norm_attention(z)\n",
    "\n",
    "        y = self.feed_forward(z)\n",
    "        y = y + z\n",
    "        y = self.layer_norm_feed_forward(y)\n",
    "        return y\n",
    "\n",
    "class Linformer(nn.Module):\n",
    "    def __init__(\n",
    "        self,\n",
    "        n_layers,\n",
    "        d_embed,\n",
    "        d_ff,\n",
    "        n_heads,\n",
    "        voc_size,\n",
    "        max_length,\n",
    "        d_proj,\n",
    "        dropout=0.1,\n",
    "    ):\n",
    "        super().__init__()\n",
    "        self.n_layers = n_layers\n",
    "        self.d_embed = d_embed\n",
    "        self.d_ff = d_ff\n",
    "        self.num_heads = n_heads\n",
    "        self.max_length = max_length\n",
    "        self.voc_size = voc_size\n",
    "        self.d_proj = d_proj\n",
    "        self.dropout = dropout\n",
    "        self.transformer_stack = nn.ModuleList(\n",
    "            [LinformerLayer(\n",
    "                d_embed=d_embed,\n",
    "                d_ff=d_ff,\n",
    "                n_heads=n_heads,\n",
    "                d_proj=d_proj,\n",
    "                max_length=max_length,\n",
    "                dropout=self.dropout\n",
    "            ) for _ in range(n_layers)]\n",
    "        )\n",
    "\n",
    "\n",
    "        self.token_embeddings = nn.Embedding(\n",
    "            num_embeddings=self.voc_size, embedding_dim=self.d_embed\n",
    "        )\n",
    "        self.position_embeddings = nn.Embedding(\n",
    "            num_embeddings=self.max_length, embedding_dim=self.d_embed\n",
    "        )\n",
    "        self.out_layer_norm = LayerNorm(self.d_embed)\n",
    "        self.embedding_norm = LayerNorm(self.d_embed)\n",
    "        self.lm_head = nn.Linear(self.d_embed, self.voc_size)\n",
    "\n",
    "    def forward(self, input_ids, attention_mask):\n",
    "        token_vectors = self.token_embeddings(input_ids)\n",
    "        position_vectors = self.position_embeddings(\n",
    "            torch.arange(input_ids.shape[-1], device=input_ids.device)\n",
    "        )[None, :, :]\n",
    "        z = token_vectors + position_vectors\n",
    "        z = self.embedding_norm(z)\n",
    "        for layer in self.transformer_stack:\n",
    "            z = layer(z, attention_mask) + z\n",
    "        y = self.out_layer_norm(z)\n",
    "        logits = self.lm_head(y)\n",
    "        return logits"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "jkPL4EpdoJPG"
   },
   "source": [
    "### Transformer Architecture (Self-Attention)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "id": "MDrXQgoyoJPG"
   },
   "outputs": [],
   "source": [
    "class GPTMHAttention(nn.Module):\n",
    "    def __init__(self, d_embed, n_heads):\n",
    "        super().__init__()\n",
    "        self.q_proj = nn.Linear(d_embed, d_embed, bias=False)\n",
    "        self.k_proj = nn.Linear(d_embed, d_embed, bias=False)\n",
    "        self.v_proj = nn.Linear(d_embed, d_embed, bias=False)\n",
    "\n",
    "        assert (d_embed % n_heads) == 0\n",
    "        self.n_heads = n_heads\n",
    "\n",
    "    def forward(self, x, attention_mask):\n",
    "        q = self.q_proj(x)\n",
    "        k = self.k_proj(x)\n",
    "        v = self.v_proj(x)\n",
    "\n",
    "        batch_size, seq_len, d_embed = x.shape\n",
    "\n",
    "        q = q.reshape(batch_size, seq_len, self.n_heads, -1).transpose(\n",
    "            1, 2\n",
    "        )\n",
    "        k = k.reshape(batch_size, seq_len, self.n_heads, -1).transpose(1, 2)\n",
    "        v = v.reshape(batch_size, seq_len, self.n_heads, -1).transpose(1, 2)\n",
    "        s_ij = q @ k.transpose(-1, -2)\n",
    "\n",
    "        d = k.shape[-1]\n",
    "        s_ij = s_ij * (d**-0.5)\n",
    "\n",
    "        attention_mask = 1.0 - attention_mask  # (b, seq_length)\n",
    "        attention_mask = attention_mask.unsqueeze(1).unsqueeze(-1) # (b, 1, seq_length, 1)\n",
    "\n",
    "        attention_mask = attention_mask.float() * (float(\"-inf\"))  # (b, n_heads, seq_length, d_proj)\n",
    "        s_ij = s_ij + attention_mask\n",
    "\n",
    "        a_ij = torch.softmax(s_ij, dim=-1)\n",
    "        y = a_ij @ v\n",
    "        y = y.transpose(2, 1)\n",
    "\n",
    "        y = y.reshape(batch_size, seq_len, d_embed)\n",
    "        return y\n",
    "\n",
    "class GPTMHTransformerLayer(nn.Module):\n",
    "    def __init__(self, d_embed, d_ff, n_heads, dropout=0.1):\n",
    "        super().__init__()\n",
    "        self.attention = GPTMHAttention(d_embed, n_heads)\n",
    "\n",
    "        self.layer_norm_attention = LayerNorm(d_embed)\n",
    "        self.layer_norm_feed_forward = LayerNorm(d_embed)\n",
    "\n",
    "        self.dropout = dropout\n",
    "        self.feed_forward = FeedForward(d_embed, d_ff, dropout=self.dropout)\n",
    "\n",
    "    def forward(self, x, attention_mask):\n",
    "        z = self.attention(x, attention_mask)\n",
    "        z = F.dropout(z, p=self.dropout, training=self.training)\n",
    "        z = z + x\n",
    "        z = self.layer_norm_attention(z)\n",
    "\n",
    "        y = self.feed_forward(z)\n",
    "        y = y + z\n",
    "        y = self.layer_norm_feed_forward(y)\n",
    "        return y\n",
    "\n",
    "class GPTTransformer(nn.Module):\n",
    "    def __init__(\n",
    "        self,\n",
    "        n_layers,\n",
    "        d_embed,\n",
    "        d_ff,\n",
    "        n_heads,\n",
    "        voc_size,\n",
    "        max_length,\n",
    "        dropout=0.1,\n",
    "    ):\n",
    "        super().__init__()\n",
    "        self.n_layers = n_layers\n",
    "        self.d_embed = d_embed\n",
    "        self.d_ff = d_ff\n",
    "        self.num_heads = n_heads\n",
    "        self.max_length = max_length\n",
    "        self.voc_size = voc_size\n",
    "        self.dropout = dropout\n",
    "        self.transformer_stack = nn.ModuleList(\n",
    "            [GPTMHTransformerLayer(\n",
    "                d_embed=d_embed,\n",
    "                d_ff=d_ff,\n",
    "                n_heads=n_heads,\n",
    "                dropout=self.dropout\n",
    "            ) for _ in range(n_layers)]\n",
    "        )\n",
    "\n",
    "\n",
    "        self.token_embeddings = nn.Embedding(\n",
    "            num_embeddings=self.voc_size, embedding_dim=self.d_embed\n",
    "        )\n",
    "        self.position_embeddings = nn.Embedding(\n",
    "            num_embeddings=self.max_length, embedding_dim=self.d_embed\n",
    "        )\n",
    "        self.out_layer_norm = LayerNorm(self.d_embed)\n",
    "        self.embedding_norm = LayerNorm(self.d_embed)\n",
    "        self.lm_head = nn.Linear(self.d_embed, self.voc_size)\n",
    "\n",
    "    def forward(self, input_ids, attention_mask):\n",
    "        token_vectors = self.token_embeddings(input_ids)\n",
    "        position_vectors = self.position_embeddings(\n",
    "            torch.arange(input_ids.shape[-1], device=input_ids.device)\n",
    "        )[None, :, :]\n",
    "        z = token_vectors + position_vectors\n",
    "        z = self.embedding_norm(z)\n",
    "        for layer in self.transformer_stack:\n",
    "            z = layer(z, attention_mask) + z\n",
    "        y = self.out_layer_norm(z)\n",
    "        logits = self.lm_head(y)\n",
    "        return logits"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3YcdbVrKoJPH"
   },
   "source": [
    "### Loading the Dataset, the Tokenizer and building the pipeline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "V1Qp2SfEohdz"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "Requirement already satisfied: python-dateutil>=2.8.2 in c:\\users\\mlasb\\anaconda3\\envs\\cuda_python\\lib\\site-packages (from pandas->datasets) (2.9.0.post0)\n",
      "Requirement already satisfied: pytz>=2020.1 in c:\\users\\mlasb\\anaconda3\\envs\\cuda_python\\lib\\site-packages (from pandas->datasets) (2024.2)\n",
      "Requirement already satisfied: tzdata>=2022.7 in c:\\users\\mlasb\\anaconda3\\envs\\cuda_python\\lib\\site-packages (from pandas->datasets) (2024.2)\n",
      "Requirement already satisfied: six>=1.5 in c:\\users\\mlasb\\anaconda3\\envs\\cuda_python\\lib\\site-packages (from python-dateutil>=2.8.2->pandas->datasets) (1.17.0)\n",
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "%pip install datasets\n",
    "from datasets import load_dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 296,
     "referenced_widgets": [
      "07a65624f6164cd8b235155a54dc4a71",
      "ca9b7dc55015448c8cc66ca0cc1cbb6b",
      "df0e2e8132784351bcc0ec9f023af811",
      "b045cd4cc6604a2f8e7a00a26c7320cd",
      "914aa920ea6b4acf8607fa3709006b8c",
      "16e8820de48b4692a6366d30f1fb1aa3",
      "8f93409c6cf349f6a5fa9754214c88e0",
      "a3f78fbf064242908d24448d0f77caf1",
      "80c64032087f476a8c2e73c8af49f089",
      "20e39e06628e48e4a309419661ea2536",
      "518fc9a89736455f969f7594105565b0",
      "228ead2a99e94dd190d56a44b098b24f",
      "6b687d1f949046aeb48bb8d6eade0f5c",
      "ac0d6547c3a84fb1ae9b4c31294ff91d",
      "42ad3c2746ba490699edbf51d960c746",
      "18b17350d71c4e98ae1f58edf1cc4526",
      "7aed929007bd4481a600f3b373577872",
      "2edc1733a1fc48bc92dd17994816ddcb",
      "e9a398baafd9404986f3613b1fdd251a",
      "2b35df816be2476db5ea05bdd5b4ce45",
      "8e131a75c7c74da18cb990653600a5eb",
      "490eb4f062514cf19e23ad97eb33f8b1",
      "d17e7f37ace84e0e92f8243fc3f7f5ee",
      "544cbb4ad3e24a7d94f6d6a09ba9e7a7",
      "f5d4ccc8efd7407898d0b5ecd0e49b98",
      "95010f83a9a34b6db329b96199a087c2",
      "05d7c9257a2f41e6b1b7d729e86f0db5",
      "774ccabb5c7049e4ace2b35cc87d9569",
      "6281eba1ea404e959086b2291de99d22",
      "410e998f6cdf41b793610c322f2b09da",
      "1d4aa2217563457eb84ab8458254a356",
      "7cef5093942045a9b9b726b1b3dbf3fb",
      "79ad70d32c3c4249a384c2ea69e93bff"
     ]
    },
    "id": "bfw6ehM1xW6y",
    "outputId": "904303bf-f4a6-4de6-fa35-eb1fde13e56f"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dataset({\n",
      "    features: ['review', 'sentiment'],\n",
      "    num_rows: 50000\n",
      "})\n"
     ]
    }
   ],
   "source": [
    "dataset = load_dataset(\"scikit-learn/imdb\", split=\"train\")\n",
    "print(dataset)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "id": "5Fo_BkkWdt_J"
   },
   "outputs": [],
   "source": [
    "class WhiteSpaceTokenizer:\n",
    "    def __init__(self, max_voc: Optional[int] = None, max_length: int = 512):\n",
    "        self.vocab = {}\n",
    "        self.id_to_token = {}\n",
    "        self.frequencies = {}\n",
    "        self.max_voc = max_voc\n",
    "        self.max_length = max_length\n",
    "\n",
    "    def split_text(self, text: str) -> List[str]:\n",
    "        \"\"\"Converts the text to a list of tokens (substrings).\"\"\"\n",
    "        return text.split(\" \")\n",
    "\n",
    "    def encode(self, text: str) -> List[int]:\n",
    "        \"\"\"Take a text as input and return its associated tokenization, as a list of ids.\"\"\"\n",
    "        list_tokens = self.split_text(text)\n",
    "        list_ids = []\n",
    "        unknown_id = self.vocab[\"<UNK>\"]\n",
    "        for token in list_tokens:\n",
    "            list_ids.append(self.vocab.get(token, unknown_id))\n",
    "        list_ids = list_ids[: self.max_length - 2]\n",
    "        list_ids = [self.vocab[\"<BOS>\"]] + list_ids + [self.vocab[\"<EOS>\"]]\n",
    "        return list_ids\n",
    "\n",
    "    def decode(self, ids: List[int]) -> str:\n",
    "        tokens = [self.id_to_token[i] for i in ids]\n",
    "        return \" \".join(tokens)\n",
    "\n",
    "    def add_special_token(self, token: str):\n",
    "        \"\"\"Add a special token to the vocabulary.\"\"\"\n",
    "        if token not in self.vocab:\n",
    "            self.vocab[token] = len(self.vocab)\n",
    "            self.id_to_token[len(self.id_to_token)] = token\n",
    "\n",
    "    def fit(self, corpus: List[str]):\n",
    "        \"\"\"Fits the tokenizer to a list of texts to construct its vocabulary.\"\"\"\n",
    "        for text in tqdm(corpus):\n",
    "            list_tokens = self.split_text(text)\n",
    "            for token in list_tokens:\n",
    "                token_count = self.frequencies.get(token, None)\n",
    "                if token_count is None:\n",
    "                    self.frequencies[token] = 0\n",
    "\n",
    "                self.frequencies[token] += 1\n",
    "        if self.max_voc is not None:\n",
    "            self.frequencies = sorted(\n",
    "                self.frequencies.items(), key=lambda x: x[1], reverse=True\n",
    "            )\n",
    "            self.frequencies = dict(self.frequencies[: self.max_voc])\n",
    "        for i, token in enumerate(self.frequencies):\n",
    "            self.vocab[token] = i\n",
    "            self.id_to_token[i] = token\n",
    "        self.num_words = len(self.vocab)\n",
    "        self.add_special_token(\"<UNK>\")\n",
    "        self.add_special_token(\"<BOS>\")\n",
    "        self.add_special_token(\"<EOS>\")\n",
    "        print(f\"Built a vocabulary of {self.num_words} words.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 49,
     "referenced_widgets": [
      "b154863769484aaaa8f3a03fc208c7d3",
      "60420fc85bdc43c89bbafc8ea9d043c0",
      "7c5f9de41cdb4eefb72e0d4b2d55691d",
      "c77da6dc90cf4383a391ae2f32f4f7b9",
      "ef65a189978843f497461bae87a59b86",
      "b8f0b036f2b940ef93466d9546c1010b",
      "5bf99161283a493d9950610600ad228d",
      "23a8ae3354144cda976996371f99a60c",
      "1a0b4bb46a2e4bbd84d27b7f67938c07",
      "011057f978b14ad4b315714973c6dae3",
      "432fa521645945f69c6005712f35b96d"
     ]
    },
    "id": "uoU7Gao4dt_K",
    "outputId": "89062dc7-d20d-46ee-b9fa-33cc59a39cfa"
   },
   "outputs": [],
   "source": [
    "def preprocess_text(text: str) -> str:\n",
    "    # lower case\n",
    "    text = text.lower()\n",
    "\n",
    "    # string normalization.\n",
    "    text = unicodedata.normalize(\"NFD\", text).encode(\"ascii\", \"ignore\").decode()\n",
    "    text = text.replace(\"<br />\", \"\")\n",
    "\n",
    "    # Add whitespace around punctuation marks (., !)\n",
    "    text = re.sub(r\"([.!,?])\", r\" \\1 \", text)\n",
    "\n",
    "    # Remove any extra spaces that may have been added\n",
    "    text = re.sub(r\"\\s+\", \" \", text).strip()\n",
    "\n",
    "    #  remove non alpha numeric characters.\n",
    "    text = re.sub(r\"[^a-zA-Z0-9\\s.!,]\", \" \", text)\n",
    "\n",
    "    # replace numbers by the <NUM> token.\n",
    "    text = re.sub(r\"\\d+\", \"<NUM>\", text)\n",
    "\n",
    "    # remove double whitespaces.\n",
    "    text = re.sub(\" +\", \" \", text.strip())\n",
    "\n",
    "    #  remove br tags\n",
    "    return text\n",
    "\n",
    "\n",
    "# Clean the dataset\n",
    "dataset = dataset.map(lambda x: {\"text\": preprocess_text(x[\"review\"])})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 67,
     "referenced_widgets": [
      "146f79a4a05840a9bd0f3b21afda1b04",
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      "4582b60d0ab447af8b88cba427b17df3",
      "72a2450de2a54367bb4c8662c9c22dcb",
      "a545d64b8bc84c8e8aacb7bc41031092",
      "0088b14ea1d345fa8a4f4b31ea805c58",
      "f0fb65c6af5742829082d6bd708b3d79",
      "fb11a62e754d4e3bab91d844ee5a2c6f",
      "885f7675582048f1813b0e072e69c3c4"
     ]
    },
    "id": "-jig_j1Fdt_K",
    "outputId": "3a656e53-84c4-408a-f556-d9ba60095a6f"
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "66ec9bd41c2944c6aa37149fc518878f",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/50000 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Built a vocabulary of 10000 words.\n"
     ]
    }
   ],
   "source": [
    "tokenizer = WhiteSpaceTokenizer(max_voc=10000)\n",
    "tokenizer.fit(dataset[\"text\"])\n",
    "tokenizer.add_special_token(\"<PAD>\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "id": "70x_XxO5wrSq"
   },
   "outputs": [],
   "source": [
    "def preprocessing_fn(x, tokenizer):\n",
    "    x[\"input_ids\"] = tokenizer.encode(x[\"text\"])\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "id": "9IVUuJguxzvx"
   },
   "outputs": [],
   "source": [
    "class DataCollator:\n",
    "    def __init__(self, pad_token_id: int, label_pad_token_id: int = -100, max_length: int = 512):\n",
    "        self.pad_token_id = pad_token_id\n",
    "        self.label_pad_token_id = label_pad_token_id\n",
    "        self.max_length = max_length\n",
    "\n",
    "    def __call__(self, batch):\n",
    "        # max_label_length = max(len(f[\"input_ids\"]) for f in batch)\n",
    "        for feature in batch:\n",
    "            input_ids = feature[\"input_ids\"]\n",
    "            label_ids = feature[\"input_ids\"]\n",
    "            current_length = len(input_ids)\n",
    "\n",
    "            input_remainder = [\n",
    "                self.pad_token_id for _ in range(self.max_length - current_length)\n",
    "            ]\n",
    "            input_ids = input_ids + input_remainder\n",
    "\n",
    "            label_remainder = [\n",
    "                self.label_pad_token_id\n",
    "                for _ in range(self.max_length - current_length)\n",
    "            ]\n",
    "            labels = label_ids + label_remainder\n",
    "            feature[\"input_ids\"] = input_ids\n",
    "            feature[\"labels\"] = labels\n",
    "            feature[\"attention_mask\"] = [1 for _ in range(current_length)] + [\n",
    "                0 for _ in range(self.max_length - current_length)\n",
    "            ]\n",
    "        features = {\n",
    "            \"input_ids\": torch.tensor([f[\"input_ids\"] for f in batch]),\n",
    "            \"attention_mask\": torch.tensor([f[\"attention_mask\"] for f in batch]),\n",
    "            \"labels\": torch.tensor([f[\"labels\"] for f in batch]),\n",
    "        }\n",
    "        return features"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "yWZbqE2EoJPI"
   },
   "source": [
    "### Initialize the two models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "id": "qu8mTJ8yXbD6"
   },
   "outputs": [],
   "source": [
    "model_linformer = Linformer(\n",
    "    d_embed=256,\n",
    "    d_ff=1024,\n",
    "    n_heads=4,\n",
    "    n_layers=1,\n",
    "    voc_size=len(tokenizer.vocab),\n",
    "    max_length=512,\n",
    "    d_proj=128,\n",
    "    dropout=0.1,\n",
    ")\n",
    "\n",
    "model_transformer = GPTTransformer(\n",
    "    d_embed=256,\n",
    "    d_ff=1024,\n",
    "    n_heads=4,\n",
    "    n_layers=1,\n",
    "    voc_size=len(tokenizer.vocab),\n",
    "    max_length=512,\n",
    "    dropout=0.1,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "IbTWtGUfoJPJ"
   },
   "source": [
    "### Compute and compare Inference Time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 67,
     "referenced_widgets": [
      "be38e5f480be41b58f771ec8e17b876e",
      "60a36888e738492cb9ebb9b0eba906df",
      "36fa985d45ca4f148dddb994d0819626",
      "b958ec51c00e4c918d0ad2db8fdbb635",
      "15918751431648099c0e16f0aa3d6e6c",
      "095bcba05e274ccd8337f68ae6578217",
      "684f9f6990584de19a739e68d7ca8433",
      "55351f482a5642dd914f9c69932c19f1",
      "7fc2b01760374cca9111e39ecf7e5e86",
      "dc1ea27a12b1474a917314bc564e68bc",
      "012617caca664cd3863115e3f0edcc02"
     ]
    },
    "id": "z0PyTfIXoJPJ",
    "outputId": "53e4d91e-ac92-4326-f7a7-3d391838dd36"
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a5831ddd7cc64b29bf56835443bb6d5d",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Map:   0%|          | 0/128 [00:00<?, ? examples/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "128\n"
     ]
    }
   ],
   "source": [
    "n_samples = 128\n",
    "\n",
    "dataset = dataset.shuffle()\n",
    "\n",
    "splitted_dataset = dataset.select(range(n_samples))\n",
    "\n",
    "splitted_dataset = splitted_dataset.map(\n",
    "    preprocessing_fn, fn_kwargs={\"tokenizer\": tokenizer}\n",
    ")\n",
    "\n",
    "splitted_dataset = splitted_dataset.select_columns([\"input_ids\"])\n",
    "\n",
    "inference_set = splitted_dataset\n",
    "print(len(inference_set['input_ids']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "VHQ0Jl6roJPJ",
    "outputId": "cbfcd5e2-e2cf-4716-db8e-cb87516b2037"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Linformer Model:\n",
      "\n",
      "Model size: 6,118,420\n",
      "\n",
      "Transformer Model:\n",
      "\n",
      "Model size: 5,987,348\n"
     ]
    }
   ],
   "source": [
    "DEVICE = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n",
    "\n",
    "model_linformer = model_linformer.to(DEVICE)\n",
    "model_transformer = model_transformer.to(DEVICE)\n",
    "\n",
    "data_collator = DataCollator(pad_token_id=tokenizer.vocab[\"<PAD>\"])\n",
    "batch_size = 128\n",
    "\n",
    "inference_dataloader = DataLoader(\n",
    "    inference_set, batch_size=batch_size, collate_fn=data_collator\n",
    ")\n",
    "\n",
    "\n",
    "def count_parameters(model: nn.Module):\n",
    "    total_params = sum(p.numel() for p in model.parameters() if p.requires_grad)\n",
    "    return f\"{total_params:,}\"\n",
    "\n",
    "# Parameters of the 2 models\n",
    "print(\"Linformer Model:\\n\")\n",
    "print(\"Model size:\", count_parameters(model_linformer))\n",
    "\n",
    "print(\"\\nTransformer Model:\\n\")\n",
    "print(\"Model size:\", count_parameters(model_transformer))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "id": "S-CkDa1IoJPJ"
   },
   "outputs": [],
   "source": [
    "def inference_test(\n",
    "    model,\n",
    "    train_dataloader: DataLoader,\n",
    "):\n",
    "    model.to(DEVICE)  # Move model to the appropriate device\n",
    "    model.eval()\n",
    "    with torch.no_grad():\n",
    "        for batch in tqdm(train_dataloader, desc=\"Inference\"):\n",
    "            batch = {k: v.to(DEVICE) for k, v in batch.items()}\n",
    "            input_ids, attention_mask, labels = (\n",
    "                batch[\"input_ids\"],\n",
    "                batch[\"attention_mask\"],\n",
    "                batch[\"labels\"],\n",
    "            )\n",
    "\n",
    "            _ = model(input_ids, attention_mask)\n",
    "    return\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 136,
     "referenced_widgets": [
      "322276c2e7a54eb3a3b80240f6f6c61b",
      "2f32141b7ba4491f8d8c890cc2e97aff",
      "f16c1ed3870b4ea79a4edcf77d9a6525",
      "9fc7e9548ac74b8f92801554ddcff69a",
      "e0a4ae169e9740dfb157b52f17260848",
      "bdcf2b833f8a4b15b19e439841076aca",
      "00fd21f152a44394bd002a0297602c38",
      "19330568d9344ffdaf0f1e94a2740321",
      "66c0f08987ad452e8f9ee591d88f7de2",
      "9d5bac1fa7184eae8e5d22268c8882b1",
      "460281b9fb0247c99b7bfe56653e002a",
      "f495e153044b47feb754c263cba805ec",
      "edff5748674849229b894f14939ee093",
      "9a0605f595ab44289dd445ae5f213249",
      "19f1d454bacc45bf92b7b93eee8ddce2",
      "f9b5d4267f9d438692afa846430ca790",
      "97fa7a3f3abf4a68b8172461107eb4a6",
      "6da522a8e3754d7194de3c1977d99445",
      "c89d7c3d295f43f0a159bb6e15217aac",
      "cf2f6131b9dc42da8c84b268e82b64c2",
      "fd5c67f56e67455ba96a7356e8f17a7f",
      "804ba55db97a47a78dc1eb43282ca6c8"
     ]
    },
    "id": "VHrHn-UhoJPJ",
    "outputId": "a2145054-aced-4bf0-d1a0-5c94d7baeb80"
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "32a0f527eb4149b4b2cd791c8418dbdb",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Inference:   0%|          | 0/1 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Linformer inference time: 0.8132 s\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2752a3ca5913489fa62173580c84c5e7",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Inference:   0%|          | 0/1 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Transformer inference time: 0.1128 s\n"
     ]
    }
   ],
   "source": [
    "start = time.time()\n",
    "inference_time_linformer = inference_test(model_linformer, inference_dataloader)\n",
    "end = time.time()\n",
    "print(f\"Linformer inference time: {end - start:.4f} s\")\n",
    "\n",
    "start = time.time()\n",
    "inference_time_transformer = inference_test(model_transformer, inference_dataloader)\n",
    "end = time.time()\n",
    "print(f\"\\nTransformer inference time: {end - start:.4f} s\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "uoYm11rFoJPK"
   },
   "source": [
    "### Results\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "gtlKPN0toJPK"
   },
   "source": [
    "To compute those inference times, we used the previous code multiple times with various batch sizes and sequence lengths.\n",
    "\n",
    "We also need to change the Tokenizer max_length and the DataCollator max_length each time, to the same value as the max_length of the models.\n",
    "\n",
    "We couldn't go further than a sequence length of 8192, because of computational limitations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 507
    },
    "id": "GAOsKvTdoJPK",
    "outputId": "ced1c842-d64a-4628-a779-3f54ab4418e5"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "seq_batch = ['512/128', '1024/64', '2048/32', '4096/16', '8192/8']\n",
    "linformer_128 = [2.5606, 2.5641, 2.6062, 2.5106, 2.6504]\n",
    "linformer_512 = [3.2546, 3.3152, 3.3859, 3.2027, 3.4462]\n",
    "transformer = [3.2429, 4.4726, 6.4692, 11.3022, 32.7407]\n",
    "\n",
    "plt.figure(figsize=(8, 5))\n",
    "plt.plot(seq_batch, linformer_128, label='Linformer k=128', marker='o', color='purple')\n",
    "plt.plot(seq_batch, linformer_512, label='Linformer k=512', marker='+', color='red')\n",
    "plt.plot(seq_batch, transformer, label='Transformer', marker='x', linestyle='--', color='teal')\n",
    "plt.xlabel('Sequence length / batch size', fontsize=12)\n",
    "plt.ylabel('Inference Time (s)', fontsize=12)\n",
    "plt.legend()\n",
    "plt.grid(visible=True, linestyle='--', alpha=0.6)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "GIyle9HFpr7M"
   },
   "source": [
    "### Analysis of the Self attention is low rank hypothesis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "id": "Ou0QmZoUpPRf"
   },
   "outputs": [],
   "source": [
    "INF = 1e10\n",
    "\n",
    "class contextmapping(nn.Module):\n",
    "    def __init__(self, d):\n",
    "        super().__init__()\n",
    "\n",
    "        self.q_proj = Linear(d, d)\n",
    "        self.k_proj = Linear(d, d)\n",
    "        self.v_proj = Linear(d, d)\n",
    "\n",
    "    def forward(self, x):\n",
    "        q = self.q_proj(x)  # (b, l, d)\n",
    "        k = self.k_proj(x)\n",
    "\n",
    "        d = k.shape[-1]\n",
    "        s_ij = q @ k.transpose(1, 2) * d ** (-0.5)  # (b, l, l)\n",
    "\n",
    "        a_ij = torch.softmax(s_ij, dim=-1)\n",
    "        return a_ij\n",
    "\n",
    "class contextmappingwithoutdata(nn.Module):\n",
    "    def __init__(self, d):\n",
    "        super().__init__()\n",
    "\n",
    "        self.q_proj = Linear(d, d)\n",
    "        self.k_proj = Linear(d, d)\n",
    "\n",
    "    def forward(self, x, y):\n",
    "        q = self.q_proj(x)  # (b, l, d)\n",
    "        k = self.k_proj(y)\n",
    "\n",
    "        d = k.shape[-1]\n",
    "        s_ij = q @ k.transpose(1, 2) * d ** (-0.5)  # (b, l, l)\n",
    "\n",
    "        a_ij = torch.softmax(s_ij, dim=-1)\n",
    "        return a_ij\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "00Y2lUoIKdbk"
   },
   "source": [
    "## Analysis for a max lenght of 512"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "irWn69MDuc2V",
    "outputId": "b2f7b431-8ba6-4675-ce76-1ddd6323e17c"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([512])\n"
     ]
    }
   ],
   "source": [
    "for batch in inference_dataloader:\n",
    "    input = batch['input_ids'][0]\n",
    "    break\n",
    "print(input.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "jiYuyAnoqT2E",
    "outputId": "42374964-39e9-492d-8e14-3e56782bf409"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([512, 512])\n"
     ]
    }
   ],
   "source": [
    "d_embed = 256\n",
    "d_ff = 1024\n",
    "gauss_input = torch.randn([1, 512, 256])\n",
    "poisson_input = torch.poisson(torch.full((1, 512, 256), 3.))\n",
    "embedding = Embeddings(len(tokenizer.vocab), d_embed)\n",
    "embed_input = 50*embedding(input).unsqueeze(0) #since the embedding mapping was generating using a scaler factor 0.02, we cancel it with the factor 50 unless our ouptut would be too small\n",
    "cm = contextmapping(d_embed)\n",
    "out_gauss = cm(gauss_input)[0]\n",
    "out_imdb = cm(embed_input)[0]\n",
    "out_poisson = cm(poisson_input)[0]\n",
    "print(out_gauss.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 542
    },
    "id": "bnDcRZXprREv",
    "outputId": "500eb123-b611-43fb-ad50-4dcf5aa059db"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "_,S_gauss,_ = np.linalg.svd(out_gauss.detach().numpy())\n",
    "plt.plot(np.cumsum(S_gauss)/np.sum(S_gauss), label = \"Gaussian inputs\")\n",
    "_,S_imdb,_ = np.linalg.svd(out_imdb.detach().numpy())\n",
    "plt.plot(np.cumsum(S_imdb)/np.sum(S_imdb), label = \"IMDB inputs\")\n",
    "_,S_poisson,_ = np.linalg.svd(out_poisson.detach().numpy())\n",
    "plt.plot(np.cumsum(S_poisson)/np.sum(S_poisson), label = \"Poisson inputs, lambda=3\")\n",
    "plt.legend()\n",
    "plt.xlabel('Eigenvalue index')\n",
    "plt.ylabel('Normalized cumulative eigenvalue')\n",
    "plt.axhline(y=0.90, color='r', linestyle='--')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "Lg2uq0AIGWq1",
    "outputId": "06cf6604-9898-4d7e-b6a2-f983ca40e7fe"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([4096, 4096])\n"
     ]
    }
   ],
   "source": [
    "d_embed = 256\n",
    "d_ff = 1024\n",
    "gauss_input = torch.randn([1, 4096, 256])\n",
    "poisson_input = torch.poisson(torch.full((1, 4096, 256), 3.))\n",
    "out_gauss = cm(gauss_input)[0]\n",
    "out_poisson = cm(poisson_input)[0]\n",
    "print(out_gauss.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 449
    },
    "id": "WjKlunwZK8ey",
    "outputId": "b1fb53b0-116f-4063-fbe0-c027b1ca329a"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_,S_gauss,_ = np.linalg.svd(out_gauss.detach().numpy())\n",
    "plt.plot(np.cumsum(S_gauss)/np.sum(S_gauss), label = \"Gaussian inputs\")\n",
    "_,S_poisson,_ = np.linalg.svd(out_poisson.detach().numpy())\n",
    "plt.plot(np.cumsum(S_poisson)/np.sum(S_poisson), label = \"Poisson inputs, lambda=3\")\n",
    "plt.legend()\n",
    "plt.xlabel('Eigenvalue index')\n",
    "plt.ylabel('Normalized cumulative eigenvalue')\n",
    "plt.axhline(y=0.90, color='r', linestyle='--')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  }
 ],
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