chapter_transformer/3_transformer.ipynb

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    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
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    "language_info": {
      "name": "python"
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  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "<a target=\"_blank\" href=\"https://colab.research.google.com/github/ashkan-mokarian/d2l-pytorch/blob/main/chapter_transformer/3_transformer.ipynb\">\n",
        "  <img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/>\n",
        "</a>"
      ],
      "metadata": {
        "id": "lTpqL2oWLrxs"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "yjyyiM7MLp23"
      },
      "outputs": [],
      "source": [
        "%pip install d2l==1.0.0a0"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import torch\n",
        "from torch import nn\n",
        "from d2l import torch as d2l\n",
        "import math\n",
        "import pandas as pd"
      ],
      "metadata": {
        "id": "HLhv9_DZMWi7"
      },
      "execution_count": 30,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Multi-head Attention\n",
        "Here, for simplicity, and also to allow effective parallelization with a single matrix multiplication for all the heads, q,k,v have the same dimensions across all heads where $p_o = hp_q = hp_k = hp_v = numhiddens$"
      ],
      "metadata": {
        "id": "gN8cc7_zL1gp"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "class MultiHeadAttention(d2l.Module):\n",
        "    def __init__(self, num_hiddens, num_heads, dropout, bias=False, **kwargs):\n",
        "        super().__init__()\n",
        "        self.num_heads = num_heads\n",
        "        self.attention = d2l.DotProductAttention(dropout)\n",
        "        self.W_q = nn.LazyLinear(num_hiddens, bias=bias)\n",
        "        self.W_k = nn.LazyLinear(num_hiddens, bias=bias)\n",
        "        self.W_v = nn.LazyLinear(num_hiddens, bias=bias)\n",
        "        self.W_o = nn.LazyLinear(num_hiddens, bias=bias)\n",
        "\n",
        "    def forward(self, queries, keys, values, valid_lens):\n",
        "        # Shape of queries, keys, values: (batch_size, no. of queries or key-value\n",
        "        # pairs, num_hiddens)\n",
        "        # Shape of valid_lens: (batch_size) or (batch_size, no. of q or k-v pairs)\n",
        "        # After transposing, shape of q,k,v: (batch_size * num_heads, no. of\n",
        "        # queries or k-v pairs, num_hiddens/num_heads)\n",
        "        queries = self.transpose_qkv(self.W_q(queries))\n",
        "        keys = self.transpose_qkv(self.W_k(keys))\n",
        "        values = self.transpose_qkv(self.W_v(values))\n",
        "\n",
        "        if valid_lens is not None:\n",
        "            valid_lens = torch.repeat_interleave(\n",
        "                valid_lens, repeats=self.num_heads, dim=0)\n",
        "        \n",
        "        # Shape of output: (batch_size * num_heasd, no. of queries, num_hiddens / num_heads)\n",
        "        output = self.attention(queries, keys, values, valid_lens)\n",
        "        # Shape of output concat: (batch_size, no. of queries, num_hiddens)\n",
        "        output_concat = self.transpose_output(output)\n",
        "        return self.W_o(output_concat)\n",
        "    \n",
        "    def transpose_qkv(self, X):\n",
        "        \"\"\"Transpositon for parallel computation of multi-head attention.\"\"\"\n",
        "        # Shape of input X: (batch_size, no. of q or k-v pairs, num_hiddens)\n",
        "        # Desired output of X: (batch_size * num_heads, no. of q or kv-pairs, num_hiddens / num_heads)\n",
        "        # But this must be done in steps to keep the orders\n",
        "        X = X.reshape(X.shape[0], X.shape[1], self.num_heads, -1)\n",
        "        X = X.permute(0, 2, 1, 3)\n",
        "        return X.reshape(-1, X.shape[2], X.shape[3])\n",
        "    \n",
        "    def transpose_output(self, X):\n",
        "        \"\"\"Reverse of transpose_qkv\"\"\"\n",
        "        # Shape of input X: (batch_size * num_heads, no. of queries, num_hiddens / num_heads)\n",
        "        # Desired shape of output: (batch_size, no. of q, num_hiddens)\n",
        "        X = X.reshape(-1, self.num_heads, X.shape[1], X.shape[2])\n",
        "        X = X.permute(0, 2, 1, 3)\n",
        "        return X.reshape(X.shape[0], X.shape[1], -1)\n",
        "\n",
        "# Testing\n",
        "num_hiddens, num_heads = 100, 5\n",
        "attention = MultiHeadAttention(num_hiddens, num_heads, 0.5)\n",
        "batch_size, num_queries, num_kvpairs = 2, 4, 6\n",
        "valid_lens = torch.tensor([3, 2])\n",
        "X = torch.ones((batch_size, num_queries, num_hiddens))\n",
        "Y = torch.ones((batch_size, num_kvpairs, num_hiddens))\n",
        "d2l.check_shape(attention(X, Y, Y, valid_lens), (batch_size, num_queries, num_hiddens))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UkSgyTxSL1DB",
        "outputId": "7e0c4126-587d-40b4-e78f-6217d2b9bbd2"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.10/dist-packages/torch/nn/modules/lazy.py:180: UserWarning: Lazy modules are a new feature under heavy development so changes to the API or functionality can happen at any moment.\n",
            "  warnings.warn('Lazy modules are a new feature under heavy development '\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Positional Encoding"
      ],
      "metadata": {
        "id": "SmDewSlHaCzq"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "class PositionalEncoding(nn.Module):\n",
        "    def __init__(self, num_hiddens, dropout, max_len=1000):\n",
        "        super().__init__()\n",
        "        self.dropout = nn.Dropout(dropout)\n",
        "        # Create a long enough P\n",
        "        self.P = torch.zeros((1, max_len, num_hiddens))\n",
        "        X = torch.arange(max_len, dtype=torch.float32).reshape(  # This reshpae helps with broadcasting and getting the desired matrix\n",
        "            -1, 1) / torch.pow(10000, torch.arange(\n",
        "                0, num_hiddens, 2, dtype=torch.float32)/num_hiddens)\n",
        "        self.P[:, :, 0::2] = torch.sin(X)\n",
        "        self.P[:, :, 1::2] = torch.cos(X)\n",
        "    \n",
        "    def forward(self, X):\n",
        "        X = X + self.P[:, :X.shape[1], :].to(X.device)\n",
        "        return self.dropout(X)"
      ],
      "metadata": {
        "id": "g8pbSIjgP96X"
      },
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "First columns have high frequency and later columns lower, and this is adjusted by dividing by the column number j. in order to encode the position of each row, i is evaluated at that position for all columns to give a positional code."
      ],
      "metadata": {
        "id": "plen8moVhtvx"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "encoding_dim, num_steps = 32, 60\n",
        "pos_encoding = PositionalEncoding(encoding_dim, 0)\n",
        "X = pos_encoding(torch.zeros((1, num_steps, encoding_dim)))\n",
        "P = pos_encoding.P[:, :X.shape[1], :]\n",
        "d2l.plot(torch.arange(num_steps), P[0, :, 6:10].T, xlabel='Row (position)',\n",
        "         figsize=(6, 2.5), legend=[\"Col %d\" % d for d in torch.arange(6, 10)])\n",
        "\n",
        "P = P[0, :, :].unsqueeze(0).unsqueeze(0)\n",
        "d2l.show_heatmaps(P, xlabel='Column (encoding dimension)',\n",
        "                  ylabel='Row (position)', figsize=(3.5, 4), cmap='Blues')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 627
        },
        "id": "GClkr60dhtdU",
        "outputId": "c77a526b-2551-4b3c-e640-ec36472fa85c"
      },
      "execution_count": 7,
      "outputs": [
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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Positionwise Feed-Forward Networks\n",
        "Just a simple 2-layer MLP that acts on each position (token) the same."
      ],
      "metadata": {
        "id": "F7O3FVRbIrU9"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "class PositionwiseFFN(nn.Module):\n",
        "    def __init__(self, ffn_num_hiddens, ffn_num_outputs):\n",
        "        super().__init__()\n",
        "        self.dense1 = nn.LazyLinear(ffn_num_hiddens)\n",
        "        self.relu = nn.ReLU()\n",
        "        self.dense2 = nn.LazyLinear(ffn_num_outputs)\n",
        "    \n",
        "    def forward(self, X):\n",
        "        return self.dense2(self.relu(self.dense1(X)))"
      ],
      "metadata": {
        "id": "z3BtER5MIzqh"
      },
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# AddNorm"
      ],
      "metadata": {
        "id": "LwkaS5A7KWkw"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "class AddNorm(nn.Module):\n",
        "    def __init__(self, norm_shape, dropout):\n",
        "        super().__init__()\n",
        "        self.dropout = nn.Dropout(dropout)\n",
        "        self.ln = nn.LayerNorm(norm_shape)\n",
        "    \n",
        "    def forward(self, X, Y):\n",
        "        return self.ln(self.dropout(Y) + X)"
      ],
      "metadata": {
        "id": "fAuBLLCZKY7T"
      },
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# The Transformer Architecture"
      ],
      "metadata": {
        "id": "BIWLJP6KmkDG"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "class TransformerEncoderBlock(nn.Module):\n",
        "    def __init__(self, num_hiddens, ffn_num_hiddens, num_heads, dropout, bias=False):\n",
        "        super().__init__()\n",
        "        self.attention = MultiHeadAttention(num_hiddens, num_heads, dropout, bias=bias)\n",
        "        self.addnorm1 = AddNorm(num_hiddens, dropout)\n",
        "        self.addnorm2 = AddNorm(num_hiddens, dropout)\n",
        "        self.pffn = PositionwiseFFN(ffn_num_hiddens, num_hiddens)\n",
        "    \n",
        "    def forward(self, X, valid_lens):\n",
        "        Y = self.addnorm1(X, self.attention(X, X, X, valid_lens))\n",
        "        return self.addnorm2(Y, self.pffn(Y))\n",
        "\n",
        "X = torch.ones((2, 100, 24))\n",
        "valid_lens = torch.tensor([3, 2])\n",
        "encoder_blk = TransformerEncoderBlock(24, 48, 8, 0.5)\n",
        "encoder_blk.eval()\n",
        "d2l.check_shape(encoder_blk(X, valid_lens), X.shape)"
      ],
      "metadata": {
        "id": "mw8ycTnfiScp"
      },
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "class TransformerEncoder(d2l.Encoder):\n",
        "    def __init__(self, vocab_size, num_hiddens, ffn_num_hiddens, num_heads, num_blks, dropout, use_bias=False):\n",
        "        super().__init__()\n",
        "        self.num_hiddens = num_hiddens\n",
        "        self.embedding = nn.Embedding(vocab_size, num_hiddens)\n",
        "        self.pos_encoding = PositionalEncoding(num_hiddens, dropout)\n",
        "        self.blks = nn.Sequential()\n",
        "        for i in range(num_blks):\n",
        "            self.blks.add_module(f\"blk_{i}\",\n",
        "              TransformerEncoderBlock(num_hiddens, ffn_num_hiddens, num_heads, dropout, use_bias))\n",
        "\n",
        "    def forward(self, X, valid_lens):\n",
        "        # Since positional encodings have values between -1 and +1, the embeddings\n",
        "        # are rescaled before they are summed up\n",
        "        X = self.pos_encoding(self.embedding(X) * torch.sqrt(torch.tensor(self.num_hiddens)))\n",
        "        self.attention_weights = [None] * len(self.blks)\n",
        "        for i, blk in enumerate(self.blks):\n",
        "            X = blk(X, valid_lens)\n",
        "            self.attention_weights[i] = blk.attention.attention.attention_weights\n",
        "        return X\n",
        "\n",
        "encoder = TransformerEncoder(200, 24, 48, 8, 2, 0.5)\n",
        "d2l.check_shape(encoder(torch.ones((2, 100), dtype=torch.long), valid_lens), (2, 100, 24))"
      ],
      "metadata": {
        "id": "GR9FEbldMe_5"
      },
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "class TransformerDecoderBlock(nn.Module):\n",
        "    \"\"\"The i-th block in the transformer decoder\"\"\"\n",
        "    def __init__(self, num_hiddens, ffn_num_hiddens, num_heads, dropout, i):\n",
        "        super().__init__()\n",
        "        self.i = i\n",
        "        self.attention1 = MultiHeadAttention(num_hiddens, num_heads, dropout)\n",
        "        self.addnorm1 = AddNorm(num_hiddens, dropout)\n",
        "        self.attention2 = MultiHeadAttention(num_hiddens, num_heads, dropout)\n",
        "        self.addnorm2 = AddNorm(num_hiddens, dropout)\n",
        "        self.ffn = PositionwiseFFN(ffn_num_hiddens, num_hiddens)\n",
        "        self.addnorm3 = AddNorm(num_hiddens, dropout)\n",
        "\n",
        "    def forward(self, X, state):\n",
        "        enc_outputs, enc_valid_lens = state[0], state[1]\n",
        "        # During training, all the tokens of any output sequence are processed\n",
        "        # at the same time, so state[2][self.i] is None as initialized. When\n",
        "        # decoding any output sequence token by token during prediction,\n",
        "        # state[2][self.i] contains representations of the decoded output at\n",
        "        # the i-th block up to the current time step\n",
        "        if state[2][self.i] is None:\n",
        "            key_values = X\n",
        "        else:\n",
        "            key_values = torch.cat((state[2][self.i], X), dim=1)\n",
        "        state[2][self.i] = key_values\n",
        "        if self.training:\n",
        "            batch_size, num_steps, _ = X.shape\n",
        "            # Shape of dec_valid_lens: (batch_size, num_steps), where every\n",
        "            # row is [1, 2, ..., num_steps]\n",
        "            dec_valid_lens = torch.arange(\n",
        "                1, num_steps + 1, device=X.device).repeat(batch_size, 1)\n",
        "        else:\n",
        "            dec_valid_lens = None\n",
        "        # Self-attention\n",
        "        X2 = self.attention1(X, key_values, key_values, dec_valid_lens)\n",
        "        Y = self.addnorm1(X, X2)\n",
        "        # Encoder-decoder attention. Shape of enc_outputs:\n",
        "        # (batch_size, num_steps, num_hiddens)\n",
        "        Y2 = self.attention2(Y, enc_outputs, enc_outputs, enc_valid_lens)\n",
        "        Z = self.addnorm2(Y, Y2)\n",
        "        Z2 = self.ffn(Z)\n",
        "        return self.addnorm3(Z, Z2), state\n",
        "\n",
        "# Test\n",
        "decoder_blk = TransformerDecoderBlock(24, 48, 8, 0.5, 0)\n",
        "X = torch.ones((2, 100, 24))\n",
        "state = [encoder_blk(X, valid_lens), valid_lens, [None]]\n",
        "d2l.check_shape(decoder_blk(X, state)[0], X.shape)"
      ],
      "metadata": {
        "id": "h-0kKYEwPxsI"
      },
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "class TransformerDecoder(d2l.AttentionDecoder):\n",
        "    def __init__(self, vocab_size, num_hiddens, ffn_num_hiddens, num_heads,\n",
        "                 num_blks, dropout):\n",
        "        super().__init__()\n",
        "        self.num_hiddens = num_hiddens\n",
        "        self.num_blks = num_blks\n",
        "        self.embedding = nn.Embedding(vocab_size, num_hiddens)\n",
        "        self.pos_encoding = d2l.PositionalEncoding(num_hiddens, dropout)\n",
        "        self.blks = nn.Sequential()\n",
        "        for i in range(num_blks):\n",
        "            self.blks.add_module(\"block\"+str(i), TransformerDecoderBlock(\n",
        "                num_hiddens, ffn_num_hiddens, num_heads, dropout, i))\n",
        "        self.dense = nn.LazyLinear(vocab_size)\n",
        "\n",
        "    def init_state(self, enc_outputs, enc_valid_lens):\n",
        "        return [enc_outputs, enc_valid_lens, [None] * self.num_blks]\n",
        "\n",
        "    def forward(self, X, state):\n",
        "        X = self.pos_encoding(self.embedding(X) * math.sqrt(self.num_hiddens))\n",
        "        self._attention_weights = [[None] * len(self.blks) for _ in range (2)]\n",
        "        for i, blk in enumerate(self.blks):\n",
        "            X, state = blk(X, state)\n",
        "            # Decoder self-attention weights\n",
        "            self._attention_weights[0][\n",
        "                i] = blk.attention1.attention.attention_weights\n",
        "            # Encoder-decoder attention weights\n",
        "            self._attention_weights[1][\n",
        "                i] = blk.attention2.attention.attention_weights\n",
        "        return self.dense(X), state\n",
        "\n",
        "    @property\n",
        "    def attention_weights(self):\n",
        "        return self._attention_weights"
      ],
      "metadata": {
        "id": "_nrMxNNnVHZ4"
      },
      "execution_count": 19,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "data = d2l.MTFraEng(batch_size=128)\n",
        "num_hiddens, num_blks, dropout = 256, 2, 0.2\n",
        "ffn_num_hiddens, num_heads = 64, 4\n",
        "encoder = TransformerEncoder(\n",
        "    len(data.src_vocab), num_hiddens, ffn_num_hiddens, num_heads,\n",
        "    num_blks, dropout)\n",
        "decoder = TransformerDecoder(\n",
        "    len(data.tgt_vocab), num_hiddens, ffn_num_hiddens, num_heads,\n",
        "    num_blks, dropout)\n",
        "model = d2l.Seq2Seq(encoder, decoder, tgt_pad=data.tgt_vocab['<pad>'],\n",
        "                    lr=0.0015)\n",
        "trainer = d2l.Trainer(max_epochs=30, gradient_clip_val=1, num_gpus=1)\n",
        "trainer.fit(model, data)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "RyZ8SwhVVnEP",
        "outputId": "3e0bb282-6fbb-4f8a-e427-87fdd556e84f"
      },
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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      "source": [
        "engs = ['go .', 'i lost .', 'he\\'s calm .', 'i\\'m home .']\n",
        "fras = ['va !', 'j\\'ai perdu .', 'il est calme .', 'je suis chez moi .']\n",
        "preds, _ = model.predict_step(\n",
        "    data.build(engs, fras), d2l.try_gpu(), data.num_steps)\n",
        "for en, fr, p in zip(engs, fras, preds):\n",
        "    translation = []\n",
        "    for token in data.tgt_vocab.to_tokens(p):\n",
        "        if token == '<eos>':\n",
        "            break\n",
        "        translation.append(token)\n",
        "    print(f'{en} => {translation}, bleu,'\n",
        "          f'{d2l.bleu(\" \".join(translation), fr, k=2):.3f}')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aQkD5MNtVtgl",
        "outputId": "2471967c-d165-4c2c-8c0d-6497146a2988"
      },
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "go . => ['va', '!'], bleu,1.000\n",
            "i lost . => [\"j'ai\", 'perdu', '.'], bleu,1.000\n",
            "he's calm . => ['il', 'est', 'mouillé', '.'], bleu,0.658\n",
            "i'm home . => ['je', 'suis', 'chez', 'moi', '.'], bleu,1.000\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "_, dec_attention_weights = model.predict_step(\n",
        "    data.build([engs[-1]], [fras[-1]]), d2l.try_gpu(), data.num_steps, True)\n",
        "enc_attention_weights = torch.cat(model.encoder.attention_weights, 0)\n",
        "print(enc_attention_weights.shape)\n",
        "shape = (num_blks, num_heads, -1, data.num_steps)\n",
        "enc_attention_weights = enc_attention_weights.reshape(shape)\n",
        "print(enc_attention_weights.shape)\n",
        "d2l.check_shape(enc_attention_weights,\n",
        "                (num_blks, num_heads, data.num_steps, data.num_steps))\n",
        "\n",
        "d2l.show_heatmaps(\n",
        "    enc_attention_weights.cpu(), xlabel='Key positions',\n",
        "    ylabel='Query positions', titles=['Head %d' % i for i in range(1, 5)],\n",
        "    figsize=(7, 3.5))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 368
        },
        "id": "6ONaWMK4WzdF",
        "outputId": "b907b675-9417-4144-9b66-573a6aa7d5f2"
      },
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "torch.Size([8, 9, 9])\n",
            "torch.Size([2, 4, 9, 9])\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 700x350 with 9 Axes>"
            ],
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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Decoder heatmap visualizations\n",
        "I just copy pasted these, and did not read."
      ],
      "metadata": {
        "id": "Le59nSiAYXhp"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "dec_attention_weights_2d = [head[0].tolist()\n",
        "                            for step in dec_attention_weights\n",
        "                            for attn in step for blk in attn for head in blk]\n",
        "dec_attention_weights_filled = torch.tensor(\n",
        "    pd.DataFrame(dec_attention_weights_2d).fillna(0.0).values)\n",
        "shape = (-1, 2, num_blks, num_heads, data.num_steps)\n",
        "dec_attention_weights = dec_attention_weights_filled.reshape(shape)\n",
        "dec_self_attention_weights, dec_inter_attention_weights = \\\n",
        "    dec_attention_weights.permute(1, 2, 3, 0, 4)\n",
        "\n",
        "d2l.check_shape(dec_self_attention_weights,\n",
        "                (num_blks, num_heads, data.num_steps, data.num_steps))\n",
        "d2l.check_shape(dec_inter_attention_weights,\n",
        "                (num_blks, num_heads, data.num_steps, data.num_steps))\n",
        "\n",
        "d2l.show_heatmaps(\n",
        "    dec_self_attention_weights[:, :, :, :],\n",
        "    xlabel='Key positions', ylabel='Query positions',\n",
        "    titles=['Head %d' % i for i in range(1, 5)], figsize=(7, 3.5))\n",
        "\n",
        "d2l.show_heatmaps(\n",
        "    dec_inter_attention_weights, xlabel='Key positions',\n",
        "    ylabel='Query positions', titles=['Head %d' % i for i in range(1, 5)],\n",
        "    figsize=(7, 3.5))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 648
        },
        "id": "cpBG0w2eW32C",
        "outputId": "7093329f-0428-451a-e7cd-ddf00f47cf23"
      },
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 700x350 with 9 Axes>"
            ],
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