TransformerI.ipynb

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      "name": "TransformerI.ipynb",
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      "source": [
        "<a href=\"https://colab.research.google.com/github/zaidalyafeai/AttentioNN/blob/master/TransformerI.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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          "height": 221
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      },
      "source": [
        "!pip install sentencepiece\n",
        "!wget https://raw.githubusercontent.com/khvorostin/useful-english-phrases/master/07-literary-expressions.txt -O expressions.txt"
      ],
      "execution_count": 1,
      "outputs": [
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          "text": [
            "Requirement already satisfied: sentencepiece in /usr/local/lib/python3.6/dist-packages (0.1.83)\n",
            "--2019-10-24 21:51:41--  https://raw.githubusercontent.com/khvorostin/useful-english-phrases/master/07-literary-expressions.txt\n",
            "Resolving raw.githubusercontent.com (raw.githubusercontent.com)... 151.101.0.133, 151.101.64.133, 151.101.128.133, ...\n",
            "Connecting to raw.githubusercontent.com (raw.githubusercontent.com)|151.101.0.133|:443... connected.\n",
            "HTTP request sent, awaiting response... 200 OK\n",
            "Length: 57085 (56K) [text/plain]\n",
            "Saving to: ‘expressions.txt’\n",
            "\n",
            "expressions.txt     100%[===================>]  55.75K  --.-KB/s    in 0.02s   \n",
            "\n",
            "2019-10-24 21:51:41 (2.68 MB/s) - ‘expressions.txt’ saved [57085/57085]\n",
            "\n"
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          "name": "stdout"
        }
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    {
      "cell_type": "code",
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        "colab": {
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          "height": 34
        }
      },
      "source": [
        "%tensorflow_version 2.x\n",
        "import tensorflow as tf\n",
        "import numpy as np\n",
        "import sentencepiece as spm\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "TensorFlow 2.x selected.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iaxuWASijLzE",
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      "source": [
        "## Introduction \n",
        "\n",
        "Until 2017, natural language processing (NLP) was dependent on using recurrent neural networks (RNNs) which has many shortcomings: 1. no support for parallelization, 2. vanishing gradient for long sequences. For instance, in translation which is mostly seq2seq architectures, both the encoder and decoder consists of RNNs. In 2014, Bahdanau et al , suggested the use of a mechanism called \"attention\" to resolve the bottleneck of seq2seq models [1]. However, RNNs were still the main building blocks for such models and others like image captioning by Kelvin Xu et al [2]. The use of attention in [1, 2] gave a better visualization of such models. But, what if we get rid of all RNNs in the first place. Well, that is a big claim, but it worked really well in 2017. The paper was rightly called \"Attention is all you need\" by Vaswani et al. from Google AI. This is a breakthrough, since RNNs are very slow which makes parallel computations easy to implement. The model was called 'Transfomer model', in this notebook we will explain in details its main components. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EkUl87Y5h2bl",
        "colab_type": "text"
      },
      "source": [
        "## Transformer Encoder\n",
        "\n",
        "The transofmer, like other architectures for machine translation consists of encoder and decoder modules. In this notebook, we will only focus on the encoder, and in part II will focus on the decoder. \n",
        "\n",
        "![alt text](https://machinetalk.org/wp-content/uploads/2019/04/encoder.png)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XmrbrXgsYEYH",
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      },
      "source": [
        "## Tokenization\n",
        "\n",
        "Given a set of statements we would like to convert these statements to a set of integers. However, this will result in a huge vocabulary which makes training very difficult. Google offers [SentencePiece](https://github.com/google/sentencepiece) which is a model that could be trained to generate tokens for arbitrary languages. From the name, you could deduce that the model can generate pieces of words as well. In this example, we will train a model on a set of expressions from the English language. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9UVgskFrbMaO",
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        "outputId": "c10d2cf3-fd32-41c4-d854-c3ab814576a8",
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      },
      "source": [
        "# train the model on the epxressions with a fixed vocabulary size, this will create a model named en.model \n",
        "spm.SentencePieceTrainer.Train('--input=expressions.txt --model_prefix=en --vocab_size=1000 --model_type=bpe')\n",
        "\n",
        "# create the process object then load the trained model\n",
        "sp = spm.SentencePieceProcessor()\n",
        "sp.load('en.model')"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Z32M7EQ8pOQG",
        "colab_type": "text"
      },
      "source": [
        "Let us try the model on an arbitrary statement, note how the tokens can be pieces of words"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "S_qFLO2CpSbU",
        "colab_type": "code",
        "outputId": "71fd3c10-5f37-4d93-cdde-cbc0e2525ddf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "sp.encode_as_pieces('A calmness settled on his spirit')"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "['▁A', '▁calm', 'ness', '▁s', 'et', 't', 'led', '▁on', '▁his', '▁spirit']"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "N2pbXnG7pwhQ",
        "colab_type": "text"
      },
      "source": [
        "Now, let us load our dataset and convert them to padded vectors"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Iac8SK5bbuI9",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# load the expressions \n",
        "with open('expressions.txt', 'r') as f:\n",
        "  sentences = f.read().splitlines()\n",
        "\n",
        "# convert the vectors to ids \n",
        "sequences = []\n",
        "max_length = 0\n",
        "\n",
        "for sentence in sentences:\n",
        "  sequence = sp.encode_as_ids(sentence)\n",
        "  sequences.append(sequence)\n",
        "  max_length = max(max_length, len(sequence))\n",
        "\n",
        "# pad the vectors according to the longest sequence \n",
        "x = tf.keras.preprocessing.sequence.pad_sequences(sequences, maxlen = max_length)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1JjjtCUqe9Zh",
        "colab_type": "text"
      },
      "source": [
        "## Parameters\n",
        "A set of parameters that are taken from the original paper. Don't worry about them right now. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fiSSscLYoxbt",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# dimension of the vectors between consecutive modules layers \n",
        "dm = 512\n",
        "\n",
        "# number of heads in attention modules\n",
        "h = 8 \n",
        "\n",
        "# dimensnion of queries and keys \n",
        "dk = dm // 8\n",
        "\n",
        "# dimension of values \n",
        "dv = dm // 8 \n",
        "\n",
        "# sequence length \n",
        "n = max_length \n",
        "\n",
        "# size of vocabulary \n",
        "vocab_size = 1000\n",
        "\n",
        "# number of neurons in the feed forward network \n",
        "dff = 2048"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YSVKuZZfXz3H",
        "colab_type": "text"
      },
      "source": [
        "## Encoding\n",
        "Since the transformer model has no meaning of sequences of operations (they are mostly parallel) for a set of words, it is important that we keep track of the order input words. To do that, we use positional encoding. Before doing that, we will first pass the vectors through an embedding layer"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FDFnZhaUgiC3",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "e = tf.keras.layers.Embedding(vocab_size, dm)(x)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eZhKNkIhrH1C",
        "colab_type": "text"
      },
      "source": [
        "To encode the position of each word within a sequence of models we use sines and cosines. These encodings are just added to the embedding layer output so no change in the shape of e: [None, dm]. \n",
        "\n",
        "Given pos as the position within the sequence which takes the values $0 \\cdots n-1$ and $i$ as the position within the embedding dimension which takes values $0 \\cdots d_m-1$. We evaluate the encoded position for even and odd values as "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "m-mcPNbN1KsS",
        "colab_type": "text"
      },
      "source": [
        "$$\\text{PE}(\\text{pos},2i)= \\sin\\left(\\frac{\\text{pos}}{10000^{2i/d_{model}}}\\right)$$\n",
        "\n",
        "$$\\text{PE}(\\text{pos},2i+1)= \\cos\\left(\\frac{\\text{pos}}{10000^{2i/d_{model}}}\\right)$$\n",
        "\n",
        "We can combine the two formulas as \n",
        "\n",
        "$$\\text{PE}(\\text{pos},i)= \\sin\\left(\\frac{\\text{pos}}{10000^{(i-g(i))/d_{model}}}+ g(i) \\times \\frac{\\pi}{2}\\right)$$\n",
        "\n",
        "Where $g(i) = i \\,\\% \\,2$ which takes 0 for even values and 1 for odd values. Note that $\\sin(x + \\pi/2) = \\cos(x)$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ogeEJ19D1Hql",
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      "source": [
        "def g(ids):\n",
        "  return ids % 2\n",
        "\n",
        "def positional_encoding(x):\n",
        "\n",
        "  # 1. create positions within sequence and ids within dm \n",
        "  # out ids: [1, dm] pos: [n, 1]\n",
        "  ids = tf.expand_dims(tf.range(0, dm), 0)\n",
        "  pos = tf.expand_dims(tf.range(0, n), 1)\n",
        "\n",
        "  # 2. create numerator and denominator\n",
        "  # inp ids: [1, dm] pos: [n, 1] \n",
        "  # out den: [1, dm] num: [n, 1]\n",
        "  den = tf.pow(10000.0, tf.cast((ids - g(ids))/ dm, tf.float32))\n",
        "  num = tf.cast(pos, tf.float32)\n",
        "\n",
        "  # 3. division \n",
        "  # inp num: [n, 1] den: [1, dm] \n",
        "  # out encoding: [n, dm]\n",
        "  encoding = tf.sin(tf.divide(num, den)  + tf.cast(g(ids), tf.float32)* (np.pi/2))\n",
        "  return x + encoding\n",
        "  "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_-RkWoOeffxD",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "z = positional_encoding(e)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "A3RE5xk3veFD",
        "colab_type": "text"
      },
      "source": [
        "Let us visualize the encoding for a specific sequence of words. As we see from the figure there is a unique pattern for the sequence position in the y-axis. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "socxYh9DXeLV",
        "colab_type": "code",
        "outputId": "64e1c964-8780-46ce-829e-05f241e99864",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 320
        }
      },
      "source": [
        "plt.figure(figsize = (10, 5))\n",
        "plt.pcolormesh(z[0])\n",
        "plt.ylim((0, max_length))\n",
        "plt.colorbar()\n",
        "plt.show()"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Byfo+Og7XWDhF0HqDUzYdQ6Ii8VCZUAyNQW8W1z+yyL8tns3FPTvpNlA+6sVu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\n",
            "text/plain": [
              "<Figure size 720x360 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Npqxue4Ogyc_",
        "colab_type": "text"
      },
      "source": [
        "## Multi-head Self-attention"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4qRm-ll7VxLR",
        "colab_type": "text"
      },
      "source": [
        "![alt text](https://mchromiak.github.io/articles/2017/Sep/12/Transformer-Attention-is-all-you-need/img/MultiHead.png)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dRqD7sWxXfsj",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "Let us start by the output of the positional encoding function $z \\in \\mathbb{R}^{n \\times d_m}$. Note that, for simplicity we assume that we just have one batch. From the value $z$ we extract three types of vectors by applying three dense layers. The types are $K \\in \\mathbb{R}^{n \\times d_k} Q \\in \\mathbb{R}^{n \\times d_k}$ and $V \\in \\mathbb{R}^{n \\times d_v}$ called keys, queries and values respectively. In simple terms, the keys are used by the query vector to search for values. In attention, we are trying to find the closest key-value pair to the given query vector. In other words, we are trying to search for words that are closer in meaning or may refer to in the current context. For instance, in the statement `John is smart and handsome` we expect that the query words `smart` and `handsome` to have an high attention value for the key word `John`. To evaluate closensess, we a scaled dot product \n",
        "\n",
        "$$\\text{Attention}(Q, K, V) = \\text{softmax}\\left( \\frac{QK^T}{\\sqrt{d_k}}\\right)V$$\n",
        "\n",
        "This function will result in a weight vector for each query word multiplied by the value vector. For instance, for the query word `smart` we expect something like `[0.3, 0.05, 0.1, 0.05, 0.55] x v`. Hence, smaller values of the attention weight vector will result in smaller values and hence lower gradient. The authors, realized that for larger values the dot product might grow large so they divide by $\\sqrt{d_k}$ as a normalizing factor inside the softmax function. In general, this is called additive attention which is usually preferred because is fast and space efficient because we can use highly optimized matrices product to compute it. Note that, in the definition we assume that $Q, K, V$ are matrices hence it can be computed really fast for a large sequence and even batch size. There exists another form of attention, which is called product attention which was used in [1, 2]. \n",
        "\n",
        "In general this approach is called self-attention because it uses the same input vector $z$ to generate the query, key and value vectors. In the paper, the authors suggest using self-attention multiple times i.e multiple head attention. This is done by repeating the same operation multiple times which in general gave more robust results. They use $h = 8$  and then concatenate the output at the end.  \n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4UVzDMR69VXv",
        "colab_type": "text"
      },
      "source": [
        "In the following function we will create a single head attention operation. The input vector has dimensions $z \\in \\mathbb{R}^{\\text{None} \\times n \\times d_m}$ and the output $H \\in \\mathbb{R}^{\\text{None} \\times n \\times d_m}$ note how we use $\\text{None}$ to represent the batch size which could be of variable size. To make the code clearer, for each operation I show the input and output dimension shapes. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_RO6dc0biCk6",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def single_head_attention(z):\n",
        "\n",
        "  # 1. projection \n",
        "  # inp z: [None, n, dm]  \n",
        "  # out Q: [None, n, dk]  K: [None, n, dk] V: [None, n, dv]\n",
        "  V = tf.keras.layers.Dense(units = dv)(z)\n",
        "  Q = tf.keras.layers.Dense(units = dk)(z)\n",
        "  K = tf.keras.layers.Dense(units = dk)(z)\n",
        "\n",
        "  # 2. scaled dot product \n",
        "  # inp Q:  [None, n, dk] K: [None, n, dk] \n",
        "  # out score : [None, n, n] \n",
        "  score = tf.matmul(Q, K, transpose_b=True)/ tf.sqrt(dk*1.0)\n",
        "\n",
        "  # 3. evaluate the weights \n",
        "  # inp score: [None, n, n]\n",
        "  # out W: [None, n, n]\n",
        "  W = tf.nn.softmax(score, axis = 1)\n",
        "\n",
        "  # 4. evaluate the context vector \n",
        "  # inp W: [None, n, n] V: [None, n, dv]\n",
        "  # out H: [None, n, dv]\n",
        "  H = tf.matmul(W, V)\n",
        "  return H"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RwwXX1sB96C2",
        "colab_type": "text"
      },
      "source": [
        "After applying single attention we repeat the operation multiple times and then concatenate the output "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "qRCgvC__NKDJ",
        "colab": {}
      },
      "source": [
        "def multi_head_attention(z):\n",
        "\n",
        "  # according to the paper \"We found it beneficial to linearly project the queries, keys \n",
        "  # and values h times with different, learned linear projections\n",
        "  # to dk, dk and dv dimensions, respectively\".\n",
        "\n",
        "  Hs = []\n",
        "\n",
        "  # 1. apply h times \n",
        "  # inp z : [None, n, dm]\n",
        "  # out Hs: [[None, n, dv], ..., [None, n, dv]]\n",
        "  for i in range(0, h):\n",
        "\n",
        "    # single head attention \n",
        "    # inp z: [None, n, dm]\n",
        "    # out H: [None, n, dv]\n",
        "    H = single_head_attention(z)\n",
        "\n",
        "    Hs.append(H)\n",
        "\n",
        "  # 2. concatenate \n",
        "  # inp Hs: [[None, n, dv], ..., [None, n, dv]] \n",
        "  # out z : [None, n, dv * 8] => [None, n , dm]\n",
        "  z = tf.concat(Hs, axis = -1)\n",
        "  return z "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FliBr-UZ-AOP",
        "colab_type": "text"
      },
      "source": [
        "Finally, the encoder layer will be ready by applying fully connected layers. Note that the authors used residual connections $$\\text{LayerNorm}(x + \\text{Sublayer}(x))$$ "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "r8Z4jQRLhD01",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def EncoderLayer(z):\n",
        "\n",
        "  # 1. self-attention \n",
        "  # inp z : [None, n, dm]\n",
        "  # out dz: [None, n, dm]\n",
        "  dz = multi_head_attention(z)\n",
        "\n",
        "  # 2. normalization\n",
        "  # inp z: [None, n, dm] dz: [None, n, dm]\n",
        "  # out z: [None, n, dm]\n",
        "  z = tf.keras.layers.LayerNormalization()(z + dz)\n",
        "\n",
        "  # 3. feed forward \n",
        "  # inp z : [None, n, dm]\n",
        "  # out dz: [None, n, dm]\n",
        "  dz = tf.keras.layers.Dense(units = dff, activation = 'relu')(z)\n",
        "  dz = tf.keras.layers.Dense(units = dm)(dz)\n",
        "\n",
        "  # 4. normalization \n",
        "  # inp z: [None, n, dm] dz: [None, n, dm]\n",
        "  # out z: [None, n, dm]\n",
        "  z = tf.keras.layers.LayerNormalization()(z + dz)\n",
        "\n",
        "  return z "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VVRZJd5WnR_Y",
        "colab_type": "code",
        "outputId": "c7d1b50c-1bd6-4ec4-bbba-2e24cd1634ba",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "EncoderLayer(z).shape"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "TensorShape([1423, 63, 512])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6ecSrhheaNAM",
        "colab_type": "text"
      },
      "source": [
        "## References\n",
        "\n",
        "1. [Neural Machine Translation by Jointly Learning to Align and Translate](https://arxiv.org/abs/1409.0473) \n",
        "2. [Show, Attend and Tell: Neural Image Caption Generation with Visual Attention\n",
        "](https://arxiv.org/abs/1502.03044)\n",
        "3.  [Attention is all you need](https://arxiv.org/abs/1706.03762)\n",
        "4. https://www.tensorflow.org/tutorials/text/transformer"
      ]
    }
  ]
}