The attention mechanism was introduced to improve the performance of the encoder-decoder model for machine translation. The idea behind the attention mechanism was to permit the decoder to utilize the most relevant parts of the input sequence in a flexible manner, by a weighted combination of all of the encoded input vectors, with the most relevant vectors being attributed the highest weights.\u00a0<\/span><\/p>\n In this tutorial, you will discover the attention mechanism and its implementation.\u00a0<\/span><\/p>\n After completing this tutorial, you will know:<\/p>\n Let\u2019s get started.\u00a0<\/span><\/p>\n The Attention Mechanism from Scratch This tutorial is divided into three parts; they are:<\/p>\n The attention mechanism was introduced by Bahdanau et al. (2014)<\/a>, to address the bottleneck problem that arises with the use of a fixed-length encoding vector, where the decoder would have limited access to the information provided by the input. This is thought to become especially problematic for long and\/or complex sequences, where the dimensionality of their representation would be forced to be the same as for shorter or simpler sequences.<\/p>\n We had seen<\/a> that Bahdanau et al.\u2019s attention mechanism<\/i> is divided into the step-by-step computations of the alignment scores<\/i>, the weights<\/i> and the context vector<\/i>:<\/p>\n $$e_{t,i} = a(mathbf{s}_{t-1}, mathbf{h}_i)$$<\/p>\n $$alpha_{t,i} = text{softmax}(e_{t,i})$$<\/p>\n $$mathbf{c}_t = sum_{i=1}^T alpha_{t,i} mathbf{h}_i$$<\/p>\n Bahdanau et al. had implemented an RNN for both the encoder and decoder.\u00a0<\/span><\/p>\n However, the attention mechanism can be re-formulated into a general form that can be applied to any sequence-to-sequence (abbreviated to seq2seq) task, where the information may not necessarily be related in a sequential fashion.\u00a0<\/span><\/p>\n In other words, the database doesn\u2019t have to consist of the hidden RNN states at different steps, but could contain any kind of information instead.<\/i><\/p>\n \u2013 Advanced Deep Learning with Python<\/a>, 2019.<\/p>\n<\/blockquote>\n The general attention mechanism makes use of three main components, namely the queries<\/i>, $mathbf{Q}$, the keys<\/i>, $mathbf{K}$, and the values<\/i>, $mathbf{V}$.\u00a0<\/span><\/p>\n If we had to compare these three components to the attention mechanism as proposed by Bahdanau et al., then the query would be analogous to the previous decoder output, $mathbf{s}_{t-1}$, while the values would be analogous to the encoded inputs, $mathbf{h}_i$. In the Bahdanau attention mechanism, the keys and values are the same vector.<\/p>\n In this case,\u00a0we can think of the vector\u00a0$mathbf{s}_{t-1}$\u00a0as a\u00a0query\u00a0executed against a database of key-value pairs, where\u00a0the keys are vectors and\u00a0the hidden states\u00a0$mathbf{h}_i$\u00a0are the values.<\/i><\/p>\n \u2013 Advanced Deep Learning with Python<\/a>, 2019.<\/p>\n<\/blockquote>\n The general attention mechanism then performs the following computations:<\/p>\n $$e_{mathbf{q},mathbf{k}_i} = mathbf{q} cdot mathbf{k}_i$$<\/p>\n $$alpha_{mathbf{q},mathbf{k}_i} = text{softmax}(e_{mathbf{q},mathbf{k}_i})$$<\/p>\n $$text{attention}(mathbf{q}, mathbf{K}, mathbf{V}) = sum_i alpha_{mathbf{q},mathbf{k}_i} mathbf{v}_{mathbf{k}_i}$$<\/p>\n Within the context of machine translation, each word in an input sentence would be attributed its own query, key and value vectors. These vectors are generated by multiplying the encoder\u2019s representation of the specific word under consideration, with three different weight matrices that would have been generated during training.\u00a0<\/span><\/p>\n In essence, when the generalized attention mechanism is presented with a sequence of words, it takes the query vector attributed to some specific word in the sequence and scores it against each key in the database. In doing so, it captures how the word under consideration relates to the others in the sequence. Then it scales the values according to the attention weights (computed from the scores), in order to retain focus on those words that are relevant to the query. In doing so, it produces an attention output for the word under consideration.\u00a0<\/span><\/p>\n In this section, we will explore how to implement the general attention mechanism using the NumPy and SciPy libraries in Python.\u00a0<\/span><\/p>\n For simplicity, we will initially calculate the attention for the first word in a sequence of four. We will then generalize the code to calculate an attention output for all four words in matrix form.\u00a0<\/span><\/p>\n Hence, let\u2019s start by first defining the word embeddings of the four different words for which we will be calculating the attention. In actual practice, these word embeddings would have been generated by an encoder, however for this particular example we shall be defining them manually.\u00a0<\/span><\/p>\n The next step generates the weight matrices, which we will eventually be multiplying to the word embeddings to generate the queries, keys and values. Here, we shall be generating these weight matrices randomly, however in actual practice these would have been learned during training.\u00a0<\/span><\/p>\n Notice how the number of rows of each of these matrices is equal to the dimensionality of the word embeddings (which in this case is three) to allow us to perform the matrix multiplication.<\/p>\n Subsequently, the query, key and value vectors for each word are generated by multiplying each word embedding by each of the weight matrices.\u00a0<\/span><\/p>\n Considering only the first word for the time being, the next step scores its query vector against all of the key vectors using a dot product operation.\u00a0<\/span><\/p>\n The score values are subsequently passed through a softmax operation to generate the weights. Before doing so, it is common practice to divide the score values by the square root of the dimensionality of the key vectors (in this case, three), to keep the gradients stable.\u00a0<\/span><\/p>\n Finally, the attention output is calculated by a weighted sum of all four value vectors.\u00a0<\/span><\/p>\n For faster processing, the same calculations can be implemented in matrix form to generate an attention output for all four words in one go:<\/p>\n This section provides more resources on the topic if you are looking to go deeper.<\/p>\n In this tutorial, you discovered the attention mechanism and its implementation.<\/p>\n Specifically, you learned:<\/p>\n Do you have any questions? The post The Attention Mechanism from Scratch<\/a> appeared first on Machine Learning Mastery<\/a>.<\/p>\n<\/div>\n Go to Source<\/a><\/p>\n","protected":false},"excerpt":{"rendered":" Author: Stefania Cristina The attention mechanism was introduced to improve the performance of the encoder-decoder model for machine translation. 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Photo by Nitish Meena<\/a>, some rights reserved.<\/p>\n<\/div>\nTutorial Overview<\/b><\/h2>\n
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The Attention Mechanism<\/b><\/h2>\n
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The General Attention Mechanism<\/b><\/h2>\n
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The General Attention Mechanism with NumPy and SciPy<\/b><\/h2>\n
# encoder representations of four different words\r\nword_1 = array([1, 0, 0])\r\nword_2 = array([0, 1, 0])\r\nword_3 = array([1, 1, 0])\r\nword_4 = array([0, 0, 1])<\/pre>\n
...\r\n# generating the weight matrices\r\nrandom.seed(42) # to allow us to reproduce the same attention values\r\nW_Q = random.randint(3, size=(3, 3))\r\nW_K = random.randint(3, size=(3, 3))\r\nW_V = random.randint(3, size=(3, 3))<\/pre>\n
...\r\n# generating the queries, keys and values\r\nquery_1 = word_1 @ W_Q\r\nkey_1 = word_1 @ W_K\r\nvalue_1 = word_1 @ W_V\r\n\r\nquery_2 = word_2 @ W_Q\r\nkey_2 = word_2 @ W_K\r\nvalue_2 = word_2 @ W_V\r\n\r\nquery_3 = word_3 @ W_Q\r\nkey_3 = word_3 @ W_K\r\nvalue_3 = word_3 @ W_V\r\n\r\nquery_4 = word_4 @ W_Q\r\nkey_4 = word_4 @ W_K\r\nvalue_4 = word_4 @ W_V<\/pre>\n
...\r\n# scoring the first query vector against all key vectors\r\nscores = array([dot(query_1, key_1), dot(query_1, key_2), dot(query_1, key_3), dot(query_1, key_4)])<\/pre>\n
...\r\n# computing the weights by a softmax operation\r\nweights = softmax(scores \/ key_1.shape[0] ** 0.5)<\/pre>\n
...\r\n# computing the attention by a weighted sum of the value vectors\r\nattention = (weights[0] * value_1) + (weights[1] * value_2) + (weights[2] * value_3) + (weights[3] * value_4)\r\n\r\nprint(attention)<\/pre>\n<\/p>\n
[0.98522025 1.74174051 0.75652026]<\/pre>\n
from numpy import array\r\nfrom numpy import random\r\nfrom numpy import dot\r\nfrom scipy.special import softmax\r\n\r\n# encoder representations of four different words\r\nword_1 = array([1, 0, 0])\r\nword_2 = array([0, 1, 0])\r\nword_3 = array([1, 1, 0])\r\nword_4 = array([0, 0, 1])\r\n\r\n# stacking the word embeddings into a single array\r\nwords = array([word_1, word_2, word_3, word_4])\r\n\r\n# generating the weight matrices\r\nrandom.seed(42)\r\nW_Q = random.randint(3, size=(3, 3))\r\nW_K = random.randint(3, size=(3, 3))\r\nW_V = random.randint(3, size=(3, 3))\r\n\r\n# generating the queries, keys and values\r\nQ = words @ W_Q\r\nK = words @ W_K\r\nV = words @ W_V\r\n\r\n# scoring the query vectors against all key vectors\r\nscores = Q @ K.transpose()\r\n\r\n# computing the weights by a softmax operation\r\nweights = softmax(scores \/ K.shape[1] ** 0.5, axis=1)\r\n\r\n# computing the attention by a weighted sum of the value vectors\r\nattention = weights @ V\r\n\r\nprint(attention)<\/pre>\n<\/p>\n
[[0.98522025 1.74174051 0.75652026]\r\n [0.90965265 1.40965265 0.5 ]\r\n [0.99851226 1.75849334 0.75998108]\r\n [0.99560386 1.90407309 0.90846923]]<\/pre>\n<\/p>\n
Further Reading<\/b><\/h2>\n
Books<\/b><\/h3>\n
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Papers<\/b><\/h3>\n
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Summary<\/b><\/h2>\n
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\nAsk your questions in the comments below and I will do my best to answer.<\/p>\n