Attention Is All You Need

I am reading this paper because it was recommended as part of Ilya Sutskever's approx. 30 papers that he recommended to John Carmack to learn what really matters for machine learning / AI today. This paper introduces a new simple architecture, the Transformer, based solely on attention mechanisms, dispensing with recurrence and convolutions entirely.

Reference Link to PDF of Paper

The dominant sequence transduction models are based on complex recurrent or convolutional neural networks that include an encoder and a decoder. The best performing models also connect the encoder and decoder through an attention mechanism. This paper proposes a new architecture, the Transformer, based solely on attention mechanisms, dispensing with recurrence and convolutions entirely. The results on machine translation tasks show that these models are superior in quality while being more parallelizable and requiring significantly less time to train.

Recurrent neural networks, long short-term memory, and gated recurrent neural networks in particular, have been firmly established as state of the art approaches in sequence modeling and transduction problems such as language modeling and machine translation. Recurrent models typically factor computation along the symbol positions of the input and output sequences. Aligning the positions to steps i computation time, they generate a sequence of hidden states, $h_t$, as a function of the previous state $h_{t-1}$ and the input for position $t$. This inherently sequential nature precludes parallelization within training examples, which becomes critical at longer sequence lengths, as memory constraints limit batching across examples. Attention mechanisms have become an integral part of compelling sequence modeling and transduction models in various tasks, allowing modeling of dependencies without regard to their distance in the input or output sequences. This work proposes the Transformer, a model architecture schewing recurrence and instead relying entirely on an attention mechanism to draw global dependencies between input and output. The Transformer allows for significantly more parallelization and can reach a new state of the art in translation quality after being trained for as little as 12 hours on eight P100 GPUs.

Self-attention is an attention mechanism relating different positions of a single sequence in order to compute a representation of the sequence. Self-attention has been used successfully in a variety of tasks including reading comprehension, abstractive summarization, textual entailment and learning task-independent representations.The Transformer is the first transduction model relying entirely on self-attention to compute representations of its input and output without using sequence-aligned RNNs or convolution.

Most competitive neural sequence transduction models have an encoder-decoder structure. Here, the encoder maps an input sequence of symbol represntations $(x_1,\dots ,x_n)$ to a sequence of continuous representations $\mathbf{\text{z}}=(z_1,\dots ,z_n)$. Given $\mathbf{\text{z}}$, the decoder then generates an output sequence $(y_1,\dots ,y_m)$ of symbols one element at a time, At each step the model is auto-regressive, consuming the previously generated symbols as additional input when generating the next.

The Transformer follows this overall architecture using stacked self-attention and point-wise, fully connected layers for both the encoder and decoder.

Encoder: The encoder is composed of a stack of $N=6$ identical layers. Each layer has two sub-layers. The first is a multi-head self-attention mechanism, and the second is a simple, position-wise fully connected feed-forward network. The architecture employs a residual connection around each of the two sub-layers, followed by layer normalization. The output of each sub-layer is $\text{LayerNorm}(x+\text{Sublayer}(x))$, where $\text{Sublayer}(x)$ is the function implemented by the sub-layer itself. To facilitate these residual connections, all sub-layers in the model, as well as the embedding layers, produce outputs of dimension $d_{\text{model}}=512$.

Decoder: The decoder is also composed of a stack of $N=6$ identical layers. In addition to the two sub-layers in each encoder-layer, the decoder inserts a third sub-layer, which performs multi-head attention over the output of the encoder stack. Similar to the encoder, we employ residual connections around each of the sub-layers, followed by layer normalization. We also modify the self-attention sub-layer in the decoder stack to prevent positions from attending to subsequent positions. This masking, combined with the fact that the output embeddings are offset by one position, ensures that the predictions for position $i$ can depend only on the known outputs less than $i$.

An attention function can be described as mapping a query and a set of key-value pairs to an output, where the query, keys, values, and output are all vectors. The output is computed as a weighted sum of the values, where the weights are assigned to each value is computed by a compatibility function of the query with the corresponding key.

Transformer’s attention is called ”Scaled Dot Product Attention”. The input consists of queries and keys of dimension $d_k$, and values of dimension $d_v$. We compute the dot products of the query and all keys, divide each by $\sqrt{d_k}$ and apply a softmax function to obtain the weights on the values. In practice, we compute the attention function on a set of queries simultaneously, packed together into a matrix $Q$. The keys and values are also packed together into matrices $K$ and $V$. We compute the matrix of outputs as:

The two most commonly used attention functions are additive attention, and dot-product (multiplicative) attention. Dot-product attention is identical to our algorithm, except for the scaling factor of $\frac{1}{\sqrt{d_k}}$. Additive attention computes the compatibility function using a feed-forward network with a single hidden layer. While the two are similar in theoretical complexity, dot-product attention is much faster and more space-efficient in practice, since it can be implemented using optimized matmul code.

Instead of performing a single attention function with $d_m\mathit{odel}$-dimensional keys, values, and queries, it was found to be beneficial to linearly project the queries, keys, and values $h$ times with different, learned linear projections to $d_k$, $d_k$, and $d_v$ dimensions, respectively. On each of these projected versions of queries, keys, and values, we then perform the attention function in parallel, yielding $d_v$-dimensional output values. These are concatenated and once again projected, resulting in the final values. Multi-head attention allows the model to jointly attend to information from different representation subspaces at different positions. With a single attention head, averaging inhibits this.

Where the projections are parameter matrices $W_i^Q\in R^{d_{\text{model}\times d_k}},W_i^K\in R^{d_{\text{model}\times d_k}},W_i^V\in R^{d_{\text{model}\times d_v}}\text{ and }{W}^O\in R^{h{d}_v\times d_{\text{model}}}$ . This work employs 8 attention heads.

The Transormer uses multi-head attention in three different ways:

• In ”encoder-decoder attention” layers, the queries come from the previous decoder layer, and the memory keys and values come from the output of the encoder. This allows every position in the decoder to attend over all positions in the input sequence. This mimics the typical encoder-decoder attention mechanisms in sequence-to-sequence models.
• The encoder contains self-attention layers, In a self-attention layer all of the keys, values, and queries come from the same place, in this case, the output of the previous layer in the encoder. Each position in the encoder can attend to all positions in the previous layer of the encoder.
• Similarly, self-attention layers in the decoder allow each position in the decoder to attend to all positions in the decoder up to and including that position. We need to prevent leftward information flow in the decoder to preserve the auto-regressive property. We implement this inside of scaled dot-product attention by masking out all values in the input of the softmax which correspond to illegal connections.

In addition to attention sub-layers, each of the layers in the decoder and encoder contains a fully connected feed-forward network, which is applied to each position separately and identically. This consists of two linear transformations with a ReLU activation in between.

While the linear transformations are the same across different positions, they use different parameters from layer to layer. Another way of describing this is as two convolutions with kernel size 1. The dimensionality of the input and output is $d_{\text{model}}=512$ and the inner-layer has dimensionality $d_{ff}=2048$.

Similarly to other sequence transduction models, we use learned embeddings to convert the input tokens and output tokens to vectors of dimension $d_{\text{model}}$. We also use the usual learned linear transformation and softmax function to convert the decoder output to predicted next-token probabilities.

Since the model contains no recurrence and no convolution, in order for the model to make use of the order of the sequence, information bout the relative or absolute position of the tokens in the sequence must be injected into the model. ”Positional encodings” are added to the input embeddings at the bottoms of the encoder and decoder stacks. The positional encodings have the same dimension $d_{\text{model}}$ as the embeddings, so that the two can be summed. There are many choices of positional encodings - learned and fixed.