# Attention Is All You Need
**Authors**:
- Ashish Vaswani (Google Brain)
- &Noam Shazeer (Google Brain)
- &Niki Parmar (Google Research)
- &Jakob Uszkoreit (Google Research)
- &Llion Jones (Google Research)
- &Aidan N. Gomez (University of Toronto)
- &Ćukasz Kaiser (Google Brain)
- &Illia Polosukhin
> Equal contribution. Listing order is random. Jakob proposed replacing RNNs with self-attention and started the effort to evaluate this idea.
Ashish, with Illia, designed and implemented the first Transformer models and has been crucially involved in every aspect of this work. Noam proposed scaled dot-product attention, multi-head attention and the parameter-free position representation and became the other person involved in nearly every detail. Niki designed, implemented, tuned and evaluated countless model variants in our original codebase and tensor2tensor. Llion also experimented with novel model variants, was responsible for our initial codebase, and efficient inference and visualizations. Lukasz and Aidan spent countless long days designing various parts of and implementing tensor2tensor, replacing our earlier codebase, greatly improving results and massively accelerating our research.
Work performed while at Google Brain.Work performed while at Google Research.
Provided proper attribution is provided, Google hereby grants permission to reproduce the tables and figures in this paper solely for use in journalistic or scholarly works.
Abstract
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. We propose a new simple network architecture, the Transformer, based solely on attention mechanisms, dispensing with recurrence and convolutions entirely. Experiments on two machine translation tasks show these models to be superior in quality while being more parallelizable and requiring significantly less time to train. Our model achieves 28.4 BLEU on the WMT 2014 English-to-German translation task, improving over the existing best results, including ensembles, by over 2 BLEU. On the WMT 2014 English-to-French translation task, our model establishes a new single-model state-of-the-art BLEU score of 41.8 after training for 3.5 days on eight GPUs, a small fraction of the training costs of the best models from the literature. We show that the Transformer generalizes well to other tasks by applying it successfully to English constituency parsing both with large and limited training data.
1 Introduction
Recurrent neural networks, long short-term memory [13] and gated recurrent [7] 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 [35, 2, 5]. Numerous efforts have since continued to push the boundaries of recurrent language models and encoder-decoder architectures [38, 24, 15].
Recurrent models typically factor computation along the symbol positions of the input and output sequences. Aligning the positions to steps in computation time, they generate a sequence of hidden states $h_{t}$ , as a function of the previous hidden 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. Recent work has achieved significant improvements in computational efficiency through factorization tricks [21] and conditional computation [32], while also improving model performance in case of the latter. The fundamental constraint of sequential computation, however, remains.
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 [2, 19]. In all but a few cases [27], however, such attention mechanisms are used in conjunction with a recurrent network.
In this work we propose the Transformer, a model architecture eschewing 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 twelve hours on eight P100 GPUs.
2 Background
The goal of reducing sequential computation also forms the foundation of the Extended Neural GPU [16], ByteNet [18] and ConvS2S [9], all of which use convolutional neural networks as basic building block, computing hidden representations in parallel for all input and output positions. In these models, the number of operations required to relate signals from two arbitrary input or output positions grows in the distance between positions, linearly for ConvS2S and logarithmically for ByteNet. This makes it more difficult to learn dependencies between distant positions [12]. In the Transformer this is reduced to a constant number of operations, albeit at the cost of reduced effective resolution due to averaging attention-weighted positions, an effect we counteract with Multi-Head Attention as described in section 3.2.
Self-attention, sometimes called intra-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 sentence representations [4, 27, 28, 22].
End-to-end memory networks are based on a recurrent attention mechanism instead of sequence-aligned recurrence and have been shown to perform well on simple-language question answering and language modeling tasks [34].
To the best of our knowledge, however, 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. In the following sections, we will describe the Transformer, motivate self-attention and discuss its advantages over models such as [17, 18] and [9].
3 Model Architecture
<details>
<summary>Figures/ModalNet-21.png Details</summary>
### Visual Description
## Diagram: Transformer Architecture
### Overview
The image is a diagram illustrating the architecture of a Transformer model, a neural network architecture widely used in natural language processing. It shows the flow of data through the encoder (left) and decoder (right) components, highlighting key layers like multi-head attention, feed-forward networks, and normalization steps.
### Components/Axes
* **Input:** The diagram starts with "Inputs" at the bottom, feeding into an "Input Embedding" block (pink).
* **Positional Encoding:** A "Positional Encoding" block is added to the input embedding.
* **Encoder Stack:** The left side represents the encoder, which consists of N<sub>x</sub> (N subscript x) layers. Each layer contains:
* "Multi-Head Attention" (orange)
* "Add & Norm" (yellow)
* "Feed Forward" (blue)
* "Add & Norm" (yellow)
* **Decoder Stack:** The right side represents the decoder, which also consists of N<sub>x</sub> (N subscript x) layers. Each layer contains:
* "Masked Multi-Head Attention" (orange)
* "Add & Norm" (yellow)
* "Multi-Head Attention" (orange)
* "Add & Norm" (yellow)
* "Feed Forward" (blue)
* "Add & Norm" (yellow)
* **Output:** The output of the decoder goes through a "Linear" layer (purple) and a "Softmax" layer (green) to produce "Output Probabilities" at the top.
* **Outputs (shifted right):** The bottom right shows "Outputs (shifted right)" feeding into an "Output Embedding" block (pink), with "Positional Encoding" added.
### Detailed Analysis or ### Content Details
* **Encoder:** The input embeddings are combined with positional encodings. This combined representation is then passed through a stack of N<sub>x</sub> encoder layers. Each encoder layer consists of a multi-head attention mechanism followed by an add & norm layer, and then a feed-forward network followed by another add & norm layer. The output of each encoder layer is fed into the next encoder layer in the stack.
* **Decoder:** The decoder mirrors the encoder in its stacked architecture. The input to the decoder is the output embedding combined with positional encoding, and the output of the encoder stack. Each decoder layer contains a masked multi-head attention mechanism followed by an add & norm layer, a multi-head attention mechanism followed by an add & norm layer, and then a feed-forward network followed by another add & norm layer. The masked multi-head attention prevents the decoder from attending to future tokens. The output of the final decoder layer is passed through a linear layer and then a softmax layer to produce the output probabilities.
* **Residual Connections and Normalization:** "Add & Norm" blocks indicate residual connections (adding the input of a layer to its output) and layer normalization.
* **Arrows:** Arrows indicate the direction of data flow.
### Key Observations
* The diagram highlights the key components of the Transformer architecture: input embeddings, positional encoding, multi-head attention, feed-forward networks, residual connections, and layer normalization.
* The encoder and decoder have a similar structure, with stacked layers of attention and feed-forward networks.
* The "Masked Multi-Head Attention" in the decoder is crucial for autoregressive generation, where the model predicts the next token based on the previously generated tokens.
* The N<sub>x</sub> notation indicates that the encoder and decoder can have multiple layers, allowing the model to learn complex relationships in the data.
### Interpretation
The diagram illustrates the Transformer architecture, which is a powerful and versatile neural network architecture that has achieved state-of-the-art results in a variety of natural language processing tasks. The use of multi-head attention allows the model to attend to different parts of the input sequence, while the residual connections and layer normalization help to stabilize training and improve performance. The encoder-decoder structure allows the model to handle sequence-to-sequence tasks, such as machine translation and text summarization. The diagram provides a clear and concise overview of the Transformer architecture, making it a valuable resource for anyone interested in learning more about this important topic.
</details>
Figure 1: The Transformer - model architecture.
Most competitive neural sequence transduction models have an encoder-decoder structure [5, 2, 35]. Here, the encoder maps an input sequence of symbol representations $(x_{1},...,x_{n})$ to a sequence of continuous representations $\mathbf{z}=(z_{1},...,z_{n})$ . Given $\mathbf{z}$ , the decoder then generates an output sequence $(y_{1},...,y_{m})$ of symbols one element at a time. At each step the model is auto-regressive [10], 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, shown in the left and right halves of Figure 1, respectively.
3.1 Encoder and Decoder Stacks
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. We employ a residual connection [11] around each of the two sub-layers, followed by layer normalization [1]. That is, the output of each sub-layer is $\mathrm{LayerNorm}(x+\mathrm{Sublayer}(x))$ , where $\mathrm{Sublayer}(x)$ 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 fact that the output embeddings are offset by one position, ensures that the predictions for position $i$ can depend only on the known outputs at positions less than $i$ .
3.2 Attention
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 weight assigned to each value is computed by a compatibility function of the query with the corresponding key.
3.2.1 Scaled Dot-Product Attention
We call our particular attention "Scaled Dot-Product Attention" (Figure 2). 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 with 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:
$$
\mathrm{Attention}(Q,K,V)=\mathrm{softmax}(\frac{QK^{T}}{\sqrt{d_{k}}})V \tag{1}
$$
The two most commonly used attention functions are additive attention [2], 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 highly optimized matrix multiplication code.
While for small values of $d_{k}$ the two mechanisms perform similarly, additive attention outperforms dot product attention without scaling for larger values of $d_{k}$ [3]. We suspect that for large values of $d_{k}$ , the dot products grow large in magnitude, pushing the softmax function into regions where it has extremely small gradients To illustrate why the dot products get large, assume that the components of $q$ and $k$ are independent random variables with mean $0$ and variance $1$ . Then their dot product, $q· k=\sum_{i=1}^{d_{k}}q_{i}k_{i}$ , has mean $0$ and variance $d_{k}$ .. To counteract this effect, we scale the dot products by $\frac{1}{\sqrt{d_{k}}}$ .
3.2.2 Multi-Head Attention
Scaled Dot-Product Attention
<details>
<summary>Figures/ModalNet-19.png Details</summary>
### Visual Description
## Diagram: Scaled Dot-Product Attention
### Overview
The image is a diagram illustrating the flow of data through a scaled dot-product attention mechanism, a key component in transformer models. It shows the sequence of operations performed on input vectors Q, K, and V, culminating in a final matrix multiplication.
### Components/Axes
The diagram consists of the following components, arranged vertically from bottom to top:
* **Input Vectors:**
* Q: Query vector
* K: Key vector
* V: Value vector
* **Processing Blocks:**
* MatMul (bottom): Matrix Multiplication (lavender)
* Scale: Scaling operation (yellow)
* Mask (opt.): Optional masking operation (pink)
* SoftMax: Softmax activation function (light green)
* MatMul (top): Matrix Multiplication (lavender)
* **Arrows:** Arrows indicate the direction of data flow.
### Detailed Analysis
1. **Input Vectors:**
* Q and K are inputs to the first MatMul block. Arrows point upwards from Q and K into the MatMul block.
* V is input directly to the second MatMul block at the top. An arrow points upwards from V to the top MatMul block.
2. **MatMul (bottom):**
* The first step is a matrix multiplication of Q and K. The output of this block is fed into the "Scale" block.
3. **Scale:**
* The "Scale" block scales the output from the first MatMul block. The output of this block is fed into the "Mask (opt.)" block.
4. **Mask (opt.):**
* This block represents an optional masking operation. The output of this block is fed into the "SoftMax" block.
5. **SoftMax:**
* The "SoftMax" block applies the softmax function to the masked (or unmasked) output. The output of this block is fed into the second MatMul block.
6. **MatMul (top):**
* The final step is a matrix multiplication of the output from the SoftMax block and the V vector. The output of this block is the final result of the scaled dot-product attention mechanism.
### Key Observations
* The diagram clearly shows the sequential flow of data through the different operations.
* The "Mask (opt.)" block indicates that masking is an optional step in the process.
* The diagram highlights the importance of matrix multiplication and the softmax function in the attention mechanism.
### Interpretation
The diagram illustrates the scaled dot-product attention mechanism, which is a crucial component of transformer models. The mechanism calculates the attention weights by first computing the dot product of the query (Q) and key (K) vectors, scaling the result, applying an optional mask, and then passing it through a softmax function. These attention weights are then used to weight the value (V) vectors, producing a weighted sum that represents the attention output. This process allows the model to focus on the most relevant parts of the input sequence when making predictions. The optional masking step is used to prevent the model from attending to certain parts of the input sequence, such as padding tokens or future tokens in a sequence.
</details>
Multi-Head Attention
<details>
<summary>Figures/ModalNet-20.png Details</summary>
### Visual Description
## Diagram: Scaled Dot-Product Attention Mechanism
### Overview
The image is a diagram illustrating the Scaled Dot-Product Attention mechanism, a key component in transformer models. It shows the flow of data through linear transformations, the attention calculation, concatenation, and a final linear transformation.
### Components/Axes
* **Input Layers (Bottom):**
* V (Value): Input to a "Linear" transformation.
* K (Key): Input to a "Linear" transformation.
* Q (Query): Input to a "Linear" transformation.
* **Linear Transformations:** Three "Linear" blocks, each receiving input from V, K, and Q respectively.
* **Scaled Dot-Product Attention:** A central, larger block labeled "Scaled Dot-Product Attention". It receives input from the three "Linear" blocks.
* **Output from Attention:** An arrow labeled "h" exits from the right side of the "Scaled Dot-Product Attention" block.
* **Concat:** A block labeled "Concat" receives input from the "Scaled Dot-Product Attention" block.
* **Output Layer (Top):** A "Linear" block receives input from the "Concat" block.
* **Arrows:** Arrows indicate the direction of data flow between the components.
### Detailed Analysis
1. **Input:** The diagram starts with three inputs: V (Value), K (Key), and Q (Query).
2. **Linear Transformations:** Each input (V, K, Q) is passed through a "Linear" transformation. These transformations are represented by rectangular blocks with rounded corners.
3. **Scaled Dot-Product Attention:** The outputs of the three "Linear" transformations are fed into the "Scaled Dot-Product Attention" block. This block calculates the attention weights based on the dot product of the query and keys, scaled by the dimension of the keys.
4. **Output from Attention:** The output from the "Scaled Dot-Product Attention" block is labeled "h".
5. **Concatenation:** The output from the "Scaled Dot-Product Attention" block is then passed to a "Concat" block, where the attention outputs are concatenated.
6. **Final Linear Transformation:** The concatenated output is passed through a final "Linear" transformation.
7. **Data Flow:** The arrows indicate the flow of data from the inputs, through the transformations, to the final output.
### Key Observations
* The diagram clearly illustrates the sequence of operations in the Scaled Dot-Product Attention mechanism.
* The use of "Linear" transformations before and after the attention calculation is highlighted.
* The "Concat" block suggests that multiple attention heads might be used, and their outputs are concatenated.
### Interpretation
The diagram represents the Scaled Dot-Product Attention mechanism, a core component of the Transformer architecture. The mechanism computes attention weights by taking the dot product of the query (Q) with all keys (K), scaling the result, and then applying a softmax function to obtain the weights on the values (V). The "Linear" transformations before and after the attention calculation allow the model to learn different representations of the input data. The concatenation step suggests the use of multi-head attention, where the attention mechanism is applied multiple times in parallel with different learned linear projections, and the results are concatenated to capture different aspects of the input. The final "Linear" transformation projects the concatenated output to the desired output dimension. The output "h" represents the context-aware representation learned by the attention mechanism.
</details>
Figure 2: (left) Scaled Dot-Product Attention. (right) Multi-Head Attention consists of several attention layers running in parallel.
Instead of performing a single attention function with $d_{\text{model}}$ -dimensional keys, values and queries, we found it 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, as depicted in Figure 2.
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.
| | $\displaystyle\mathrm{MultiHead}(Q,K,V)$ | $\displaystyle=\mathrm{Concat}(\mathrm{head_{1}},...,\mathrm{head_{h}})W^{O}$ | |
| --- | --- | --- | --- |
Where the projections are parameter matrices $W^{Q}_{i}â\mathbb{R}^{d_{\text{model}}Ă d_{k}}$ , $W^{K}_{i}â\mathbb{R}^{d_{\text{model}}Ă d_{k}}$ , $W^{V}_{i}â\mathbb{R}^{d_{\text{model}}Ă d_{v}}$ and $W^{O}â\mathbb{R}^{hd_{v}Ă d_{\text{model}}}$ .
In this work we employ $h=8$ parallel attention layers, or heads. For each of these we use $d_{k}=d_{v}=d_{\text{model}}/h=64$ . Due to the reduced dimension of each head, the total computational cost is similar to that of single-head attention with full dimensionality.
3.2.3 Applications of Attention in our Model
The Transformer 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 such as [38, 2, 9].
- 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 (setting to $-â$ ) all values in the input of the softmax which correspond to illegal connections. See Figure 2.
3.3 Position-wise Feed-Forward Networks
In addition to attention sub-layers, each of the layers in our encoder and decoder 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.
$$
\mathrm{FFN}(x)=\max(0,xW_{1}+b_{1})W_{2}+b_{2} \tag{2}
$$
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 input and output is $d_{\text{model}}=512$ , and the inner-layer has dimensionality $d_{ff}=2048$ .
3.4 Embeddings and Softmax
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. In our model, we share the same weight matrix between the two embedding layers and the pre-softmax linear transformation, similar to [30]. In the embedding layers, we multiply those weights by $\sqrt{d_{\text{model}}}$ .
3.5 Positional Encoding
Since our model contains no recurrence and no convolution, in order for the model to make use of the order of the sequence, we must inject some information about the relative or absolute position of the tokens in the sequence. To this end, we add "positional encodings" 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 [9].
In this work, we use sine and cosine functions of different frequencies:
| | $\displaystyle PE_{(pos,2i)}=sin(pos/10000^{2i/d_{\text{model}}})$ | |
| --- | --- | --- |
where $pos$ is the position and $i$ is the dimension. That is, each dimension of the positional encoding corresponds to a sinusoid. The wavelengths form a geometric progression from $2\pi$ to $10000· 2\pi$ . We chose this function because we hypothesized it would allow the model to easily learn to attend by relative positions, since for any fixed offset $k$ , $PE_{pos+k}$ can be represented as a linear function of $PE_{pos}$ .
We also experimented with using learned positional embeddings [9] instead, and found that the two versions produced nearly identical results (see Table 3 row (E)). We chose the sinusoidal version because it may allow the model to extrapolate to sequence lengths longer than the ones encountered during training.
4 Why Self-Attention
In this section we compare various aspects of self-attention layers to the recurrent and convolutional layers commonly used for mapping one variable-length sequence of symbol representations $(x_{1},...,x_{n})$ to another sequence of equal length $(z_{1},...,z_{n})$ , with $x_{i},z_{i}â\mathbb{R}^{d}$ , such as a hidden layer in a typical sequence transduction encoder or decoder. Motivating our use of self-attention we consider three desiderata.
One is the total computational complexity per layer. Another is the amount of computation that can be parallelized, as measured by the minimum number of sequential operations required.
The third is the path length between long-range dependencies in the network. Learning long-range dependencies is a key challenge in many sequence transduction tasks. One key factor affecting the ability to learn such dependencies is the length of the paths forward and backward signals have to traverse in the network. The shorter these paths between any combination of positions in the input and output sequences, the easier it is to learn long-range dependencies [12]. Hence we also compare the maximum path length between any two input and output positions in networks composed of the different layer types.
Table 1: Maximum path lengths, per-layer complexity and minimum number of sequential operations for different layer types. $n$ is the sequence length, $d$ is the representation dimension, $k$ is the kernel size of convolutions and $r$ the size of the neighborhood in restricted self-attention.
$$
O(n^{2}\cdot d) O(1) O(1) O(n\cdot d^{2}) O(n) O(n) O(k\cdot n\cdot d^{2}) O(1) O(log_{k}(n)) O(r\cdot n\cdot d) O(1) O(n/r) \tag{1}
$$
As noted in Table 1, a self-attention layer connects all positions with a constant number of sequentially executed operations, whereas a recurrent layer requires $O(n)$ sequential operations. In terms of computational complexity, self-attention layers are faster than recurrent layers when the sequence length $n$ is smaller than the representation dimensionality $d$ , which is most often the case with sentence representations used by state-of-the-art models in machine translations, such as word-piece [38] and byte-pair [31] representations. To improve computational performance for tasks involving very long sequences, self-attention could be restricted to considering only a neighborhood of size $r$ in the input sequence centered around the respective output position. This would increase the maximum path length to $O(n/r)$ . We plan to investigate this approach further in future work.
A single convolutional layer with kernel width $k<n$ does not connect all pairs of input and output positions. Doing so requires a stack of $O(n/k)$ convolutional layers in the case of contiguous kernels, or $O(log_{k}(n))$ in the case of dilated convolutions [18], increasing the length of the longest paths between any two positions in the network. Convolutional layers are generally more expensive than recurrent layers, by a factor of $k$ . Separable convolutions [6], however, decrease the complexity considerably, to $O(k· n· d+n· d^{2})$ . Even with $k=n$ , however, the complexity of a separable convolution is equal to the combination of a self-attention layer and a point-wise feed-forward layer, the approach we take in our model.
As side benefit, self-attention could yield more interpretable models. We inspect attention distributions from our models and present and discuss examples in the appendix. Not only do individual attention heads clearly learn to perform different tasks, many appear to exhibit behavior related to the syntactic and semantic structure of the sentences.
5 Training
This section describes the training regime for our models.
5.1 Training Data and Batching
We trained on the standard WMT 2014 English-German dataset consisting of about 4.5 million sentence pairs. Sentences were encoded using byte-pair encoding [3], which has a shared source-target vocabulary of about 37000 tokens. For English-French, we used the significantly larger WMT 2014 English-French dataset consisting of 36M sentences and split tokens into a 32000 word-piece vocabulary [38]. Sentence pairs were batched together by approximate sequence length. Each training batch contained a set of sentence pairs containing approximately 25000 source tokens and 25000 target tokens.
5.2 Hardware and Schedule
We trained our models on one machine with 8 NVIDIA P100 GPUs. For our base models using the hyperparameters described throughout the paper, each training step took about 0.4 seconds. We trained the base models for a total of 100,000 steps or 12 hours. For our big models,(described on the bottom line of table 3), step time was 1.0 seconds. The big models were trained for 300,000 steps (3.5 days).
5.3 Optimizer
We used the Adam optimizer [20] with $\beta_{1}=0.9$ , $\beta_{2}=0.98$ and $\epsilon=10^{-9}$ . We varied the learning rate over the course of training, according to the formula:
$$
lrate=d_{\text{model}}^{-0.5}\cdot\min({step\_num}^{-0.5},{step\_num}\cdot{warmup\_steps}^{-1.5}) \tag{3}
$$
This corresponds to increasing the learning rate linearly for the first $warmup\_steps$ training steps, and decreasing it thereafter proportionally to the inverse square root of the step number. We used $warmup\_steps=4000$ .
5.4 Regularization
We employ three types of regularization during training:
Residual Dropout
We apply dropout [33] to the output of each sub-layer, before it is added to the sub-layer input and normalized. In addition, we apply dropout to the sums of the embeddings and the positional encodings in both the encoder and decoder stacks. For the base model, we use a rate of $P_{drop}=0.1$ .
Label Smoothing
During training, we employed label smoothing of value $\epsilon_{ls}=0.1$ [36]. This hurts perplexity, as the model learns to be more unsure, but improves accuracy and BLEU score.
6 Results
6.1 Machine Translation
Table 2: The Transformer achieves better BLEU scores than previous state-of-the-art models on the English-to-German and English-to-French newstest2014 tests at a fraction of the training cost.
| Model | BLEU | | Training Cost (FLOPs) | | |
| --- | --- | --- | --- | --- | --- |
| EN-DE | EN-FR | | EN-DE | EN-FR | |
| ByteNet [18] | 23.75 | | | | |
| Deep-Att + PosUnk [39] | | 39.2 | | | $1.0· 10^{20}$ |
| GNMT + RL [38] | 24.6 | 39.92 | | $2.3· 10^{19}$ | $1.4· 10^{20}$ |
| ConvS2S [9] | 25.16 | 40.46 | | $9.6· 10^{18}$ | $1.5· 10^{20}$ |
| MoE [32] | 26.03 | 40.56 | | $2.0· 10^{19}$ | $1.2· 10^{20}$ |
| Deep-Att + PosUnk Ensemble [39] | | 40.4 | | | $8.0· 10^{20}$ |
| GNMT + RL Ensemble [38] | 26.30 | 41.16 | | $1.8· 10^{20}$ | $1.1· 10^{21}$ |
| ConvS2S Ensemble [9] | 26.36 | 41.29 | | $7.7· 10^{19}$ | $1.2· 10^{21}$ |
| Transformer (base model) | 27.3 | 38.1 | | $3.3· 10^{18}$ | |
| Transformer (big) | 28.4 | 41.8 | | $2.3· 10^{19}$ | |
On the WMT 2014 English-to-German translation task, the big transformer model (Transformer (big) in Table 2) outperforms the best previously reported models (including ensembles) by more than $2.0$ BLEU, establishing a new state-of-the-art BLEU score of $28.4$ . The configuration of this model is listed in the bottom line of Table 3. Training took $3.5$ days on $8$ P100 GPUs. Even our base model surpasses all previously published models and ensembles, at a fraction of the training cost of any of the competitive models.
On the WMT 2014 English-to-French translation task, our big model achieves a BLEU score of $41.0$ , outperforming all of the previously published single models, at less than $1/4$ the training cost of the previous state-of-the-art model. The Transformer (big) model trained for English-to-French used dropout rate $P_{drop}=0.1$ , instead of $0.3$ .
For the base models, we used a single model obtained by averaging the last 5 checkpoints, which were written at 10-minute intervals. For the big models, we averaged the last 20 checkpoints. We used beam search with a beam size of $4$ and length penalty $\alpha=0.6$ [38]. These hyperparameters were chosen after experimentation on the development set. We set the maximum output length during inference to input length + $50$ , but terminate early when possible [38].
Table 2 summarizes our results and compares our translation quality and training costs to other model architectures from the literature. We estimate the number of floating point operations used to train a model by multiplying the training time, the number of GPUs used, and an estimate of the sustained single-precision floating-point capacity of each GPU We used values of 2.8, 3.7, 6.0 and 9.5 TFLOPS for K80, K40, M40 and P100, respectively..
6.2 Model Variations
Table 3: Variations on the Transformer architecture. Unlisted values are identical to those of the base model. All metrics are on the English-to-German translation development set, newstest2013. Listed perplexities are per-wordpiece, according to our byte-pair encoding, and should not be compared to per-word perplexities.
| | $N$ | $d_{\text{model}}$ | $d_{\text{ff}}$ | $h$ | $d_{k}$ | $d_{v}$ | $P_{drop}$ | $\epsilon_{ls}$ | train | PPL | BLEU | params |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| steps | (dev) | (dev) | $Ă 10^{6}$ | | | | | | | | | |
| base | 6 | 512 | 2048 | 8 | 64 | 64 | 0.1 | 0.1 | 100K | 4.92 | 25.8 | 65 |
| (A) | | | | 1 | 512 | 512 | | | | 5.29 | 24.9 | |
| 4 | 128 | 128 | | | | 5.00 | 25.5 | | | | | |
| 16 | 32 | 32 | | | | 4.91 | 25.8 | | | | | |
| 32 | 16 | 16 | | | | 5.01 | 25.4 | | | | | |
| (B) | | | | | 16 | | | | | 5.16 | 25.1 | 58 |
| 32 | | | | | 5.01 | 25.4 | 60 | | | | | |
| (C) | 2 | | | | | | | | | 6.11 | 23.7 | 36 |
| 4 | | | | | | | | | 5.19 | 25.3 | 50 | |
| 8 | | | | | | | | | 4.88 | 25.5 | 80 | |
| 256 | | | 32 | 32 | | | | 5.75 | 24.5 | 28 | | |
| 1024 | | | 128 | 128 | | | | 4.66 | 26.0 | 168 | | |
| 1024 | | | | | | | 5.12 | 25.4 | 53 | | | |
| 4096 | | | | | | | 4.75 | 26.2 | 90 | | | |
| (D) | | | | | | | 0.0 | | | 5.77 | 24.6 | |
| 0.2 | | | 4.95 | 25.5 | | | | | | | | |
| 0.0 | | 4.67 | 25.3 | | | | | | | | | |
| 0.2 | | 5.47 | 25.7 | | | | | | | | | |
| (E) | | positional embedding instead of sinusoids | | 4.92 | 25.7 | | | | | | | |
| big | 6 | 1024 | 4096 | 16 | | | 0.3 | | 300K | 4.33 | 26.4 | 213 |
To evaluate the importance of different components of the Transformer, we varied our base model in different ways, measuring the change in performance on English-to-German translation on the development set, newstest2013. We used beam search as described in the previous section, but no checkpoint averaging. We present these results in Table 3.
In Table 3 rows (A), we vary the number of attention heads and the attention key and value dimensions, keeping the amount of computation constant, as described in Section 3.2.2. While single-head attention is 0.9 BLEU worse than the best setting, quality also drops off with too many heads.
In Table 3 rows (B), we observe that reducing the attention key size $d_{k}$ hurts model quality. This suggests that determining compatibility is not easy and that a more sophisticated compatibility function than dot product may be beneficial. We further observe in rows (C) and (D) that, as expected, bigger models are better, and dropout is very helpful in avoiding over-fitting. In row (E) we replace our sinusoidal positional encoding with learned positional embeddings [9], and observe nearly identical results to the base model.
6.3 English Constituency Parsing
Table 4: The Transformer generalizes well to English constituency parsing (Results are on Section 23 of WSJ)
To evaluate if the Transformer can generalize to other tasks we performed experiments on English constituency parsing. This task presents specific challenges: the output is subject to strong structural constraints and is significantly longer than the input. Furthermore, RNN sequence-to-sequence models have not been able to attain state-of-the-art results in small-data regimes [37].
We trained a 4-layer transformer with $d_{model}=1024$ on the Wall Street Journal (WSJ) portion of the Penn Treebank [25], about 40K training sentences. We also trained it in a semi-supervised setting, using the larger high-confidence and BerkleyParser corpora from with approximately 17M sentences [37]. We used a vocabulary of 16K tokens for the WSJ only setting and a vocabulary of 32K tokens for the semi-supervised setting.
We performed only a small number of experiments to select the dropout, both attention and residual (section 5.4), learning rates and beam size on the Section 22 development set, all other parameters remained unchanged from the English-to-German base translation model. During inference, we increased the maximum output length to input length + $300$ . We used a beam size of $21$ and $\alpha=0.3$ for both WSJ only and the semi-supervised setting.
Our results in Table 4 show that despite the lack of task-specific tuning our model performs surprisingly well, yielding better results than all previously reported models with the exception of the Recurrent Neural Network Grammar [8].
In contrast to RNN sequence-to-sequence models [37], the Transformer outperforms the BerkeleyParser [29] even when training only on the WSJ training set of 40K sentences.
7 Conclusion
In this work, we presented the Transformer, the first sequence transduction model based entirely on attention, replacing the recurrent layers most commonly used in encoder-decoder architectures with multi-headed self-attention.
For translation tasks, the Transformer can be trained significantly faster than architectures based on recurrent or convolutional layers. On both WMT 2014 English-to-German and WMT 2014 English-to-French translation tasks, we achieve a new state of the art. In the former task our best model outperforms even all previously reported ensembles.
We are excited about the future of attention-based models and plan to apply them to other tasks. We plan to extend the Transformer to problems involving input and output modalities other than text and to investigate local, restricted attention mechanisms to efficiently handle large inputs and outputs such as images, audio and video. Making generation less sequential is another research goals of ours.
The code we used to train and evaluate our models is available at https://github.com/tensorflow/tensor2tensor.
Acknowledgements
We are grateful to Nal Kalchbrenner and Stephan Gouws for their fruitful comments, corrections and inspiration.
References
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Attention Visualizations
<details>
<summary>x1.png Details</summary>
### Visual Description
## Diagram: Text Association Diagram
### Overview
The image is a diagram showing the association of words in two phrases. The phrases are "It is in this spirit that a majority of American governments have passed new laws since 2009" and "making the registration or voting process more difficult <EOS> <pad> <pad> <pad> <pad> <pad> <pad> <pad> <pad> <pad> <pad> <pad>". The diagram connects the word "2009" from the first phrase to several words in the second phrase, indicating a relationship or association between them. The legend at the bottom shows the colors associated with each word in the second phrase.
### Components/Axes
* **Phrases:** Two phrases are displayed vertically, one above the other.
* **Connections:** Lines connect the word "2009" in the first phrase to several words in the second phrase.
* **Legend:** A color-coded legend at the bottom associates colors with specific words in the second phrase.
### Detailed Analysis or ### Content Details
**First Phrase (Top):**
* "It"
* "is"
* "in"
* "this"
* "spirit"
* "that"
* "a"
* "majority"
* "of"
* "American"
* "governments"
* "have"
* "passed"
* "new"
* "laws"
* "since"
* "2009"
**Second Phrase (Bottom):**
* "making"
* "the"
* "registration"
* "or"
* "voting"
* "process"
* "more"
* "difficult"
* "<EOS>"
* "<pad>" (repeated multiple times)
**Connections and Legend:**
* **Purple:** "making"
* **Pink:** "the"
* **Light Gray:** "registration" or "voting"
* **Green:** "process"
* **Red:** "more"
* **Brown:** "difficult"
* **Dark Gray:** "<EOS>"
The word "2009" in the first phrase is connected to the following words in the second phrase with the corresponding colors:
* "making" (purple)
* "the" (pink)
* "registration" or "voting" (light gray)
* "process" (green)
* "more" (red)
* "difficult" (brown)
### Key Observations
The diagram highlights the association between the year "2009" and the phrase "making the registration or voting process more difficult." The connections suggest that the passage of new laws since 2009 is related to making the registration or voting process more difficult.
### Interpretation
The diagram visually represents a claim or argument that the laws passed since 2009 have contributed to making the voter registration or voting process more difficult. The connections between "2009" and the words "making," "registration," "voting," "process," "more," and "difficult" emphasize this relationship. The use of color-coding helps to distinguish the different words and their connections. The presence of "<EOS>" (End of Sentence) and "<pad>" (padding) suggests this diagram may be related to a natural language processing model or analysis.
</details>
Figure 3: An example of the attention mechanism following long-distance dependencies in the encoder self-attention in layer 5 of 6. Many of the attention heads attend to a distant dependency of the verb âmakingâ, completing the phrase âmakingâŠmore difficultâ. Attentions here shown only for the word âmakingâ. Different colors represent different heads. Best viewed in color.
<details>
<summary>x2.png Details</summary>
### Visual Description
## Parallel Coordinates Plot: Sentence Alignment
### Overview
The image is a parallel coordinates plot visualizing the alignment between two sentences. Each vertical axis represents a word in the sentences, and the lines connect corresponding words. The sentences appear to be: "The Law will never be perfect, but its application should be just. This is what we are missing in my opinion. <EOS> <pad>" and "The Law will never be perfect, but its application should be just. This is what we are missing in my opinion. <EOS> <pad>". The lines are colored in shades of purple, with darker lines indicating stronger alignment or more frequent connections between words.
### Components/Axes
* **Vertical Axes:** Each vertical axis represents a word from the sentences. The words are listed along the top and bottom of the plot.
* The words are: "The", "Law", "will", "never", "be", "perfect", "but", "its", "application", "should", "be", "just", "this", "is", "what", "we", "are", "missing", "in", "my", "opinion", "<EOS>", "<pad>"
* **Lines:** The lines connect corresponding words between the two sentences. The thickness and darkness of the lines indicate the strength or frequency of the alignment.
### Detailed Analysis or ### Content Details
The plot shows a strong alignment between the two sentences, as evidenced by the many lines connecting identical words.
* **"The"**: The first word "The" in both sentences is connected by a thick, dark purple line.
* **"Law"**: The second word "Law" in both sentences is connected by a thick, dark purple line.
* **"will"**: The third word "will" in both sentences is connected by a thick, dark purple line.
* **"never"**: The fourth word "never" in both sentences is connected by a thick, dark purple line.
* **"be"**: The fifth word "be" in both sentences is connected by a thick, dark purple line.
* **"perfect"**: The sixth word "perfect" in both sentences is connected by a thick, dark purple line.
* **"but"**: The seventh word "but" in both sentences is connected by a thick, dark purple line.
* **"its"**: The eighth word "its" in both sentences is connected by a thick, dark purple line.
* **"application"**: The ninth word "application" in both sentences is connected by a thick, dark purple line.
* **"should"**: The tenth word "should" in both sentences is connected by a thick, dark purple line.
* **"be"**: The eleventh word "be" in both sentences is connected by a thick, dark purple line.
* **"just"**: The twelfth word "just" in both sentences is connected by a thick, dark purple line.
* **"this"**: The thirteenth word "this" in both sentences is connected by a thick, dark purple line.
* **"is"**: The fourteenth word "is" in both sentences is connected by a thick, dark purple line.
* **"what"**: The fifteenth word "what" in both sentences is connected by a thick, dark purple line.
* **"we"**: The sixteenth word "we" in both sentences is connected by a thick, dark purple line.
* **"are"**: The seventeenth word "are" in both sentences is connected by a thick, dark purple line.
* **"missing"**: The eighteenth word "missing" in both sentences is connected by a thick, dark purple line.
* **"in"**: The nineteenth word "in" in both sentences is connected by a thick, dark purple line.
* **"my"**: The twentieth word "my" in both sentences is connected by a thick, dark purple line.
* **"opinion"**: The twenty-first word "opinion" in both sentences is connected by a thick, dark purple line.
* **"<EOS>"**: The twenty-second word "<EOS>" in both sentences is connected by a thick, dark purple line.
* **"<pad>"**: The twenty-third word "<pad>" in both sentences is connected by a thick, dark purple line.
### Key Observations
* The plot clearly shows a one-to-one correspondence between the words in the two sentences.
* The sentences are identical.
### Interpretation
The parallel coordinates plot visualizes the alignment between two identical sentences. The strong, direct connections between corresponding words indicate a perfect match. This type of visualization can be useful for comparing sentences in machine translation or text summarization tasks, where the goal is to identify relationships between words and phrases in different texts. In this specific case, the plot confirms that the two sentences are identical.
</details>
<details>
<summary>x3.png Details</summary>
### Visual Description
## Diagram: Textual Dependency Tree
### Overview
The image presents a dependency tree diagram, visually representing the relationships between words in two similar phrases. The diagram highlights how the phrases diverge and converge, showing the flow of dependency.
### Components/Axes
* **Nodes:** Each node represents a word in the phrase. The words are arranged vertically.
* **Edges:** The edges (lines) connect the words, indicating the relationships between them.
* **Colors:** Two colors are used for the edges and the vertical bars next to the first word of each phrase: purple and light brown.
* **Text:** The text consists of two phrases, each ending with "<EOS>" and "<pad>".
### Detailed Analysis or ### Content Details
**Phrase 1 (Purple):**
* "The"
* "Law"
* "will"
* "never"
* "be"
* "perfect"
* "."
* "but"
* "its"
* "this"
* "is"
* "what"
* "we"
* "are"
* "missing"
* "."
* "in"
* "my"
* "opinion"
* "."
* "<EOS>"
* "<pad>"
**Phrase 2 (Light Brown):**
* "The"
* "Law"
* "will"
* "never"
* "be"
* "perfect"
* "."
* "but"
* "its"
* "application"
* "should"
* "be"
* "just"
* "."
* "this"
* "is"
* "what"
* "we"
* "are"
* "missing"
* "."
* "in"
* "my"
* "opinion"
* "."
* "<EOS>"
* "<pad>"
**Dependency Flow:**
* The phrases start identically: "The Law will never be perfect . but its".
* The purple phrase continues directly to "this is what we are missing . in my opinion . <EOS> <pad>".
* The light brown phrase diverges at "its" to "application should be just . this is what we are missing . in my opinion . <EOS> <pad>".
* Both phrases converge again at "this is what we are missing . in my opinion . <EOS> <pad>".
### Key Observations
* The phrases share a common starting sequence.
* The phrases diverge at the word "its".
* The phrases converge again after the divergence.
* The diagram visually represents the structural similarity and differences between the two phrases.
### Interpretation
The diagram illustrates how two phrases can share a common structure but diverge at a specific point, leading to different meanings or contexts. The convergence after the divergence suggests that despite the difference, the phrases ultimately convey a similar sentiment or idea. The diagram could be used to analyze the structure of language, compare different sentence constructions, or visualize the flow of information in a text.
</details>
Figure 4: Two attention heads, also in layer 5 of 6, apparently involved in anaphora resolution. Top: Full attentions for head 5. Bottom: Isolated attentions from just the word âitsâ for attention heads 5 and 6. Note that the attentions are very sharp for this word.
<details>
<summary>x4.png Details</summary>
### Visual Description
## Alignment Diagram: Sentence Alignment
### Overview
The image is an alignment diagram showing the relationships between two sentences. The diagram consists of two parallel lists of words, one above the other, with green lines connecting words in the top list to words in the bottom list. The thickness of the lines indicates the strength or frequency of the alignment.
### Components/Axes
* **Top List:** Contains the words: "The", "Law", "will", "never", "be", "perfect", ".", "but", "its", "application", "should", "be", "just", "-", "this", "is", "what", "we", "are", "missing", ".", "in", "my", "opinion", "<EOS>", "<pad>"
* **Bottom List:** Contains the words: "The", "Law", "will", "never", "be", "perfect", ".", "but", "its", "application", "should", "be", "just", "-", "this", "is", "what", "we", "are", "missing", ".", "in", "my", "opinion", "<EOS>", "<pad>"
* **Connections:** Green lines connect words from the top list to the bottom list, indicating alignment. The thickness of the lines varies, suggesting different levels of alignment strength.
### Detailed Analysis or Content Details
* **"The"**: The first "The" in the top list is strongly connected to the first "The" in the bottom list with a thick green line.
* **"Law"**: The word "Law" in the top list is strongly connected to the word "Law" in the bottom list with a thick green line.
* **"will"**: The word "will" in the top list is strongly connected to the word "will" in the bottom list with a thick green line.
* **"never"**: The word "never" in the top list is strongly connected to the word "never" in the bottom list with a thick green line.
* **"be"**: The word "be" in the top list is strongly connected to the word "be" in the bottom list with a thick green line.
* **"perfect"**: The word "perfect" in the top list is strongly connected to the word "perfect" in the bottom list with a thick green line.
* **"."**: The period in the top list is strongly connected to the period in the bottom list with a thick green line.
* **"but"**: The word "but" in the top list is strongly connected to the word "but" in the bottom list with a thick green line.
* **"its"**: The word "its" in the top list is strongly connected to the word "its" in the bottom list with a thick green line.
* **"application"**: The word "application" in the top list is strongly connected to the word "application" in the bottom list with a thick green line.
* **"should"**: The word "should" in the top list is strongly connected to the word "should" in the bottom list with a thick green line.
* **"be"**: The word "be" in the top list is strongly connected to the word "be" in the bottom list with a thick green line.
* **"just"**: The word "just" in the top list is strongly connected to the word "just" in the bottom list with a thick green line.
* **"-"**: The dash in the top list is strongly connected to the dash in the bottom list with a thick green line.
* **"this"**: The word "this" in the top list is strongly connected to the word "this" in the bottom list with a thick green line.
* **"is"**: The word "is" in the top list is strongly connected to the word "is" in the bottom list with a thick green line.
* **"what"**: The word "what" in the top list is strongly connected to the word "what" in the bottom list with a thick green line.
* **"we"**: The word "we" in the top list is strongly connected to the word "we" in the bottom list with a thick green line.
* **"are"**: The word "are" in the top list is strongly connected to the word "are" in the bottom list with a thick green line.
* **"missing"**: The word "missing" in the top list is strongly connected to the word "missing" in the bottom list with a thick green line.
* **"."**: The period in the top list is strongly connected to the period in the bottom list with a thick green line.
* **"in"**: The word "in" in the top list is strongly connected to the word "in" in the bottom list with a thick green line.
* **"my"**: The word "my" in the top list is strongly connected to the word "my" in the bottom list with a thick green line.
* **"opinion"**: The word "opinion" in the top list is strongly connected to the word "opinion" in the bottom list with a thick green line.
* **"<EOS>"**: The tag "<EOS>" in the top list is strongly connected to the tag "<EOS>" in the bottom list with a thick green line.
* **"<pad>"**: The tag "<pad>" in the top list is strongly connected to the tag "<pad>" in the bottom list with a thick green line.
### Key Observations
* The diagram shows a one-to-one alignment between the two sentences.
* The thickness of the lines indicates a strong alignment between corresponding words.
* The sentences are identical.
### Interpretation
The alignment diagram visually represents the relationship between two identical sentences. The strong, direct connections between corresponding words indicate a perfect alignment, suggesting that the sentences are semantically and structurally equivalent. This type of diagram is often used in machine translation or natural language processing to visualize how words or phrases in one sentence correspond to words or phrases in another. In this case, the diagram confirms that the two sentences are identical, which might be a baseline or a control case in a more complex analysis.
</details>
<details>
<summary>x5.png Details</summary>
### Visual Description
## Alignment Diagram: Sentence Alignment
### Overview
The image is an alignment diagram showing the correspondence between two sentences. The diagram consists of two rows of words, one above the other, with lines connecting words that are considered aligned. The thickness and color intensity of the lines indicate the strength or confidence of the alignment.
### Components/Axes
* **Top Row:** The sentence "The Law will never be perfect . but its application should be just . this is what we are missing . in my opinion <EOS> <pad>"
* **Bottom Row:** The sentence "The Law will never be perfect . but its application should be just . this is what we are missing . in my opinion <EOS> <pad>"
* **Connections:** Red lines of varying thickness connect words in the top row to words in the bottom row, indicating alignment. Thicker, darker lines suggest stronger alignment.
### Detailed Analysis or Content Details
The diagram shows the alignment between two identical sentences. Here's a breakdown of the alignments:
* **"The"**: The first "The" in the top row is strongly aligned with the first "The" in the bottom row (thick red line).
* **"Law"**: The word "Law" in the top row is strongly aligned with the word "Law" in the bottom row (thick red line).
* **"will"**: The word "will" in the top row is strongly aligned with the word "will" in the bottom row (thick red line).
* **"never"**: The word "never" in the top row is strongly aligned with the word "never" in the bottom row (thick red line).
* **"be"**: The word "be" in the top row is strongly aligned with the word "be" in the bottom row (thick red line).
* **"perfect"**: The word "perfect" in the top row is strongly aligned with the word "perfect" in the bottom row (thick red line).
* **"."**: The period in the top row is strongly aligned with the period in the bottom row (thick red line).
* **"but"**: The word "but" in the top row is strongly aligned with the word "but" in the bottom row (thick red line).
* **"its"**: The word "its" in the top row is strongly aligned with the word "its" in the bottom row (thick red line).
* **"application"**: The word "application" in the top row is strongly aligned with the word "application" in the bottom row (thick red line).
* **"should"**: The word "should" in the top row is strongly aligned with the word "should" in the bottom row (thick red line).
* **"be"**: The word "be" in the top row is strongly aligned with the word "be" in the bottom row (thick red line).
* **"just"**: The word "just" in the top row is strongly aligned with the word "just" in the bottom row (thick red line).
* **"."**: The period in the top row is strongly aligned with the period in the bottom row (thick red line).
* **"this"**: The word "this" in the top row is strongly aligned with the word "this" in the bottom row (thick red line).
* **"is"**: The word "is" in the top row is strongly aligned with the word "is" in the bottom row (thick red line).
* **"what"**: The word "what" in the top row is strongly aligned with the word "what" in the bottom row (thick red line).
* **"we"**: The word "we" in the top row is strongly aligned with the word "we" in the bottom row (thick red line).
* **"are"**: The word "are" in the top row is strongly aligned with the word "are" in the bottom row (thick red line).
* **"missing"**: The word "missing" in the top row is strongly aligned with the word "missing" in the bottom row (thick red line).
* **"."**: The period in the top row is strongly aligned with the period in the bottom row (thick red line).
* **"in"**: The word "in" in the top row is strongly aligned with the word "in" in the bottom row (thick red line).
* **"my"**: The word "my" in the top row is strongly aligned with the word "my" in the bottom row (thick red line).
* **"opinion"**: The word "opinion" in the top row is strongly aligned with the word "opinion" in the bottom row (thick red line).
* **"<EOS>"**: The token "<EOS>" in the top row is strongly aligned with the token "<EOS>" in the bottom row (thick red line).
* **"<pad>"**: The token "<pad>" in the top row is strongly aligned with the token "<pad>" in the bottom row (thick red line).
### Key Observations
* The alignment is almost perfect, with each word in the top sentence aligning directly to the corresponding word in the bottom sentence.
* The lines are generally thick and dark red, indicating high confidence in the alignments.
### Interpretation
The diagram demonstrates a perfect alignment between two identical sentences. This could be a baseline or a control case in a natural language processing task, such as machine translation or paraphrase detection. The strong, direct alignments suggest a high degree of similarity and correspondence between the two sentences. The "<EOS>" token likely signifies the end of the sentence, and "<pad>" is likely a padding token used to ensure consistent sequence lengths.
</details>
Figure 5: Many of the attention heads exhibit behaviour that seems related to the structure of the sentence. We give two such examples above, from two different heads from the encoder self-attention at layer 5 of 6. The heads clearly learned to perform different tasks.