# 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
\n
## Diagram: Transformer Model Architecture
### Overview
The image depicts the architecture of a Transformer model, a deep learning model commonly used in natural language processing. The diagram illustrates the encoder and decoder components, highlighting the key layers and connections within each. It shows the flow of data through the model, from input embeddings to output probabilities.
### Components/Axes
The diagram consists of two main stacks, labeled "Nx" on the right side, representing multiple layers. The left stack represents the encoder, and the right stack represents the decoder. Key components include:
* **Inputs:** The initial data fed into the encoder.
* **Outputs (shifted right):** The output of the decoder, shifted one position to the right for autoregressive prediction.
* **Positional Encoding:** A method to add information about the position of tokens in the sequence.
* **Input Embedding:** Converts input tokens into vector representations.
* **Output Embedding:** Converts output tokens into vector representations.
* **Masked Multi-Head Attention:** Attention mechanism used in the decoder to prevent looking ahead at future tokens.
* **Multi-Head Attention:** Attention mechanism used in both encoder and decoder to weigh the importance of different parts of the input sequence.
* **Add & Norm:** Residual connections and layer normalization.
* **Feed Forward:** Fully connected feedforward network.
* **Linear:** Linear transformation layer.
* **Softmax:** Activation function to produce probability distribution over output tokens.
* **Output Probabilities:** The final output of the model, representing the predicted probabilities for each token.
### Detailed Analysis or Content Details
The diagram shows a clear flow of information:
**Encoder (Left Stack):**
1. **Inputs** are passed through **Input Embedding**.
2. **Positional Encoding** is added to the embedded inputs.
3. The combined signal goes through multiple layers (Nx) of:
* **Add & Norm**
* **Multi-Head Attention**
* **Add & Norm**
* **Feed Forward**
**Decoder (Right Stack):**
1. **Outputs (shifted right)** are passed through **Output Embedding**.
2. **Positional Encoding** is added to the embedded outputs.
3. The combined signal goes through multiple layers (Nx) of:
* **Add & Norm**
* **Masked Multi-Head Attention**
* **Add & Norm**
* **Feed Forward**
4. The output of the final decoder layer is passed through:
* **Add & Norm**
* **Linear**
* **Softmax** to produce **Output Probabilities**.
The connections between the encoder and decoder are represented by arrows, indicating that the output of the encoder is used as input to the decoder's attention mechanisms. The "Nx" label indicates that the encoder and decoder stacks are repeated multiple times, creating a deep network.
### Key Observations
* The diagram emphasizes the use of attention mechanisms as a core component of the Transformer architecture.
* The residual connections ("Add & Norm") are present in every layer, facilitating gradient flow during training.
* The decoder uses a "Masked Multi-Head Attention" layer, which is crucial for autoregressive sequence generation.
* The positional encoding is added to both the input and output embeddings, indicating its importance in capturing sequential information.
### Interpretation
The diagram illustrates the key architectural elements of a Transformer model, which has revolutionized the field of natural language processing. The use of attention mechanisms allows the model to focus on relevant parts of the input sequence, while the residual connections and layer normalization improve training stability. The encoder-decoder structure enables the model to map input sequences to output sequences, making it suitable for tasks such as machine translation, text summarization, and question answering. The "Nx" notation highlights the depth of the model, which is crucial for capturing complex relationships in the data. The diagram provides a high-level overview of the Transformer architecture, without delving into the specific mathematical details of each component. It is a visual representation of a powerful and versatile deep learning model.
</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
\n
## Diagram: Attention Mechanism Flow
### Overview
The image depicts a diagram illustrating the flow of operations within an attention mechanism, likely used in a neural network architecture. The diagram shows a series of processing steps, represented as rectangular boxes, connected by arrows indicating the direction of data flow. Inputs 'Q' and 'K' feed into the initial processing, and 'V' is used later in the flow.
### Components/Axes
The diagram consists of the following components:
* **Inputs:** Q, K, V (positioned at the bottom of the diagram)
* **Processing Steps:**
* MatMul (Matrix Multiplication) - appears twice, once at the bottom and once near the top.
* Scale - positioned between the bottom MatMul and Mask.
* Mask (opt.) - indicating an optional masking operation.
* SoftMax - positioned above Mask.
* MatMul - positioned at the top.
* **Arrows:** Indicate the direction of data flow between the components.
* **Colors:** Each processing step is represented by a different color:
* MatMul: Purple
* Scale: Yellow
* Mask (opt.): Pink
* SoftMax: Green
### Detailed Analysis or Content Details
The diagram shows a sequential flow of operations:
1. Inputs Q and K are fed into the first MatMul operation (purple box).
2. The output of the first MatMul is passed to the Scale operation (yellow box).
3. The output of Scale is passed to the Mask (opt.) operation (pink box). The "(opt.)" indicates this step is optional.
4. The output of Mask is passed to the SoftMax operation (green box).
5. The output of SoftMax is passed to the second MatMul operation (purple box).
6. Input V is fed directly into the second MatMul operation (purple box).
The diagram does not contain any numerical values or specific parameters. It is a conceptual representation of the process.
### Key Observations
The diagram highlights the core components of an attention mechanism. The optional Mask step suggests the possibility of handling missing or irrelevant data. The use of two MatMul operations indicates a transformation of the input data at different stages. The flow is primarily linear, with a clear direction from inputs to output.
### Interpretation
This diagram illustrates a simplified attention mechanism, commonly used in sequence-to-sequence models and transformers. The attention mechanism allows the model to focus on different parts of the input sequence when generating the output.
* **Q (Query):** Represents the current state or context.
* **K (Key):** Represents the keys associated with each element in the input sequence.
* **V (Value):** Represents the values associated with each element in the input sequence.
The first MatMul operation (Q and K) calculates the attention weights, indicating the relevance of each element in the input sequence to the current context. The Scale operation likely normalizes these weights. The Mask operation allows the model to ignore certain elements in the input sequence. The SoftMax operation converts the weights into a probability distribution. Finally, the second MatMul operation (SoftMax output and V) calculates the weighted sum of the values, producing the attention output.
The diagram suggests a process of calculating attention weights based on the relationship between the query and keys, and then using these weights to selectively attend to the values. This allows the model to focus on the most relevant parts of the input sequence, improving its performance on tasks such as machine translation and text summarization.
</details>
Multi-Head Attention
<details>
<summary>Figures/ModalNet-20.png Details</summary>
### Visual Description
\n
## Diagram: Scaled Dot-Product Attention Mechanism
### Overview
The image depicts a diagram illustrating the Scaled Dot-Product Attention mechanism, a core component of the Transformer architecture used in natural language processing and other machine learning tasks. The diagram shows the flow of data through several linear transformations and the attention layer itself.
### Components/Axes
The diagram consists of the following components:
* **Inputs:** V, K, Q (representing Value, Key, and Query respectively)
* **Linear Transformations:** Three "Linear" blocks taking Q, K, and V as inputs.
* **Scaled Dot-Product Attention:** A large purple block labeled "Scaled Dot-Product Attention".
* **Concat:** A yellow block labeled "Concat".
* **Output Linear Transformation:** A "Linear" block at the top of the diagram.
* **h:** A label with the value 'h' attached to the right side of the Scaled Dot-Product Attention block.
The diagram uses arrows to indicate the flow of data between these components.
### Detailed Analysis or Content Details
The diagram shows a sequential flow of operations:
1. **Inputs:** The process begins with three inputs: V, K, and Q.
2. **Linear Transformations:** Each input (V, K, Q) is passed through a separate "Linear" transformation block.
3. **Scaled Dot-Product Attention:** The outputs of the three "Linear" blocks are fed into the "Scaled Dot-Product Attention" block.
4. **Concatenation:** The output of the "Scaled Dot-Product Attention" block is then passed to a "Concat" block.
5. **Output Linear Transformation:** Finally, the output of the "Concat" block is passed through another "Linear" transformation block to produce the final output.
6. **h:** The label 'h' is positioned on the right side of the Scaled Dot-Product Attention block, potentially indicating a hyperparameter or dimension related to the attention mechanism.
The arrows indicate a unidirectional flow of information from bottom to top. The arrows connecting the "Linear" blocks to the "Scaled Dot-Product Attention" block are gray. The arrow connecting the "Scaled Dot-Product Attention" block to the "Concat" block is also gray. The arrow connecting the "Concat" block to the final "Linear" block is also gray.
### Key Observations
The diagram illustrates a clear sequence of operations, highlighting the key steps involved in the Scaled Dot-Product Attention mechanism. The use of "Linear" transformations suggests that the inputs are being projected into different spaces before being used in the attention calculation. The "Concat" block likely combines the outputs of the attention mechanism in some way.
### Interpretation
This diagram represents a simplified view of the Scaled Dot-Product Attention mechanism. The attention mechanism is a crucial component of the Transformer architecture, enabling the model to focus on different parts of the input sequence when making predictions. The "Scaled Dot-Product Attention" block performs the core attention calculation, while the "Linear" transformations and "Concat" block prepare the inputs and combine the outputs. The 'h' label likely represents the number of attention heads, a key parameter in the Transformer architecture. The diagram effectively conveys the flow of information and the key components involved in this important machine learning technique. The diagram does not provide any numerical data or specific parameter values, but rather focuses on the structural relationships between the components.
</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.
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Attention Visualizations
<details>
<summary>x1.png Details</summary>
### Visual Description
\n
## Alluvial Diagram: Phrase Association
### Overview
The image presents an alluvial diagram visualizing the association between phrases. The diagram shows how phrases on the left side connect to phrases on the right side, with the width of the connecting flows indicating the strength of the association. The diagram appears to be analyzing text, likely related to political or legislative changes.
### Components/Axes
The diagram consists of two vertical axes, one on the left and one on the right. Each axis displays a series of phrases. The phrases are:
* **Left Axis:** "It is in spirit that a majority of American governments have passed new laws since 2009 making the registration or voting process more difficult."
* **Right Axis:** "It is in spirit that a majority of American governments have passed new laws since 2009 making the registration or voting process more difficult <pad> <pad> <pad> <pad> EOS"
The connections between phrases are represented by colored flows. The color scheme is as follows (approximate):
* Pink: Represents connections between phrases.
* Gray: Represents connections between phrases.
* Green: Represents connections between phrases.
* Red: Represents connections between phrases.
* Blue: Represents connections between phrases.
### Detailed Analysis
The diagram shows a strong association between the entire phrase on the left and the same phrase on the right, followed by "<pad>", "<pad>", "<pad>", "<pad>", and "EOS". The width of the flows indicates the strength of these associations.
* The phrase "It is in spirit that a majority of American governments have passed new laws since 2009 making the registration or voting process more difficult" on the left is strongly connected to the same phrase on the right. This connection is represented by a thick pink flow.
* There are also weaker connections to the "<pad>" tokens, represented by thinner gray, green, red, and blue flows.
* The final connection is to "EOS", represented by a thin blue flow.
The flows converge towards the right, indicating that the initial phrase is associated with the subsequent tokens. The "<pad>" tokens likely represent padding or filler words in a text processing context. "EOS" likely stands for "End of Sentence".
### Key Observations
* The dominant association is between the complete phrase on both sides, suggesting the diagram is highlighting the repetition or presence of this phrase in a dataset.
* The presence of "<pad>" tokens suggests the data was preprocessed, potentially for natural language processing tasks.
* The "EOS" token indicates the end of a sentence or text segment.
### Interpretation
This diagram likely represents the output of a text analysis process, possibly related to identifying and tracking the occurrence of a specific phrase within a larger corpus of text. The phrase "It is in spirit that a majority of American governments have passed new laws since 2009 making the registration or voting process more difficult" appears to be a key element in the analyzed data. The diagram suggests that this phrase is frequently followed by padding tokens and an end-of-sentence marker, indicating it often appears as a complete thought or sentence.
The use of an alluvial diagram suggests an attempt to visualize the flow of information or the relationships between different elements within the text. The diagram could be used to identify patterns, trends, or anomalies in the data. The fact that the phrase is strongly associated with padding and EOS tokens suggests it is a relatively self-contained unit of meaning.
The diagram doesn't provide any quantitative data beyond the relative widths of the flows, but it offers a visual representation of the associations between phrases, which can be useful for qualitative analysis. The diagram is a visualization of the frequency of the phrase and its context within the analyzed text.
</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
\n
## Chart: Attention Matrix / Alignment Plot
### Overview
The image depicts an attention matrix or alignment plot, visually representing relationships between a sequence of words. The x-axis and y-axis both display the same sequence of words: "The", "Law", "will", "never", "be", "perfect", "but", "its", "application", "should", "be", "just", "this", "is", "what", "we", "are", "missing", "in", "my", "opinion", "<EOS>", "<pad>". Lines connect words on the x-axis to words on the y-axis, with line intensity indicating the strength of the relationship. The lines are a light purple color.
### Components/Axes
* **X-axis:** "The", "Law", "will", "never", "be", "perfect", "but", "its", "application", "should", "be", "just", "this", "is", "what", "we", "are", "missing", "in", "my", "opinion", "<EOS>", "<pad>".
* **Y-axis:** "The", "Law", "will", "never", "be", "perfect", "but", "its", "application", "should", "be", "just", "this", "is", "what", "we", "are", "missing", "in", "my", "opinion", "<EOS>", "<pad>".
* **Lines:** Represent attention weights or alignment scores between words. The intensity of the lines is not easily quantifiable from the image.
* **Special Tokens:** "<EOS>" (End of Sentence) and "<pad>" (Padding) are included in the sequence.
### Detailed Analysis
The chart shows a complex network of connections between the words. Here's a breakdown of some notable connections, noting the difficulty in precise quantification:
* **"The" to "Law":** A strong connection exists between "The" and "Law", indicated by a relatively thick line.
* **"Law" to "will":** A connection exists between "Law" and "will".
* **"will" to "never":** A connection exists between "will" and "never".
* **"never" to "be":** A connection exists between "never" and "be".
* **"be" to "perfect":** A connection exists between "be" and "perfect".
* **"perfect" to "but":** A connection exists between "perfect" and "but".
* **"but" to "its":** A connection exists between "but" and "its".
* **"its" to "application":** A connection exists between "its" and "application".
* **"application" to "should":** A connection exists between "application" and "should".
* **"should" to "be":** A connection exists between "should" and "be".
* **"be" to "just":** A connection exists between "be" and "just".
* **"just" to "this":** A connection exists between "just" and "this".
* **"this" to "is":** A connection exists between "this" and "is".
* **"is" to "what":** A connection exists between "is" and "what".
* **"what" to "we":** A connection exists between "what" and "we".
* **"we" to "are":** A connection exists between "we" and "are".
* **"are" to "missing":** A connection exists between "are" and "missing".
* **"missing" to "in":** A connection exists between "missing" and "in".
* **"in" to "my":** A connection exists between "in" and "my".
* **"my" to "opinion":** A connection exists between "my" and "opinion".
* **"opinion" to "<EOS>":** A connection exists between "opinion" and "<EOS>".
* **"<EOS>" to "<pad>":** A connection exists between "<EOS>" and "<pad>".
* **Self-Attention:** Many words have connections to themselves (e.g., "The" to "The", "Law" to "Law"), indicating self-attention.
The lines are generally sparse, meaning most words do *not* have strong connections to most other words.
### Key Observations
* The chart appears to represent the attention weights learned by a model (likely a neural network) processing the given sentence.
* The connections are not symmetrical; the attention from "A" to "B" is not necessarily the same as from "B" to "A".
* The presence of "<EOS>" and "<pad>" suggests this is likely output from a sequence-to-sequence model or a transformer.
* The connections are relatively localized, meaning words tend to attend to nearby words in the sequence.
### Interpretation
This attention matrix visualizes how a model focuses on different parts of the input sequence when processing it. The lines represent the model's "attention" â which words it considers most relevant when dealing with a particular word. The strong connection between "The" and "Law" suggests the model recognizes "Law" as the primary subject being discussed. The connections forming a chain through the sentence indicate the model is processing the sentence sequentially. The connections to "<EOS>" and "<pad>" are expected, as these tokens mark the end of the sentence and padding for batch processing.
The sparsity of the connections suggests the model is not attending to every word equally, which is a desirable property for efficient processing. The pattern of connections provides insight into the model's understanding of the sentence's structure and meaning. The model appears to be capturing the relationships between words in a way that aligns with human intuition about sentence structure.
</details>
<details>
<summary>x3.png Details</summary>
### Visual Description
\n
## Diagram: Sentence Alignment/Dependency Visualization
### Overview
The image depicts a diagram illustrating a potential alignment or dependency relationship between two sentences. The sentences are presented horizontally, and a purple line connects words in the first sentence to corresponding words in the second sentence. The diagram appears to be related to natural language processing or computational linguistics, specifically focusing on how words in one sentence relate to words in another.
### Components/Axes
The diagram consists of two identical sentences positioned one above the other. Each sentence is broken down into individual words. A purple line connects the word "Law" in the first sentence to the word "Law" in the second sentence, and the word "application" in the first sentence to the word "application" in the second sentence. The sentences are:
"The Law will never be perfect but its application should be just - this is what we are missing in my opinion EOS pad>"
### Detailed Analysis or Content Details
The diagram highlights a direct correspondence between the words "The Law" and "application" in both sentences. The sentences are identical. The words "EOS" and "pad>" appear at the end of each sentence, likely representing end-of-sentence and padding tokens used in a computational context.
### Key Observations
The diagram focuses on a limited subset of words within the sentences, suggesting that these words are considered particularly important for the relationship being visualized. The connection between "Law" and "application" could indicate a focus on the practical implementation or consequences of the law. The presence of "EOS" and "pad>" suggests this is a representation used in a machine learning or NLP pipeline.
### Interpretation
The diagram likely represents a simplified view of a more complex process, such as machine translation, text summarization, or semantic analysis. The purple lines indicate a strong alignment or dependency between the corresponding words in the two sentences. This could be used to train a model to identify similar relationships in other texts. The fact that the sentences are identical suggests the diagram is illustrating a baseline or self-alignment scenario, perhaps as a starting point for more complex comparisons. The inclusion of "EOS" and "pad>" tokens indicates that the sentences are being treated as sequences of data for a computational model. The diagram is not presenting data in the traditional sense, but rather a visualization of relationships between textual elements. It's a representation of linguistic structure, not a statistical chart.
</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
\n
## Diagram: Dependency Graph of Words
### Overview
The image depicts a dependency graph visualizing relationships between words in a sentence or sequence. The words are arranged horizontally, and lines connect them, indicating dependencies. The graph appears to represent a linguistic structure, potentially from a natural language processing task.
### Components/Axes
The diagram consists of the following components:
* **Words:** The words are listed along the horizontal axis, from left to right: "The", "Law", "will", "never", "be", "perfect", "but", "its", "application", "should", "just", "this", "is", "what", "we", "are", "missing", "in", "my", "opinion", "<EOS>", "pad".
* **Lines:** Green lines connect the words, representing dependencies. The lines originate from words on the bottom row and terminate on words in the top row.
* **Vertical Axis:** The vertical position of the words and lines indicates the dependency relationships.
* **Legend:** A vertical green bar on the far right labeled "<EOS>" and "pad".
### Detailed Analysis
The diagram shows a complex network of dependencies. Here's a breakdown of the connections:
* "The" connects to "Law".
* "Law" connects to "will".
* "will" connects to "never".
* "never" connects to "be".
* "be" connects to "perfect".
* "perfect" connects to "but".
* "but" connects to "its".
* "its" connects to "application".
* "application" connects to "should".
* "should" connects to "just".
* "just" connects to "this".
* "this" connects to "is".
* "is" connects to "what".
* "what" connects to "we".
* "we" connects to "are".
* "are" connects to "missing".
* "missing" connects to "in".
* "in" connects to "my".
* "my" connects to "opinion".
* "opinion" connects to "<EOS>".
* "<EOS>" connects to "pad".
The lines are not strictly one-to-one; some words have multiple incoming connections. For example, "be" receives a connection from "never" and "perfect".
### Key Observations
The diagram illustrates a sequential dependency structure. The connections suggest a grammatical or semantic relationship between the words. The presence of "<EOS>" (End of Sentence) and "pad" suggests this is a representation of a sentence or a sequence of tokens used in a language model. The lines are relatively dense, indicating a high degree of interconnectedness between the words.
### Interpretation
This diagram likely represents the output of a dependency parser, a component of many natural language processing systems. Dependency parsing aims to identify the grammatical relationships between words in a sentence. The lines in the diagram represent these relationships, showing which words modify or depend on others.
The sequence of words suggests a statement about the law: "The Law will never be perfect, but its application should just this is what we are missing in my opinion." The diagram visually represents how the parser has broken down this sentence into its constituent parts and identified the relationships between them.
The "<EOS>" and "pad" tokens are common in NLP tasks, where "<EOS>" marks the end of a sentence and "pad" is used to fill shorter sequences to a uniform length for batch processing. The diagram's structure suggests it could be part of a larger system for analyzing or generating text. The density of connections indicates a complex sentence structure. The diagram is a visual representation of the syntactic structure of the sentence.
</details>
<details>
<summary>x5.png Details</summary>
### Visual Description
\n
## Diagram: Connection Map of Words
### Overview
The image depicts a connection map between words, visualized as a series of lines connecting each word to every other word. The words are arranged horizontally along both the x and y axes. The lines are a reddish-pink color and appear to represent some form of relationship or association between the words. The background is a light gray.
### Components/Axes
The diagram consists of the following words, arranged along both axes:
* "The"
* "Law"
* "will"
* "never"
* "be"
* "perfect"
* "but"
* "its"
* "application"
* "should"
* "just"
* "this"
* "is"
* "what"
* "we"
* "are"
* "missing"
* "in"
* "my"
* "opinion"
* "<EOS>"
* "<pad>"
There are no explicit axis titles or a legend. The axes are implicitly defined by the arrangement of the words.
### Detailed Analysis
The diagram shows a full connection matrix, meaning every word is connected to every other word with a line. The lines are all the same color, indicating that the type of relationship between the words is consistent across all connections. The lines are relatively thin and numerous, creating a dense network of connections.
There is no numerical data associated with the connections. The diagram is purely visual, representing the presence or absence of a connection between words.
### Key Observations
The diagram demonstrates that every word is related to every other word in the set. The density of the connections suggests a high degree of interconnectedness between the concepts represented by these words. The inclusion of "<EOS>" and "<pad>" suggests this data may be related to a language model or text processing task, where these tokens are used for sentence boundary and padding purposes.
### Interpretation
This diagram likely represents a co-occurrence or association matrix derived from a corpus of text. Each line indicates that two words appeared together within a certain context (e.g., within a sentence or a fixed-size window). The diagram suggests that all the words in the set are relevant to the same underlying topic or domain. The presence of "<EOS>" and "<pad>" further supports the hypothesis that this diagram is a visualization of data used in natural language processing.
The diagram doesn't reveal the *strength* of the relationships between words, only their *existence*. It's possible that some connections are more frequent or significant than others, but this information is not conveyed in the visualization. The diagram is a high-level overview of the relationships between words, and further analysis would be needed to understand the nuances of these connections.
The choice of words ("Law", "perfect", "opinion", "missing") suggests a possible theme related to legal reasoning, evaluation, or critique. However, without knowing the source text, it's difficult to draw definitive conclusions.
</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.