Attention

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Created: =dateformat(this.file.ctime,"dd MMM yyyy, hh:mm a") | Modified: =dateformat(this.file.mtime,"dd MMM yyyy, hh:mm a") Tags: knowledge

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Overview

Introduction

• Prerequisite to Transformers

• In NLP, transformers and attention have been utilized successfully for many tasks

  • Crucial to understand how attention emerged from NLP, since it is now SoTA for vision too

  Memory is attention through time. ~ Alex Graves 2020

Attention mechanism emerged naturally from problems that deal with time-series data (sequences).

Recurrent Neural Networks (RNNs)

• Before attention was using Sequence to Sequence (Seq2Seq) to handle sequences
• Elements of the sequence called tokens (can be text, pixels, images, videos)
• ⇒ Goal: Transform input sequence (source) to new sequence (target)
  • where can be any length
• RNNs were king of such tasks, since there is a preference to treat sequences sequentially
• RNN based architectures used to work very well with (Long Short-Term Memory) LSTM, (Gated Recurrent Units) GRU components
• But only for small sequences

Limitations of RNNs

• Only works well for small sequences
  • intermediate representation $z$ cannot encode all information from inputs ⇒ bottleneck problem
  • forgets information from timesteps further behind
• Stacked RNN layer creates vanishing gradient problem
  • 

Core Idea for Attention

• Aim to solve 1) problem with longer sequences 2) vanishing gradient problem with the idea that: The context vector z should have access to all parts of the input sequence instead of just the last one.
• i.e. form direct connection with each timestamp

Look at all the different words at the same time and learn to “pay attention“ to the correct ones depending on the task.

• Attention is simply a notion of memory, gained from attending at multiple inputs through time.

Types of Attention

1. Implicit vs Explicit Attention Implicit
   • DNNs already learn some implicit version of attention
   • e.g. focusing on certain parts of the inputs compared to others
   • Visualized by looking at partial derivatives with respect to the input
     • Ideas for GradCAM?
     • Jacobian Matrix
   Explicit
   • Asking the network to ‘weigh’ its sensitivity to the input based on memory from previous inputs
   • Main type of attention whenever it is mentioned
2. Hard vs Soft Attention Hard
   • Can be described by discrete variables
   • Non-differentiable
     • cannot use gradient descent
   • Train them using RL techniques such as policy gradients, REINFORCE algorithm
     • but they have high variance
   • Consider as a switch mechanism to determine whether to attend to a region or not, which means that the function has many abrupt changes over its domain
   Soft
   • Can be described by continuous variables
   • Parametrized by differentiable functions
     • The function varies smoothly over its domain and, as a result, it is differentiable
   Given the full sequence is available, can mainly consider the soft attention instead, such that we can use backprop.

Broad categories of Attention Mechanisms

Name	Definition	Citation
Self-Attention(&)	Relating different positions of the same input sequence. Theoretically the self-attention can adopt any score functions above, but just replace the target sequence with the same input sequence.	Cheng2016
Global/Soft	Attending to the entire input state space.	Xu2015
Local/Hard	Attending to the part of input state space; i.e. a patch of the input image.	Xu2015; Luong2015
(&) Also, referred to as “intra-attention” in Cheng et al., 2016 and some other papers.

For now consider global, soft attention.

Original Attention Mechanism Formulation

In the encoder-decoder RNN case, given previous state in the decoder as ${\text{y}}_{i-1}$ and the the hidden state $\text{h}=h_1,h_2,h_n$, we have something like this:

$$\begin{array}{r}{\text{e}}_i=\mathrm{attentio}{\mathrm{n}}_{\mathrm{net}}\left(y_{i-1},\text{h}\right)\in R{}^n\end{array}$$

The index $i$ indicates the prediction step. Essentially, we define a score between the hidden state of the decoder and all the hidden states of the encoder.

More specifically, for each hidden state (denoted by $j$) $h_1,h_2,h_n$​ we will calculate a scalar (known as an “alignment score” per Bahdanau 2014): $e_{ij}=\mathrm{attentio}{\mathrm{n}}_{\mathrm{net}}\left({\text{y}}_{i-1},h_j\right)$ Then, to form a probability distribution, and to distribute the scores far from each other, $e_{ij}$ is added into a softmax such that ${\alpha }_{ij}$ (known as the “weights” per Bahdanau 2014) is obtained: ${\alpha }_{ij}=\frac{\exp \left(e_{ij}\right)}{{\sum }_{k=1}^{T_x}\exp \left(e_{ik}\right)}=\mathrm{softmax}(e_{ij})$ Lastly, intermediate representation of attention $z_i$ (known as the “context vector” per Bahdanau 2014) is obtained: $z_i={\sum }_{j=1}^T{\alpha }_{ij}{\text{h}}_j$ Therefore:

• Attention $z_i$ is defined as weighted average of values, where the weighting is a learned function
• ${\alpha }_{ij}$ can be thought of as data-dependent dynamic weights

But, this formulation is independent of the choice in modelling attention.

Types of Attention Mechanism Formulations

Name	Alignment score function	Citation
Content-base attention	$\text{score}({\mathbf{s}}_t,{\mathbf{h}}_i)=\text{cosine}[{\mathbf{s}}_t,{\mathbf{h}}_i]$ where $\text{cosine}$ refers to the cosine similarity metric.	Graves2014
Additive(*)	$\text{score}({\mathbf{s}}_t,{\mathbf{h}}_i)={\mathbf{v}}_a^{\top }\tanh ({\mathbf{W}}_a[{\mathbf{s}}_{t-1};{\mathbf{h}}_i])$ which refers to the familiar neural network approach with an activation function.	Bahdanau2015
Location-Base	${\alpha }_{t,i}=\text{softmax}({\mathbf{W}}_a{\mathbf{s}}_t)$ Note: This simplifies the softmax alignment to only depend on the target position.	Luong2015
General	$\text{score}({\mathbf{s}}_t,{\mathbf{h}}_i)={\mathbf{s}}_t^{\top }{\mathbf{W}}_a{\mathbf{h}}_i$ where ${\mathbf{W}}_a$ is a trainable weight matrix in the attention layer.	Luong2015
Dot-Product	$\text{score}({\mathbf{s}}_t,{\mathbf{h}}_i)={\mathbf{s}}_t^{\top }{\mathbf{h}}_i$	Luong2015
Scaled Dot-Product(^)	$\text{score}({\mathbf{s}}_t,{\mathbf{h}}_i)=\frac{{\mathbf{s}}_t^{\top }{\mathbf{h}}_i}{\sqrt{n}}$ Note: very similar to the dot-product attention except for a scaling factor; where n is the dimension of the source hidden state.	Vaswani2017
Notes:

• The symbol $s_t$​ denotes the predictions (previous sections used $y_t$ or $y_{i-1}$​), while different $\mathbf{W}$ indicate trainable matrices.
• (*) Referred to as “concat” in Luong, et al., 2015 and as “additive attention” in Vaswani, et al., 2017.
• (^) It adds a scaling factor $1/\sqrt{n}$, motivated by the concern when the input is large, the softmax function may have an extremely small gradient, hard for efficient learning.

Most popular till now is Additive(*) by Bahdanau:

• Parametrize attention as small fully connected neural network
• Means that attention is set of trainable weights
• And that it can be tuned with standard backpropagaion

But this method limitations:

• Computational complexity
  • NN to train with $O(T^2)$ weights, where $T$ is the length of input and output sentence ⇒ addressed by local attention

Local Attention

• consider only a subset of the input units/tokens
• can also be merely seen as hard attention since we need to take a hard decision first, to exclude some input units Note: colors in the attention indicate that these weights are constantly changing while in convolution and fully connected layers they are slowly changing by gradient descent

Self-Attention

• Also, referred to as “intra-attention” in Cheng et al., 2016 and some other papers.
• Key component to Transformers (further elaborated there) and Vision Transformers (ViT)

Main Idea

• Define attention of the same sequence
• Instead of input-output sequence association, look for scores between elements of the sequence.
• Can be regarded as a (k-vertex) connected undirected weighted graph. Undirected indicates that the matrix is symmetric.
• ${self-attention}_{net}(x,x)$ instead of previous $\mathrm{attentio}{\mathrm{n}}_{\mathrm{net}}\left(y_{i-1},\text{h}\right)$
• Can be computed in any trainable way
• End goal: create a meaningful representation of the sequence before transforming to another

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Conclusion

Advantages of Attention

• Usually eliminates the vanishing gradient problem, as they provide direct connections between the encoder states and the decoder.
  • Conceptually acts similarly as skip connections in CNNs.
• Explainability
  • By inspecting the distribution of attention weights, we can gain insights into the behavior of the model, as well as to understand its limitations.

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Theoretical References

Papers

Articles

• How Attention works in Deep Learning: understanding the attention mechanism in sequence models | AI Summer
• Lilian Weng - Attention? Attention!
• Understanding and Coding Self-Attention, Multi-Head Attention, Cross-Attention, and Causal-Attention in LLMs

Courses

• DeepMind’s deep learning videos 2020 with UCL: Attention and Memory in Deep Learning, Alex Graves

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Code References

Methods

Tools, Frameworks

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