Understanding Transformers: A Detailed Guide for Beginners

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 Introduction

Transformers are a powerful type of neural network architecture that have revolutionized natural language processing (NLP). They excel at capturing relationships between words in a sentence, making them the backbone of various language models like BERT and GPT.

1. Traditional Approaches: The Limitations

In traditional NLP models, such as recurrent neural networks (RNNs) or long short-term memory networks (LSTMs), the model processes words sequentially. This sequential processing makes it challenging to capture long-range dependencies and understand the entire context of a sentence.

2. Enter Transformers: Self-Attention Mechanism

Transformers introduced a breakthrough mechanism called self-attention. It allows the model to weigh the importance of different words in a sentence, considering the relationships between all words simultaneously.

Formulation:

Given a sequence of input vectors $X=[x_1,x_2,\mathrm{.}\mathrm{.}\mathrm{.},x_n]$, the self-attention mechanism computes a set of attention scores $A=[a_1,a_2,\mathrm{.}\mathrm{.}\mathrm{.},a_n]$ where each attention score $a_i$ represents the importance of the corresponding word $x_i$.

$a_i=\frac{e^{(W_q{x}_i)\cdot (W_k{x}_i)}}{\sqrt{d}}$

​e(Wq​xi​)⋅(Wk​xi​)​

Here:

• $W_q$ and $W_k$ are weight matrices for query and key projections.
• $d$ is the dimensionality of the word vectors.

3. Multi-Head Attention: Looking from Different Angles

To capture different aspects of the relationships between words, transformers use multiple attention heads. Each head provides a different perspective or angle on the relationships.

Formulation:

For $h$ attention heads, the output of the multi-head attention is computed as follows:

$\text{MultiHead}(X)=\text{Concat}({\text{Head}}_1(X),{\text{Head}}_2(X),\mathrm{.}\mathrm{.}\mathrm{.},{\text{Head}}_h(X))\cdot W_o$

Here:

• ${\text{Head}}_i(X)$ is the output of the $i$-th attention head.
• $W_o$ is the output weight matrix.

4. Stacking Layers: Building Deeper Understanding

Transformers consist of multiple layers of self-attention and feedforward neural networks. Stacking these layers allows the model to learn increasingly complex relationships and abstractions in the data.

Formulation:

The output of a transformer layer is computed as follows:

$\text{Output}=\text{LayerNorm}(\text{MultiHead}(\text{Input})+\text{Input})$

Here:

• $\text{LayerNorm}$ is a layer normalization operation.

5. Bidirectionality: Capturing Context from Both Sides

Unlike traditional models that read text from left to right or right to left, transformers are bidirectional. They consider the entire context from both directions, capturing richer relationships between words.

Putting It All Together: Example

Let's consider a simple example:

Input Sentence: "The cat sat on the mat."

Tokenization:                       $X=\left[\begin{array}{c}\text{The}\\ \text{cat}\\ \text{sat}\\ \text{on}\\ \text{the}\\ \text{mat}\\ \text{.}\end{array}\right]$

Self-Attention Calculation: $A=\left[\begin{array}{c}{a}_1\\ a_2\\ a_3\\ a_4\\ a_5\\ a_6\\ a_7\end{array}\right]=\text{SelfAttention}(X)$

Multi-Head Attention: $$

$\text{MultiHead}(X)=\text{Concat}({\text{Head}}_1(X),{\text{Head}}_2(X))\cdot W_o$

$=\text{Concat}({\text{Head}}_1(X),{\text{Head}}_2(X))\cdot W_o$

Stacking Layers: $$

$\text{Output}=\text{LayerNorm}(\text{MultiHead}(\text{Input})+\text{Input})$

$=\text{LayerNorm}(\text{MultiHead}(\text{Input})+\text{Input})$

This example shows a simplified version of how a transformer processes a sentence through self-attention and multiple layers.

Conclusion

Transformers are a powerful tool for understanding language, capturing relationships between words, and building sophisticated language models. As you delve deeper into NLP, these concepts will serve as the foundation for understanding models like BERT and GPT.

 

If you're looking to delve deeper into the implementation and understanding of a basic Transformer, you can explore a notebook available at the following link: Basic Transformer Implementation. This notebook likely provides a step-by-step guide on how to build and comprehend the workings of a fundamental Transformer model using PyTorch. It could be a valuable resource for learners aiming to grasp the core concepts and structure of the Transformer architecture.