Case Study

The Transformer Architecture: A Comprehensive Mathematical Walkthrough from Encoder to Decoder

An in-depth exploration of how Transformers process and generate language, illustrated with step-by-step mathematical explnation through an example.

---

Introduction

This article provides a comprehensive mathematical walkthrough of the Transformer architecture, introduced by Vaswani et al. in 2017. The Transformer has revolutionized natural language processing (NLP) by relying entirely on attention mechanisms, enabling models to capture long-range dependencies more effectively and parallelize computations for improved performance and efficiency.

Using a simple yet illustrative example:

• Input Sentence: "Ajish works as an AI"
• Predicted Next Word: "Engineer"

the article dissects each component of the Transformer model—from the encoder's input embeddings to the decoder's output generation. It explains the mathematical operations involved in each step, the rationale behind them, and how they contribute to the overall efficacy of the architecture.

Contents

• Understanding Transformers
  • What is a Transformer?
  • Why Transformers?
• Part I: The Encoder
  • Step 1: Tokenization and Input Representation
  • Step 2: Positional Encoding
  • Step 3: Multi-Head Self-Attention
  • Step 4: Add & Norm
  • Step 5: Position-Wise Feed-Forward Network
  • Step 6: Stacking Multiple Encoder Layers
• Part II: The Decoder
  • Step 7: Shifted Right Input and Embedding
  • Step 8: Masked Multi-Head Self-Attention
  • Step 9: Encoder-Decoder Attention
  • Step 10: Add & Norm and Feed-Forward Network
  • Step 11: Stacking Multiple Decoder Layers
  • Step 12: Final Linear Layer and Softmax
• Conclusion
• References