The Math Behind Attention Mechanisms in Large Language Models

Jul 10, 2024

The Math Behind Attention Mechanisms in Large Language Models

Introduction

  • Presenter: Louis Serrano
  • Main Focus: Attention mechanisms in large language models
  • Importance: Key step in the success of Transformers
  • Structure: This is the second video in a series of three
    • First video: High-level overview of attention
    • This video: Detailed math behind attention
    • Third video: Putting it all together to show how Transformers work

Key Concepts

  • Context Understanding: Words gravitate towards each other based on context.
  • Transformer: Groundbreaking paper "Attention is All You Need".

Similarity Between Words

  • Similarity measures can be computed using:
    • Dot Product
    • Cosine Similarity

Embeddings

  • Embeddings: Representing words or text in high-dimensional space
    • Similar words are placed close together in this space.
  • Contextual Placement: Example with the word "apple"
    • Can be a fruit or a technology brand based on context.
    • Context is provided by neighboring words.

Attention Step

  • Gravity Analogy: Similar words have a strong gravitational pull.
  • Similarity Measure: High similarity for similar words, low for different words
    • Example: Cherry and orange are similar (high similarity).
    • Cherry and phone are different (low similarity).
  • Similarity Calculations:
    • Dot Product: High for similar words, low/zero for different words.
    • Cosine Similarity: Measure of angle between word vectors (0 to 1).
    • Scaled Dot Product: Dividing dot product by the square root of vector length to manage large values.

Example Calculation

  • Similarities between words such as "an apple and orange"
    • Each word is moved based on the similarity with other words.
    • Normalization: Ensure coefficients add to one.
    • Softmax Function: Convert coefficients to positive values, preserving order.

Keys, Queries, and Values Matrices

  • Keys and Queries Matrices: Modify embeddings to best calculate similarities.
    • Transform original embeddings to improve attention.
  • Values Matrix: Optimize for moving words and finding the next word in a sentence.
    • Moves words in embedding optimized for next-word prediction.
  • Linear Transformations: Concatenate and scale embeddings for better context capture.

Summary Steps

  1. Compute similarity (dot product) between words.
  2. Adjust similarity with Softmax to ensure coefficients add up to one.
  3. Use keys and queries matrices to create optimized embedding for similarity calculation.
  4. Use values matrix to move words in an embedding optimized for next-word prediction.

Multi-Head Attention

  • Multiple Heads: Use multiple sets of key, query, and value matrices to capture various contexts.
    • Concatenate results into a high-dimensional embedding.
    • Apply a final linear transformation to manage dimensions and improve results.

Training with Transformers

  • Training: Key, query, and value matrices are learned during the training of the Transformer.
  • Multi-layer Setup: Each layer refines the embeddings through repeated processing.

Conclusion

  • Attention in Transformers: Essential for understanding and generating text contextually.
  • Third Video Teaser: Upcoming video will cover Transformer models in-depth.
  • Resources: Mention of courses, book, and additional learning materials.

Acknowledgements

  • Thanks to contributors and colleagues who helped understand and explain the concepts.