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A Novel Spinor-Based Embedding Model for Transformers

Rick White

TL;DR

This paper proposes a novel approach to word embeddings in Transformer models by utilizing spinors from geometric algebra to enhance the expressiveness and robustness of language representations.

Abstract

This paper proposes a novel approach to word embeddings in Transformer models by utilizing spinors from geometric algebra. Spinors offer a rich mathematical framework capable of capturing complex relationships and transformations in high-dimensional spaces. By encoding words as spinors, we aim to enhance the expressiveness and robustness of language representations. We present the theoretical foundations of spinors, detail their integration into Transformer architectures, and discuss potential advantages and challenges.

A Novel Spinor-Based Embedding Model for Transformers

TL;DR

This paper proposes a novel approach to word embeddings in Transformer models by utilizing spinors from geometric algebra to enhance the expressiveness and robustness of language representations.

Abstract

This paper proposes a novel approach to word embeddings in Transformer models by utilizing spinors from geometric algebra. Spinors offer a rich mathematical framework capable of capturing complex relationships and transformations in high-dimensional spaces. By encoding words as spinors, we aim to enhance the expressiveness and robustness of language representations. We present the theoretical foundations of spinors, detail their integration into Transformer architectures, and discuss potential advantages and challenges.
Paper Structure (82 sections, 22 equations, 8 figures)

This paper contains 82 sections, 22 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Background
  3. Word Embeddings
  4. Geometric Algebra and Spinors
  5. Clifford Algebra
  6. Spinors
  7. Proposed Method
  8. Spinor Representation of Words
  9. Embedding Function
  10. Encoding Semantic Relationships
  11. Integration with Transformer Models
  12. Embedding Layer
  13. Spinor Operations in Self-Attention
  14. Attention Mechanism
  15. Positional Encoding
  16. ...and 67 more sections

Figures (8)

  • Figure 1: Rotation from "actor" to "actress" in spinor space
  • Figure 2: 720-degree rotation in spinor space
  • Figure 3: Rotation representing verb tense changes
  • Figure 4: Reflection representing antonyms
  • Figure 5: Reflection representing negation
  • ...and 3 more figures