Attention's Gravitational Field:A Power-Law Interpretation of Positional Correlation

TL;DR

This paper introduces the Attention Gravitational Field (AGF), a novel interpretation of positional relationships in Large Language Models, linking them to a power-law and gravitational analogy to improve understanding and model performance.

Contribution

It presents the AGF concept, decouples positional encodings from semantics, and demonstrates its theoretical and empirical alignment with physical laws, advancing interpretability and optimization.

Findings

AGF aligns with Newton's Law of Universal Gravitation

Decoupling positional encodings improves model accuracy

AGF shows consistency with learning and stability curves

Abstract

This paper explores the underlying principles of positional relationships and encodings within Large Language Models (LLMs) and introduces the concept of the Attention Gravitational Field (AGF). By decoupling positional encodings from semantic embeddings, we optimize the model architecture and achieve superior accuracy compared to prevailing encoding methods. Furthermore, we provide an in-depth analysis of AGF, demonstrating its intrinsic consistency with learning and stability curves, as well as its empirical alignment with Newton's Law of Universal Gravitation. By offering a rigorous theoretical exploration of these phenomena, this work represents a significant step toward interpreting the Attention mechanism and unlocks new possibilities for future research in model optimization and interpretability.