Traveling Words: A Geometric Interpretation of Transformers

TL;DR

This paper offers a geometric interpretation of transformer models, showing how layer normalization and attention mechanisms operate on a hyper-sphere to model semantic relationships, validated through probing a GPT-2 model.

Contribution

It introduces a novel geometric perspective that explains transformer inner workings, connecting properties like iterative refinement and contextual embeddings.

Findings

Layer normalization confines features to a hyper-sphere.

Early layers show distinct query-key attention patterns.

Deeper layers exhibit subject-specific attention heads.

Abstract

Transformers have significantly advanced the field of natural language processing, but comprehending their internal mechanisms remains a challenge. In this paper, we introduce a novel geometric perspective that elucidates the inner mechanisms of transformer operations. Our primary contribution is illustrating how layer normalization confines the latent features to a hyper-sphere, subsequently enabling attention to mold the semantic representation of words on this surface. This geometric viewpoint seamlessly connects established properties such as iterative refinement and contextual embeddings. We validate our insights by probing a pre-trained 124M parameter GPT-2 model. Our findings reveal clear query-key attention patterns in early layers and build upon prior observations regarding the subject-specific nature of attention heads at deeper layers. Harnessing these geometric insights, we present an intuitive understanding of transformers, depicting them as processes that model the trajectory of word particles along the hyper-sphere.