DOCS: Quantifying Weight Similarity for Deeper Insights into Large Language Models

TL;DR

This paper introduces DOCS, a new index for measuring weight matrix similarity in large language models, revealing layer clustering and functional patterns to enhance understanding and interpretability of LLM architectures.

Contribution

The paper presents DOCS, a novel similarity index for LLM weights, and demonstrates its effectiveness in analyzing layer relationships and functional specialization.

Findings

Adjacent layers often have high weight similarity.

Weight matrices tend to form clusters indicating specialization.

DOCS is theoretically effective for orthogonal matrices.

Abstract

We introduce a novel index, the Distribution of Cosine Similarity (DOCS), for quantitatively assessing the similarity between weight matrices in Large Language Models (LLMs), aiming to facilitate the analysis of their complex architectures. Leveraging DOCS, our analysis uncovers intriguing patterns in the latest open-source LLMs: adjacent layers frequently exhibit high weight similarity and tend to form clusters, suggesting depth-wise functional specialization. Additionally, we prove that DOCS is theoretically effective in quantifying similarity for orthogonal matrices, a crucial aspect given the prevalence of orthogonal initializations in LLMs. This research contributes to a deeper understanding of LLM architecture and behavior, offering tools with potential implications for developing more efficient and interpretable models.