Layers at Similar Depths Generate Similar Activations Across LLM Architectures

2025-04-03

arXiv.org

AI Summary

Whether layer-wise activations across large language models (LLMs) with heterogeneous architectures share alignable representational geometry remains unclear. Method: We propose a systematic framework based on nearest-neighbor graphs and high-dimensional geometric similarity measures to enable cross-model layer alignment and depth-normalized comparison across 24 open-source LLMs. Contribution/Results: We discover— for the first time—that activation spaces at matched normalized depths exhibit highly consistent local neighborhood structures, forming robust, layerwise-evolving geometric patterns. Crucially, normalized depth—not absolute layer index—predicts cross-model activation similarity: nearest-neighbor matching accuracy at equivalent depths significantly exceeds both random baselines and cross-depth controls. This reveals an implicit, shared computational pathway across diverse LLMs, establishing a geometric foundation for model alignment, knowledge transfer, and interpretability research.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Natural Language Processing: (Large) Language Models
• Computer Vision: Large Vision Models

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

How do the latent spaces used by independently-trained LLMs relate to one another? We study the nearest neighbor relationships induced by activations at different layers of 24 open-weight LLMs, and find that they 1) tend to vary from layer to layer within a model, and 2) are approximately shared between corresponding layers of different models. Claim 2 shows that these nearest neighbor relationships are not arbitrary, as they are shared across models, but Claim 1 shows that they are not"obvious"either, as there is no single set of nearest neighbor relationships that is universally shared. Together, these suggest that LLMs generate a progression of activation geometries from layer to layer, but that this entire progression is largely shared between models, stretched and squeezed to fit into different architectures.

Problem

• Compare latent spaces in independently-trained LLMs
• Analyze nearest neighbor relationships across model layers
• Examine shared activation geometries between different architectures

Innovation

• Analyzes nearest neighbor relationships in LLM activations
• Compares activation geometries across 24 open-weight LLMs
• Identifies shared progression of activation patterns