Investigating Representation Universality: Case Study on Genealogical Representations

TL;DR

This paper explores whether large language models universally encode graph-structured knowledge using geometric structures, providing experimental evidence across multiple models and architectures to understand their internal representations.

Contribution

It introduces novel methods to identify and verify geometric subspaces in LLMs related to graph knowledge and compares representations across diverse models and architectures.

Findings

Identified a tree-like subspace in residual streams for genealogy questions

Validated causal effect of this subspace via activation patching

Quantified representational alignment across different models

Abstract

Motivated by interpretability and reliability, we investigate whether large language models (LLMs) deploy universal geometric structures to encode discrete, graph-structured knowledge. To this end, we present two complementary experimental evidence that might support universality of graph representations. First, on an in-context genealogy Q&A task, we train a cone probe to isolate a tree-like subspace in residual stream activations and use activation patching to verify its causal effect in answering related questions. We validate our findings across five different models. Second, we conduct model stitching experiments across models of diverse architectures and parameter counts (OPT, Pythia, Mistral, and LLaMA, 410 million to 8 billion parameters), quantifying representational alignment via relative degradation in the next-token prediction loss. Generally, we conclude that the lack of ground truth representations of graphs makes it challenging to study how LLMs represent them. Ultimately, improving our understanding of LLM representations could facilitate the development of more interpretable, robust, and controllable AI systems.