Polar probe linearly decodes semantic structures from LLMs

2026-05-13

AI Summary

This work investigates how large language models construct complex semantic structures through conceptual binding. The authors propose a polar-coordinate probing method based on embedding distance and direction to decode, within linear subspaces of intermediate model layers, both the existence of relational structure between entities (encoded by distance) and the specific relation type (encoded by direction). This study provides the first evidence that large language models organize semantic information according to simple geometric principles, demonstrating the probe’s generalization across diverse domains. Experimental results show that the method effectively recovers ground-truth semantic structures, with performance improving as model scale increases, and reveal a strong correlation between probing accuracy and the model’s ability to answer structured queries.

Abstract

How do artificial neural networks bind concepts to form complex semantic structures? Here, we propose a simple neural code, whereby the existence and the type of relations between entities are represented by the distance and the direction between their embeddings, respectively. We test this hypothesis in a variety of Large Language Models (LLMs), each input with natural-language descriptions of minimalist tasks from five different domains: arithmetic, visual scenes, family trees, metro maps and social interactions. Results show that the true semantic structures can be linearly recovered with a Polar Probe targeting a subspace of LLMs' layer activations. Second, this code emerges mostly in middle layers and improves with LLM performance. Third, these Polar Probes successfully generalize to new entities and relation types, but degrades with the size of the semantic structure. Finally, the quality of the polar representation correlates with the LLM's ability to answer questions about the semantic structure. Together, these findings suggest that LLMs learn to build complex semantic structures by binding representations with a simple geometrical principle.

Problem

• semantic structures
• concept binding
• Large Language Models
• neural representation
• relational reasoning

Innovation

• Polar Probe
• semantic structure
• embedding geometry
• Large Language Models
• relational binding