Formalizing Latent Thoughts: Four Axioms of Thought Representation in LLMs

Hugging Face Daily Papers Papers
axiomatic-evaluation latent-thought-representations llm-reasoning representation-quality functional-axioms

Summary

Introduces an axiomatic evaluation framework for latent thought representations in LLMs, revealing that current representations fail to satisfy four fundamental functional axioms (Causality, Minimality, Separability, Stability) across 23 reasoning tasks, indicating a structural gap in representation quality.

We introduce an axiomatic evaluation framework for latent thought representations in LLMs, comprising metrics that are independent of downstream benchmark scores and reveal representational failures that benchmark accuracy masks. Existing evaluations conflate representation quality with model capacity. Therefore, failures cannot be attributed to the representation rather than to the model that processes it. We formalize four functional axioms (Causality, Minimality, Separability, and Stability) and define a quantitative measure for each, computed directly on the representation independently of downstream accuracy. We audit open-weight LLMs across 23 reasoning tasks (e.g., Spatial Reasoning, Factual QA). We find that no candidate satisfies all four axioms simultaneously, that the representations distinguish task type reliably but cannot distinguish between two questions within the same task, and that the representations encode little information beyond what is already present in the input embedding. The failure is consistent across dense, reasoning-distilled, and RL-trained model families, indicating that the gap is structural rather than a property of model size or training procedure.
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Source: https://huggingface.co/papers/2606.27378

Abstract

An axiomatic evaluation framework reveals systematic failures in latent thought representations of LLMs across multiple reasoning tasks, demonstrating that current representations fail to satisfy fundamental functional axioms consistently across different model architectures.

We introduce anaxiomatic evaluation frameworkforlatent thought representationsinLLMs, comprising metrics that are independent ofdownstream benchmark scoresand reveal representational failures that benchmark accuracy masks. Existing evaluations conflaterepresentation qualitywithmodel capacity. Therefore, failures cannot be attributed to the representation rather than to the model that processes it. We formalize fourfunctional axioms(Causality,Minimality,Separability, andStability) and define a quantitative measure for each, computed directly on the representation independently of downstream accuracy. We auditopen-weight LLMsacross 23reasoning tasks(e.g.,Spatial Reasoning,Factual QA). We find that no candidate satisfies all four axioms simultaneously, that the representations distinguish task type reliably but cannot distinguish between two questions within the same task, and that the representations encode little information beyond what is already present in the input embedding. The failure is consistent across dense, reasoning-distilled, and RL-trained model families, indicating that the gap is structural rather than a property of model size or training procedure.

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