Paper 2606.27378
Formalizing Latent Thoughts: Four Axioms of Thought Representation in LLMs
- Published
- May 2026
- Research lab
- Independent
- Citations
- 0
- GitHub
- 7 stars
01 In brief
Summary
This paper introduces an axiomatic evaluation framework for latent thought representations in LLMs, defining four functional axioms: Causality, Minimality, Separability, and Stability.
Each axiom is quantified by a metric computed directly on the representation, independent of downstream task accuracy.
The authors audit five open-weight LLMs (Llama-3.1 8B, Llama-3.3 70B, DS-R1-Qwen 32B, Skywork-OR1 32B, GPT-OSS 20B) across 23 BBEH reasoning tasks, evaluating candidates from Soft Thinking, Latent Thinking, and hidden states.
Results show that no candidate satisfies all four axioms simultaneously.
Representations distinguish task type but fail to distinguish between questions within the same task, and they encode little information beyond the input embedding.
This failure is consistent across dense, reasoning-distilled, and RL-trained models, indicating a structural gap.
The framework provides a measurement protocol that exposes representational failures masked by benchmark accuracy, offering explicit optimization targets for future thought representation development.
02 From the paper
Abstract
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.