Revealed Rationality: Label-Free Evaluation and Regularization from Representation Theorems

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.

Large language models (LLMs) are increasingly used as automatic judges for summarization and dialogue evaluation. Prior work has documented biases such as position, verbosity, and style preferences, but largely focuses on outcomes, leaving judge explanations underexplored. We instead ask whether LLM judges are cue-invariant, i.e., whether their rankings and explanations remain stable when non-evidential cues are perturbed while holding the underlying texts fixed. We introduce a suite of cue interventions (Blind, Truth, Flip, Placebo, Reveal-After) and tie-aware metrics that quantify outcome anchoring and rationale anchoring, including label-aligned rhetoric and explanation drift, alongside consistency and stereotype-intrusion checks. We design anchoring attacks using verbosity and confidence cues, and compare two mitigations: structured chain-of-thought prompting and PROOF-BEFORE-PREFERENCE (evidence lock, score, rank). Using a new dataset of 1,000 summaries from traditional extractive models and LLMs, we find substantial cue-anchored rationalization under label and placebo perturbations, while PROOF-BEFORE-PREFERENCE markedly improves cue invariance over baselines.

Reinforcement learning with verifiable rewards (RLVR) enhances the reasoning of large language models (LLMs), but standard RLVR often depends on human-annotated answers or carefully curated reward specifications. In machine-checkable domains, label-free alternatives such as majority voting or LLM-as-a-judge remove annotation cost but can introduce false positives that destabilize training. We introduce JURY-RL, a label-free RLVR framework that decouples answer proposal from reward disposal: votes from model rollouts propose a candidate answer, and a formal verifier determines whether that candidate can receive positive reward. Concretely, only rollouts matching the plurality-voted answer are rewarded when that answer is successfully verified in Lean. When verification is inconclusive, we invoke ResZero (Residual-Zero), a fallback reward that discards the unverified plurality proposal and redistributes a zero-mean, variance-preserving signal over the residual answers. This design maintains a stable optimization gradient without reinforcing unverifiable consensus. Across three backbone models trained on mathematical data, JURY-RL consistently outperforms other label-free baselines on mathematical reasoning benchmarks and transfers competitively to code generation and general benchmarks. It attains pass@1 performance comparable to supervised ground-truth training, with superior generalization demonstrated by higher pass@k and response diversity.