Measuring Reward Hacking and Reasoning-Answer Decoupling Under Position-Confounded Optimization

LLMs as a Jury: Cross-Model Consensus Can Outperform Process Reward Models for LLM Reasoning

Selecting the correct answer from a pool of candidate reasoning chains is the engine of test-time scaling, yet the standard selectors each carry a cost: self-consistency inherits the errors of the single model it resamples, and trained reward models need labeled data and transfer poorly off-distribution. We study a third signal, free at inference time: cross-model consensus, the degree to which independently trained models, each solving the problem once, agree on a final answer. We treat the panel as an LLM-jury, in which the verification signal is the structure of agreement itself, with no model scoring another's work. Across seven benchmarks it selects correct answers better than self-consistency and far better than a model scoring its own candidates: on competition math it closes the entire gap to an oracle selector, while self-scoring closes almost none. The mechanism is error decorrelation: independently trained models err differently, so their wrong answers scatter while the correct one accumulates agreement. We make this precise with a parameter-free law, derived in closed form, that predicts consensus accuracy from three measured panel statistics to a mean absolute error of $0.03$ and exposes the method's ceiling: a shared-error floor where models share a misconception, near zero on math but non-trivial on science. Against four trained verifiers spanning discriminative, outcome, and generative reward models, the free LLM-jury matches the strongest inside their math training domain and is the top selector outside it. Cross-model consensus is thus a verifier we can characterize in advance: a law that says when to trust it, and a floor that marks where it cannot.

Where the Verifier Fails: A Category-Level Audit of Reward Signals in RLVR

Reinforcement learning with verifiable rewards (RLVR) and standard benchmark evaluation both rely on an automatic verifier that turns a free text answer into a binary reward. Prior work reports that one evaluation harness accepts only about 94% of its own ground truth answers, blaming LaTeX parsing. That is an aggregate: it does not say which answer forms consume the error budget. We supply the decomposition. We apply metamorphic testing to the verifier rather than the model, generating certified equivalent answer variants, that is, rewrites that preserve mathematical meaning by construction, so that any rejection is a provable false negative needing no human adjudication. We then measure rejection per answer category across four widely used verifiers over 307,420 verdicts. We find three things. (1) Self validation ranges from 53.8% to 95.2% on identical inputs, a spread of 41.3 points. The published figure describes one implementation, not the task; two configurations of the same library disagree on 49.9% of pairs. (2) The residual is not spread across parsing categories but concentrated in whitespace and punctuation, which account for 93.0% of in contract failures for the default LaTeX configuration. A trailing period or newline dominates the budget. (3) Separating rejection from execution failure shows that verifiers with similar aggregate error fail for opposite reasons, and that a reference numeric cascade accepts off by one wrong answers as a step function of magnitude, from 0% below 10^4 to 100% at or above, because its relative tolerance is scale invariant.

Reinforcement Learning from Epistemic Regret: Learning Why, Not Just What

An Empirical Study of Reward Specification and Benchmark Reliability in GRPO-based LLM Unlearning

This work compares four reward designs that span lexical suppression, anti-refusal shaping, rubric-based broad answering, and an explicit refusal contrast, and shows that optimization success is not equivalent to behavioral unlearning: RWKU forget scores, held-out completion audits, terminal training-rollout audits, and training dynamics can point to different conclusions.

Learning When to Trust via Selective Context Preference Optimization

Language models increasingly condition their answers on external signals, and a single misleading one can turn a correct answer wrong. The obvious remedy, training models to resist such signals, hides a failure mode: a model that ignores all context looks robust yet is useless when the context is worth trusting. We recast the problem as selective trust and introduce MIST, a human-annotated benchmark that renders each reasoning item under four matched conditions (clean, misleading, correct-context, and irrelevant-context), together with SC2W, a paired metric counting how often a misleading signal flips a clean-correct answer to wrong. Across a comprehensive benchmark study, we observe that such a susceptibility is universal. We then propose SCOPE, which mines clean-correct/misleading-wrong failures and optimizes a standard Direct Preference Optimization (DPO) objective over matched preference pairs balanced equally across all four conditions, rather than over misleading items alone. Our approach substantially reduces SC2W on popular open-sourced models while preserving accuracy when the added context is clean, correct, or irrelevant. With this work, we argue that models should be judged on selective trust, not on resistance alone.

Funnel of Thoughts: Efficient Test-Time Scaling via Early Voting and Rollout Pruning

Large Reasoning Models produce diverse, sometimes inconsistent answers across repeated queries on the same problem, so multi-sample inference is a prerequisite for reliable deployment. Majority voting at k rollouts is the standard solution and the de facto accuracy target for this regime, but it is prohibitively expensive at the scale LRMs require. We introduce Funnel of Thoughts (FoT), an inference-time method that preserves the full 32-trajectory voted accuracy while halving its attention FLOPs, a 28.8% reduction in full-model inference cost. Across 115K reasoning trajectories from six LRMs, we find that unproductive trajectories often reveal themselves through repeated hesitation markers such as"Wait","Actually", and"perhaps."These trajectories are less likely to reach the correct answer and consume disproportionate attention FLOPs, degenerating into no-answer loops in the worst case. Built on this training-free lexical signal, FoT identifies the vocabulary that captures these pathological patterns and prunes affected trajectories before completion, reducing online generation attention FLOPs by 56.1% and wall time by 37.6% without any additional model inference; the same signal transfers without retuning across held-out architectures and out-of-domain tasks.