Wrong Prediction, Right Answer: Recovering Evidence from Collapsed LLM Sequence Scores

Should we trust Large Language Models (LLMs) with high accuracy? LLMs achieve high accuracy on reasoning benchmarks, but correctness alone does not reveal the quality of the reasoning used to produce it. This highlights a fundamental limitation of outcome-based evaluation: models may arrive at correct answers through flawed reasoning, and models with substantially different reasoning capabilities can nevertheless exhibit similar benchmark accuracy, for example due to memorization or over-optimization. In this paper, we ask: given existing benchmarks, can we move beyond outcome-based evaluation to assess the quality of reasoning itself? We seek metrics that (1) differentiate models with similar accuracy and (2) are robust to variations in input prompts and generation configurations. To this end, we propose a reasoning score that evaluates reasoning traces along dimensions such as faithfulness, coherence, utility, and factuality. A remaining question is how to aggregate this score across multiple sampled traces. Naively averaging them is undesirable, particularly in long-horizon settings, where the number of possible trajectories grows rapidly, and low-confidence correct traces are more likely to be coincidental. To address this, we introduce the Filtered Reasoning Score (FRS), which computes reasoning quality using only the top-K% most confident traces. Evaluating with FRS, models that are indistinguishable under standard accuracy exhibit significant differences in reasoning quality. Moreover, models with higher FRS on one benchmark tend to perform better on other reasoning benchmarks, in both accuracy and reasoning quality. Together, these findings suggest that FRS complements accuracy by capturing a model's transferable reasoning capabilities. We open source our evaluation codebase: https://github.com/Manas2006/benchmark_reproducibility.

A standard recipe for distilling the reasoning ability of large language models (LLMs) is to sample chains of thought from the model, keep those that reach the correct final answer, and fine-tune on the survivors. When sampling fails, a common fix shows the generator the gold answer and asks it to write a chain that reaches that answer. We show that this second step degrades the training data in a way that correctness filtering cannot catch. We run a controlled experiment that fixes the generator, the problem set, and the correctness filter, and varies only whether the chain is generated under answer-conditioning, the gold answer shown with a request to reach it. Training a strong instruction-tuned reasoning model on its own answer-conditioned chains sharply lowers its verifiable-reasoning accuracy. The loss grows with difficulty, reaching as much as about 27 points on the hardest competition problems. The mechanism is legible in the chains themselves, which rationalize backward from the shown answer instead of deriving it, with the early final-answer statement as the measurable symptom. The harm is a property of the data rather than the generator, read off unlabeled generations before any fine-tuning, ordering the penalty across eight thinking models from four families, and transferring across teacher families. A prompt ablation localizes it to the rationalize-toward instruction rather than the answer's bare visibility. The practical takeaway is to generate answer-blind, because no correctness filter can see this damage in the data.

Long chains of thought (CoT) from current language models frequently contain logical gaps and unjustified leaps, limiting the gains from additional test-time compute. Improving reasoning quality directly would require process reward models, but the step-level annotations needed to train them are expensive and scarce. We find such a signal in how the model's confidence evolves during reasoning: premature confidence, the tendency to commit to an answer early and use the remaining tokens to rationalize it, strongly predicts flawed reasoning across tasks and model scales. We exploit this in progressive confidence shaping, a reinforcement learning objective that trains models to update their confidence as they reason rather than commit early -- rewarding gradual confidence growth and penalizing early commitment, with no external labels or reward models. The method improves accuracy and reasoning quality from 1.5B to 8B parameters across arithmetic (Countdown), math (DAPO, AIME), and science (ScienceQA): on Countdown, accuracy improves 3.2x (+42.0pp) and flawed reasoning drops 48pp; on AIME, Pass@64 improves 6.6pp. Consistent with this mechanism, the method also improves faithfulness: on a safety benchmark, our models more transparently surface misleading content in their reasoning traces rather than concealing it. Controlled experiments reveal that the problem and its remedy scale together: premature confidence grows with model size and task difficulty, and so do the gains from addressing it.