Curing Miracle Steps in LLM Mathematical Reasoning with Rubric Rewards

摘要

In this paper, we observe that current models are susceptible to reward hacking, leading to a substantial overestimation of a model’s reasoning ability. This is evidenced by a high incidence of “false positives”—solutions that reach the correct answer through an unsound process.Through a systematic analysis with human verification, we establish a taxonomy of these failure modes, identifying patterns like Miracle Steps—abrupt jumps to a correct output without a valid preceding derivation. Probing experiments suggest that these Miracle Steps are linked to answer-recall shortcuts, including memorization from pretraining, where the model accesses the correct answer independently of its reasoning chain.To mitigate this systemic issue, we introduce the Rubric Reward Model (RRM), a process-oriented reward function that evaluates the entire reasoning trajectory against problem-specific rubrics.The RRM explicitly penalizes logical flaws and encourages rigorous deduction.When integrated into an RL pipeline, RRM-based training consistently outperforms outcome-only supervision across four math benchmarks.Notably, it boosts Verified Pass@1024 on AIME2024 from 26.7% to 62.6% and reduces the incidence of Miracle Steps by 71%.Our work demonstrates that rewarding the solution process is crucial for building accurate and reliable models.