SAPO: Self-Adaptive Process Optimization Makes Small Reasoners Stronger

Existing self-evolution methods overlook the influence of fine-grained reasoning steps, which leads to the reasoner-verifier gap. The computational inefficiency of Monte Carlo (MC) process supervision further exacerbates the difficulty in mitigating the gap. Motivated by the Error-Related Negativity (ERN) that reasoner can localize error following incorrect decisions, guiding rapid adjustments, we propose a Self-Adaptive Process Optimization (SAPO) method for self-improvement in Small Language Models (SLMs, $\le2{\rm{B}}$). SAPO adaptively and efficiently introduces process supervision signals by actively minimizing the reasoner-verifier gap rather than relying on inefficient MC estimations. Extensive experiments demonstrate that the proposed method outperforms most existing self-evolution methods on two challenging task types: mathematics and code. Additionally, to investigate SAPO's impact on verifier performance further, this work introduces two new benchmarks, GSM_Process and MBPP_Process, for process verification.