Self-Improvement with Auxiliary Rewards: Learning from Verified Traces and Evaluating Transfer

Minju Gwak, Alan Ritter

Answer-level rewards cannot distinguish reasoning traces with equally correct outcomes. We study whether auxiliary trajectory preferences improve small-language-model self-improvement and transfer under limited supervision. We compare confidence-based (SC) and entropy-based metrics (UID-Conj.), which combines global entropy variation and local smoothness, through online reward augmentation and offline training on correct responses. Online experiments adapt Qwen3-1.7B on 30 AIME problems without reference answers; offline experiments use historical AIME problems. UID-Conj. improves the online macro-average across the adaptation benchmark and three transfer benchmarks by 2.08 percentage points over unmodified TTRL. The strongest evidence comes from offline weighted SFT: UID-Conj. exceeds uniform weighting on the same response pool by 1.93 points, with a paired prompt-bootstrap 95\% CI of [0.44, 3.44]. Benefits are task-dependent: SC rewards judged trace quality and instruction following, while UID-Conj. rewards yield stronger training outcomes in several settings. We find that auxiliary preferences can expose learning value among equally correct traces not captured during inference…