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Auxiliary trajectory preferences lifted self-improvement by 2.08 points over unmodified TTRL on a small model

AspireAI community · arXiv
Answer-level rewards cannot distinguish reasoning traces that reach equally correct outcomes. The paper asks whether auxiliary trajectory preferences help small-language-model self-improvement and transfer under limited supervision, comparing a confidence-based score against a combined entropy score that mixes global entropy variation with local smoothness, applied through online reward augmentation and offline training on correct responses. On Qwen3-1.7B adapted online over 30 AIME problems without reference answers, the combined score improved 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 supervised fine-tuning, where it beat uniform weighting by 1.93 points with a paired prompt-bootstrap 95 percent confidence interval of 0.44 to 3.44, and the benefits were task-dependent.
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