Haolin Shi
Publications
DemoPSD: Disagreement-Modulated Policy Self-Distillation
On-policy self-distillation (OPSD) has emerged as a practical method for training large language models (LLMs) to reason, where a single model acts as both the teacher and the student with different levels of information access. However, recent studies have found that the teacher's dense token-level supervision, conditioned on privileged information, can lead to overfitting to in-domain patterns, suppress exploration, and hurt cross-domain generalization, while also introducing a more fundamental issue: *privileged information leakage*, where the student encodes answer-dependent shortcuts that are unavailable at test time. We introduce **DemoPSD**, a novel framework that resolves such problems through the idea of *selective adoption of teacher guidance*. Instead of fitting the full teacher distribution, DemoPSD steers the student toward a *reverse-KL barycenter target*, a weighted geometric combination of the teacher and student distributions, that naturally balances learning from the teacher with preserving the student's own reasoning capacity. We measure the difference between their distributions and use such a discrepancy to adaptively control the blending at each token position. We provably show that DemoPSD achieves **(1)** *leakage attenuation*, i.e., effective mitigation of privileged information leakage; and **(2)** *exploration preservation*, i.e., preservation of exploration capacity under dense token-level distillation. Extensive experiments on SciKnowEval across four scientific fields show that DemoPSD outperforms both GRPO and SDPO while maintaining higher training entropy and robustly generalizing to out-of-distribution GPQA benchmarks.
Learning to Reason with Insight for Informal Theorem Proving
Although most of the automated theorem-proving approaches depend on formal proof systems, informal theorem proving can align better with large language models' (LLMs) strength in natural language processing. In this work, we identify a primary bottleneck in informal theorem proving as a lack of insight, namely the difficulty of recognizing the core techniques required to solve complex problems. To address this, we propose a novel framework designed to cultivate this essential reasoning skill and enable LLMs to perform insightful reasoning. We propose $\mathtt{DeepInsightTheorem}$, a hierarchical dataset that structures informal proofs by explicitly extracting core techniques and proof sketches alongside the final proof. To fully exploit this dataset, we design a Progressive Multi-Stage SFT strategy that mimics the human learning process, guiding the model from basic proof writing to insightful thinking. Our experiments on challenging mathematical benchmarks demonstrate that this insight-aware generation strategy significantly outperforms baselines. These results demonstrate that teaching models to identify and apply core techniques can substantially improve their mathematical reasoning.