Yicheng Zou

Yuming Yang, Mingyoung Lai, Wanxu Zhao et al.

Long chain-of-thought (CoT) trajectories provide rich supervision signals for distilling reasoning from teacher to student LLMs. However, both prior work and our experiments show that trajectories from stronger teachers do not necessarily yield better students, highlighting the importance of data-student suitability in distillation. Existing methods assess suitability primarily through student likelihood, favoring trajectories that closely align with the model's current behavior but overlooking more informative ones. Addressing this, we propose Rank-Surprisal Ratio (RSR), a simple metric that captures both alignment and informativeness to assess the suitability of a reasoning trajectory. RSR is motivated by the observation that effective trajectories typically combine low absolute probability with relatively high-ranked tokens under the student model, balancing learning signal strength and behavioral alignment. Concretely, RSR is defined as the ratio of a trajectory's average token-wise rank to its average negative log-likelihood, and is straightforward to compute and interpret. Across five student models and reasoning trajectories from 11 diverse teachers, RSR strongly correlates with post-training performance (average Spearman 0.86), outperforming existing metrics. We further demonstrate its practical utility in both trajectory selection and teacher selection.

Yicheng Zou, Samuel Lanthaler, Hossein Salahshoor

Deterministic neural operators perform well on many PDEs but can struggle with the approximation of high-frequency wave phenomena, where strong input-to-output sensitivity makes operator learning challenging, and spectral bias blurs oscillations. We argue for adopting a probabilistic approach for approximating waves in high-frequency regime, and develop our probabilistic framework using a score-based conditional diffusion operator. After demonstrating a stability analysis of the Helmholtz operator, we present our numerical experiments across a wide range of frequencies, benchmarked against other popular data-driven and machine learning approaches for waves. We show that our probabilistic neural operator consistently produces robust predictions with the lowest errors in $L^2$, $H^1$, and energy norms. Moreover, unlike all the other tested deterministic approaches, our framework remarkably captures uncertainties in the input sound speed map propagated to the solution field. We envision that our results position probabilistic operator learning as a principled and effective approach for solving complex PDEs such as Helmholtz in the challenging high-frequency regime.