arXiv:2503.22233v4 Announce Type: replace-cross Abstract: We introduce the Entropy-Driven Uncertainty Process Reward Model (EDU-PRM), a novel entropy-driven training framework for process reward modeling that enables dynamic, uncertainty-aligned segmentation of complex reasoning steps, eliminating the need for costly manual step annotations. Unlike previous Process Reward Models (PRMs) that rely on static partitioning and human labeling, EDU-PRM automatically anchors step boundaries at tokens with high predictive entropy, effectively capturing intrinsic logical transitions and facilitating efficient exploration of diverse reasoning paths. On the ProcessBench benchmark, EDU-PRM outperforms strong public PRM baselines, such as Math-Shepherd PRM and Omega PRM, and EDU-PRM achieves comparable results with SOTA models while only using 1.5% training data. Furthermore, by leveraging our proposed EDU sampling strategy, we observe accuracy boosts from 64.7% to 67.3% for generative reasoning tasks, accompanied by a reduction of 32% in token usage. These findings underscore the potential of EDU-PRM as a scalable and annotation-efficient paradigm for process supervision in mathematical reasoning, paving the way for more efficient and robust approaches to complex mathematical problem solving.

arXiv:2602.15022v1 Announce Type: cross Abstract: Many generative tasks in chemistry and science involve distributions invariant to group symmetries (e.g., permutation and rotation). A common strategy enforces invariance and equivariance through architectural constraints such as equivariant denoisers and invariant priors. In this paper, we challenge this tradition through the alternative canonicalization perspective: first map each sample to an orbit representative with a canonical pose or order, train an unconstrained (non-equivariant) diffusion or flow model on the canonical slice, and finally recover the invariant distribution by sampling a random symmetry transform at generation time. Building on a formal quotient-space perspective, our work provides a comprehensive theory of canonical diffusion by proving: (i) the correctness, universality and superior expressivity of canonical generative models over invariant targets; (ii) canonicalization accelerates training by removing diffusion score complexity induced by group mixtures and reducing conditional variance in flow matching. We then show that aligned priors and optimal transport act complementarily with canonicalization and further improves training efficiency. We instantiate the framework for molecular graph generation under $S_n \times SE(3)$ symmetries. By leveraging geometric spectra-based canonicalization and mild positional encodings, canonical diffusion significantly outperforms equivariant baselines in 3D molecule generation tasks, with similar or even less computation. Moreover, with a novel architecture Canon, CanonFlow achieves state-of-the-art performance on the challenging GEOM-DRUG dataset, and the advantage remains large in few-step generation.