arXiv:2603.29500v1 Announce Type: new Abstract: Large language models (LLMs) have recently demonstrated impressive performance on complex, multi-step reasoning tasks, especially when post-trained with outcome-rewarded reinforcement learning Guo et al. 2025. However, it has been observed that outcome rewards often overlook flawed intermediate steps, leading to unreliable reasoning steps even when final answers are correct. To address this unreliable reasoning, we propose PRoSFI (Process Reward over Structured Formal Intermediates), a novel reward method that enhances reasoning reliability without compromising accuracy. Instead of generating formal proofs directly, which is rarely accomplishable for a modest-sized (7B) model, the model outputs structured intermediate steps aligned with its natural language reasoning. Each step is then verified by a formal prover. Only fully validated reasoning chains receive high rewards. The integration of formal verification guides the model towards generating step-by-step machine-checkable proofs, thereby yielding more credible final answers. PRoSFI offers a simple and effective approach to training trustworthy reasoning models.

arXiv:2603.28776v1 Announce Type: cross Abstract: Learning to generate images with internally repeated and periodic structures poses a fundamental challenge for machine learning and computer vision models, which are typically optimised for local texture statistics and semantic realism rather than global structural consistency. This limitation is particularly pronounced in applications requiring strict control over repetition scale, spacing, and boundary coherence, such as microtopographical biomaterial surfaces. In this work, biomaterial design serves as a use case to study conditional generation of repeated patterns under weak supervision and class imbalance. We propose DF-ACBlurGAN, a structure-aware conditional generative adversarial network that explicitly reasons about long-range repetition during training. The approach integrates frequency-domain repetition scale estimation, scale-adaptive Gaussian blurring, and unit-cell reconstruction to balance sharp local features with stable global periodicity. Conditioning on experimentally derived biological response labels, the model synthesises designs aligned with target functional outcomes. Evaluation across multiple biomaterial datasets demonstrates improved repetition consistency and controllable structural variation compared to conventional generative approaches.