Evaluating Research-Level Math Proofs via Strict Step-Level Verification

Large Language Models (LLMs) struggle to rigorously verify complex mathematical proofs. Standard global evaluation approaches suffer from "context poisoning," in which superficially plausible statements mask subtle logical flaws, leading to hallucination or over-skepticism. To address this, we shift from global evaluation to strict step-level verification: our framework maintains detailed context for each deduction step and strictly constrains the sources of applied theorems. We evaluate on a carefully curated adversarial diagnostic suite of research-level proofs drawn from the FirstProof challenge. A systematic ablation study demonstrates that these deductive constraints are indispensable, as unconstrained global prompting consistently fails to localize subtle logical errors. Beyond outperforming global evaluation, our approach fundamentally alters the failure taxonomy. Error analysis reveals that, rather than exhibiting severe logical hallucinations, remaining rejections are primarily instances of "pedantic hyper-rigor" stemming from unstated domain conventions, effectively exposing implicit ambiguities within the expert benchmark itself. Our findings suggest that prompting agents to organize their verification notes in a cautious, human-mathematician-like manner can substantially improve their ability to distinguish rigorous proofs from flawed ones, with the potential to strengthen agentic reasoning on frontier mathematical concepts that the base model does not already know well, and to lay a theoretical foundation for future automated proof-review systems. Code and prompts are available at GitHub.

MMVIAD: Multi-view Multi-task Video Understanding for Industrial Anomaly Detection

Industrial anomaly detection is critical for manufacturing quality control, yet existing datasets mainly focus on static images or sparse views, which do not fully reflect continuous inspection processes in real industrial scenarios. We introduce MMVIAD (Multi-view Multi-task Video Industrial Anomaly Detection), to the best of our knowledge the first continuous multi-view video dataset for industrial anomaly detection and understanding, together with a benchmark for multi-task evaluation. MMVIAD contains object-centric 2-second inspection clips with approximately 120 degrees of camera motion, covering 48 object categories, 14 environments, and 6 structural anomaly types. It supports anomaly detection, defect classification, object classification, and anomaly visible-time localization. Systematic evaluations on MMVIAD show that current commercial and open-source video MLLMs remain far below human performance, especially for fine-grained defect recognition and temporal grounding. To improve transferable anomaly understanding, we further develop a two-stage post-training pipeline where PS-SFT (Perception-Structured Supervised Fine-Tuning) initializes perception-structured reasoning and VISTA-GRPO (Visibility-grounded Industrial Structured Temporal Anomaly Group Relative Policy Optimization) refines the model with semantic-gated defect reward and visibility-aware temporal reward, producing the final model VISTA. On MMVIAD-Unseen, VISTA improves the base model's average score across the four tasks from 45.0 to 57.5, surpassing GPT-5.4. Source code is available at https://github.com/Georgekeepmoving/MMVIAD.