arXiv:2603.22619v1 Announce Type: new Abstract: LLMs often generate seemingly valid answers to flawed or ill-posed inputs. This is not due to missing knowledge: under discriminative prompting, the same models can mostly identify such issues, yet fail to reflect this in standard generative responses. This reveals a fundamental know-act gap between discriminative recognition and generative behavior. Prior work largely characterizes this issue in narrow settings, such as math word problems or question answering, with limited focus on how to integrate these two modes. In this work, we present a comprehensive analysis using FaultyScience, a newly constructed large-scale, cross-disciplinary benchmark of faulty scientific questions. We show that the gap is pervasive and stems from token-level autoregression, which entangles task selection (validate vs. answer) with content generation, preventing discriminative knowledge from being utilized. To address this, we propose DeIllusionLLM, a task-level autoregressive framework that explicitly models this decision. Through self-distillation, the model unifies discriminative judgment and generative reasoning within a single backbone. Empirically, DeIllusionLLM substantially reduces answer-despite-error failures under natural prompting while maintaining general reasoning performance, demonstrating that self-distillation is an effective and scalable solution for bridging the discriminative-generative know-act gap

arXiv:2509.02419v2 Announce Type: replace-cross Abstract: The effectiveness of convolutional neural networks in medical image segmentation relies on large-scale, high-quality annotations, which are costly and time-consuming to obtain. Even expert-labeled datasets inevitably contain noise arising from subjectivity and coarse delineations, which disrupt feature learning and adversely impact model performance. To address these challenges, this study propose a Geometric-Structural Dual-Guided Network (GSD-Net), which integrates geometric and structural cues to improve robustness against noisy annotations. It incorporates a Geometric Distance-Aware module that dynamically adjusts pixel-level weights using geometric features, thereby strengthening supervision in reliable regions while suppressing noise. A Structure-Guided Label Refinement module further refines labels with structural priors, and a Knowledge Transfer module enriches supervision and improves sensitivity to local details. To comprehensively assess its effectiveness, we evaluated GSD-Net on six publicly available datasets: four containing three types of simulated label noise, and two with multi-expert annotations that reflect real-world subjectivity and labeling inconsistencies. Experimental results demonstrate that GSD-Net achieves state-of-the-art performance under noisy annotations, achieving improvements of 1.58% on Kvasir, 22.76% on Shenzhen, 8.87% on BU-SUC, and 1.77% on BraTS2020 under SR simulated noise. The codes of this study are available at https://github.com/ortonwang/GSD-Net.