GAMR: Geometric-Aware Manifold Regularization with Virtual Outlier Synthesis for Learning with Noisy Labels

Deep neural networks (DNNs) experience significant performance degradation when processing noisy labels, primarily due to overfitting on mislabeled data. Current mainstream approaches attempt to mitigate this issue by passively filtering clean samples during training. However, simple sample filtering within feature spaces degraded by noise struggles to distinguish between challenging samples and noisy samples, creating a bottleneck for model performance. We highlight for the first time the fundamental importance of actively reshaping feature space geometry for learning from noisy data. We propose a novel Geometry-aware Manifold Regularization Paradigm whose core idea is to explicitly construct energy barriers between data manifolds by actively synthesizing virtual outlier samples. By imposing geometric constraints that promote intra-class compactness and inter-class separation, this approach enhances the discriminability between hard and noisy samples, leading to the learning of more robust representations. Our regularization mechanism exhibits high universality, with effectiveness independent of any prior assumptions about noise patterns. It can be integrated as a standalone mechanism into existing sample selection frameworks, providing stronger robustness against diverse noisy environments. Experiments demonstrate that our paradigm achieves performance surpassing current state-of-the-art (SOTA) methods on multiple benchmarks, including CIFAR-10, with particularly pronounced advantages under more challenging asymmetric noise conditions. Furthermore, this paradigm significantly enhances the model's capability in Out-of-Distribution (OOD) detection, ensuring superior reliability and safety for deployment in open-world scenarios.

Don't Break the Boundary: Continual Unlearning for OOD Detection Based on Free Energy Repulsion

Deploying trustworthy AI in open-world environments faces a dual challenge: the necessity for robust Out-of-Distribution (OOD) detection to ensure system safety, and the demand for flexible machine unlearning to satisfy privacy compliance and model rectification. However, this objective encounters a fundamental geometric contradiction: current OOD detectors rely on a static and compact data manifold, whereas traditional classification-oriented unlearning methods disrupt this delicate structure, leading to a catastrophic loss of the model's capability to discriminate anomalies while erasing target classes. To resolve this dilemma, we first define the problem of boundary-preserving class unlearning and propose a pivotal conceptual shift: in the context of OOD detection, effective unlearning is mathematically equivalent to transforming the target class into OOD samples. Based on this, we propose the TFER (Total Free Energy Repulsion) framework. Inspired by the free energy principle, TFER constructs a novel Push-Pull game mechanism: it anchors retained classes within a low-energy ID manifold through a pull mechanism, while actively expelling forgotten classes to high-energy OOD regions using a free energy repulsion force. This approach is implemented via parameter-efficient fine-tuning, circumventing the prohibitive cost of full retraining. Extensive experiments demonstrate that TFER achieves precise unlearning while maximally preserving the model's discriminative performance on remaining classes and external OOD data. More importantly, our study reveals that the unique Push-Pull equilibrium of TFER endows the model with inherent structural stability, allowing it to effectively resist catastrophic forgetting without complex additional constraints, thereby demonstrating exceptional potential in continual unlearning tasks.

Breaking Semantic Hegemony: Decoupling Principal and Residual Subspaces for Generalized OOD Detection

While feature-based post-hoc methods have made significant strides in Out-of-Distribution (OOD) detection, we uncover a counter-intuitive Simplicity Paradox in existing state-of-the-art (SOTA) models: these models exhibit keen sensitivity in distinguishing semantically subtle OOD samples but suffer from severe Geometric Blindness when confronting structurally distinct yet semantically simple samples or high-frequency sensor noise. We attribute this phenomenon to Semantic Hegemony within the deep feature space and reveal its mathematical essence through the lens of Neural Collapse. Theoretical analysis demonstrates that the spectral concentration bias, induced by the high variance of the principal subspace, numerically masks the structural distribution shift signals that should be significant in the residual subspace. To address this issue, we propose D-KNN, a training-free, plug-and-play geometric decoupling framework. This method utilizes orthogonal decomposition to explicitly separate semantic components from structural residuals and introduces a dual-space calibration mechanism to reactivate the model's sensitivity to weak residual signals. Extensive experiments demonstrate that D-KNN effectively breaks Semantic Hegemony, establishing new SOTA performance on both CIFAR and ImageNet benchmarks. Notably, in resolving the Simplicity Paradox, it reduces the FPR95 from 31.3% to 2.3%; when addressing sensor failures such as Gaussian noise, it boosts the detection performance (AUROC) from a baseline of 79.7% to 94.9%.