Contrastive learning produces coherent semantic feature embeddings by encouraging positive samples to cluster closely while separating negative samples. However, existing contrastive learning methods lack principled guarantees on coverage within the semantic feature space. We extend conformal prediction to this setting by introducing minimum-volume covering sets equipped with learnable generalized multi-norm constraints. We propose a method that constructs conformal sets guaranteeing user-specified coverage of positive samples while maximizing negative sample exclusion. We establish theoretically that volume minimization serves as a proxy for negative exclusion, enabling our approach to operate effectively even when negative pairs are unavailable. The positive inclusion guarantee inherits the distribution-free coverage property of conformal prediction, while negative exclusion is maximized through learned set geometry optimized on a held-out training split. Experiments on simulated and real-world image datasets demonstrate improved inclusion-exclusion trade-offs compared to standard distance-based conformal baselines.

Out-of-Distribution (OoD) detection is vital for the reliability of Deep Neural Networks (DNNs).

FL further makes efforts to adapt real-world scenarios, i.e., adapting

One key challenge in Out-of-Distribution (OOD) detection is the absence of ground-truth OOD samples during training.

Hopfield Boosting, a boosting approach, which leverages modern Hopfield energy to sharpen the decision boundary between the in-distribution and OOD data.

In Tab. 1, we conduct the test on a Tesla V100 to In Tab. 2, we train five ResNet34 models for the CIFAR benchmarks (CIFAR10 and CIFAR100), The blocks, labeled as block1 to block5, correspond to the output features obtained from shallow to deep. This can be expained as the model's In Section 4.1, we introduce channel-wise average abnormality under the assumption that Gradient-based Class Activation Mapping (GradCAM) can be regarded as having only first-order independent Here we provide a proof (from [18]) for this assumption. Then based on Eq. 2, we The issue of attribution can be viewed as the assignment of credit in cooperative game theory. Null Player Axiom: If removal of a feature across all potential coalitions with other features has no impact on the output, it should be assigned zero importance. In Section 4.2, we introduce the two-stage fusion strategy for GAIA-A and in Section 5.3, we briefly Eq. 8, the effect of output component is similar to the The extensive results are shown in Tab. 3. It indicates the effectiveness of our fusion strategy.

Consequently, we investigate how attribution gradients lead to uncertain explanation outcomes and introduce two forms of abnormalities for OOD detection: the zero-deflation abnormality and the channel-wise average abnormality.