Characterizing Submanifold Region for Out-of-Distribution Detection

Detecting out-of-distribution (OOD) samples poses a significant safety challenge when deploying models in open-world scenarios. Advanced works assume that OOD and in-distributional (ID) samples exhibit a distribution discrepancy, showing an encouraging direction in estimating the uncertainty with embedding features or predicting outputs. Besides incorporating auxiliary outlier as decision boundary, quantifying a 'meaningful distance' in embedding space as uncertainty measurement is a promising strategy. However, these distances-based approaches overlook the data structure and heavily rely on the high-dimension features learned by deep neural networks, causing unreliable distances due to the 'curse of dimensionality'. In this work, we propose a data structure-aware approach to mitigate the sensitivity of distances to the 'curse of dimensionality', where high-dimensional features are mapped to the manifold of ID samples, leveraging the well-known manifold assumption. Specifically, we present a novel distance termed as tangent distance, which tackles the issue of generalizing the meaningfulness of distances on testing samples to detect OOD inputs. Inspired by manifold learning for adversarial examples, where adversarial region probability density is close to the orthogonal direction of the manifold, and both OOD and adversarial samples have common characteristic-imperceptible perturbations with shift distribution, we propose that OOD samples are relatively far away from the ID manifold, where tangent distance directly computes the Euclidean distance between samples and the nearest submanifold space-instantiated as the linear approximation of local region on the manifold. We provide empirical and theoretical insights to demonstrate the effectiveness of OOD uncertainty measurements on the low-dimensional subspace. Extensive experiments show that the tangent distance performs competitively with other post hoc OOD detection baselines on common and large-scale benchmarks, and the theoretical analysis supports our claim that ID samples are likely to reside in high-density regions, explaining the effectiveness of internal connections among ID data.