Optimal Transport-Induced Samples against Out-of-Distribution Overconfidence

TL;DR

This work identifies a theoretical link between OOD overconfidence and singularities in semi-discrete optimal transport, where transport boundaries mark semantically ambiguous regions. It introduces OTIS, a framework that samples near OT-induced singularities in a latent space constructed by an autoencoder, and trains with a confidence suppression loss to calibrate predictions in structurally uncertain zones. By solving a latent-space OT problem and selectively interpolating near high-signal singular boundaries, OTIS generates semantically coherent yet ambiguous inputs that regularize the model without sacrificing ID accuracy. Empirical results across CIFAR, MNIST, FMNIST, SVHN, and ImageNet show OTIS consistently reduces OOD overconfidence, improves detection metrics, and outperforms state-of-the-art baselines, establishing a principled path toward robust open-world classification.

Abstract

Deep neural networks (DNNs) often produce overconfident predictions on out-of-distribution (OOD) inputs, undermining their reliability in open-world environments. Singularities in semi-discrete optimal transport (OT) mark regions of semantic ambiguity, where classifiers are particularly prone to unwarranted high-confidence predictions. Motivated by this observation, we propose a principled framework to mitigate OOD overconfidence by leveraging the geometry of OT-induced singular boundaries. Specifically, we formulate an OT problem between a continuous base distribution and the latent embeddings of training data, and identify the resulting singular boundaries. By sampling near these boundaries, we construct a class of OOD inputs, termed optimal transport-induced OOD samples (OTIS), which are geometrically grounded and inherently semantically ambiguous. During training, a confidence suppression loss is applied to OTIS to guide the model toward more calibrated predictions in structurally uncertain regions. Extensive experiments show that our method significantly alleviates OOD overconfidence and outperforms state-of-the-art methods.

Figures (12)

• Figure 1: Given a semi-discrete optimal transport (OT) map from (a) a continuous base distribution to (b) a discrete target distribution over images, the singular boundaries in the source domain are mapped to (c) the semantic ambiguity set in image space, which typically contains images with features from multiple classes.
• Figure 2: Overview of our framework for generating OTIS. Input images are encoded into a latent space, where a semi-discrete optimal transport (OT) map establishes a power-diagram partition with its convex potential visualized as the upper envelope. Singularity boundaries identified from this OT map guide the generation of interpolated latent features, which are decoded to synthesize OTIS.
• Figure 3: Histograms of maximum confidence scores on OOD inputs before and after applying our method. Results are shown for ResNet-18 trained on CIFAR-10 (left) and CIFAR-100 (right).
• Figure 4: Visualizations of original inputs and corresponding OTIS from (a) CIFAR-10 and (b) ImageNet. t-SNE plots of inputs and corresponding OTIS from (c) FMNIST and (d) CIFAR-10.
• Figure 5: OOD confidence of ResNet-18 trained on (a) CIFAR-10 and (b) FMNIST under different sampling strategies. Boundary-based methods use top-$k$% singularities or random boundaries (RanB). L-Inter and I-Inter denote latent and image-level interpolation without boundary guidance.