Your Classifier Can Be Secretly a Likelihood-Based OOD Detector

Abstract

The ability to detect out-of-distribution (OOD) inputs is critical to guarantee the reliability of classification models deployed in an open environment. A fundamental challenge in OOD detection is that a discriminative classifier is typically trained to estimate the posterior probability $p(y|\mathbf{z})$ for class $y$ given an input $\mathbf{z}$, but lacks the explicit likelihood estimation of $p(\mathbf{z})$ ideally needed for OOD detection. While numerous OOD scoring functions have been proposed for classification models, these estimate scores are often heuristic-driven and cannot be rigorously interpreted as likelihood. To bridge the gap, we propose Intrinsic Likelihood (INK), which offers rigorous likelihood interpretation to modern discriminative-based classifiers. Specifically, our proposed INK score operates on the constrained latent embeddings of a discriminative classifier, which are modeled as a mixture of hyperspherical embeddings with constant norm. We draw a novel connection between the hyperspherical distribution and the intrinsic likelihood, which can be effectively optimized in modern neural networks. Extensive experiments on the OpenOOD benchmark empirically demonstrate that INK establishes a new state-of-the-art in a variety of OOD detection setups, including both far-OOD and near-OOD.