Towards Optimal Feature-Shaping Methods for Out-of-Distribution Detection

Feature shaping refers to a family of methods that exhibit state-of-the-art performance for out-of-distribution (OOD) detection. These approaches manipulate the feature representation, typically from the penultimate layer of a pre-trained deep learning model, so as to better differentiate between in-distribution (ID) and OOD samples. However, existing feature-shaping methods usually employ rules manually designed for specific model architectures and OOD datasets, which consequently limit their generalization ability. To address this gap, we first formulate an abstract optimization framework for studying feature-shaping methods. We then propose a concrete reduction of the framework with a simple piecewise constant shaping function and show that existing feature-shaping methods approximate the optimal solution to the concrete optimization problem. Further, assuming that OOD data is inaccessible, we propose a formulation that yields a closed-form solution for the piecewise constant shaping function, utilizing solely the ID data. Through extensive experiments, we show that the feature-shaping function optimized by our method improves the generalization ability of OOD detection across a large variety of datasets and model architectures. Out-of-distribution (OOD) detection aims to identify test samples that fall outside the inherent training label space, given a deep learning model pre-trained on an in-distribution (ID) training set. To detect OOD samples, OOD scores, such as maximum softmax probability (MSP) (Hendrycks & Gimpel, 2016) and energy score (Liu et al., 2020) are computed using the logits estimated by the model, where a lower score indicates a higher probability that the sample is OOD. Feature shaping (Sun et al., 2021; Djurisic et al., 2022; Xu & Lian, 2023; Song et al., 2022) refers to a family of methods that manipulate the underlying feature representations, typically from the penultimate layer of a pre-trained model, such that OOD scores can more effectively distinguish between ID and OOD data.