Learning with Adaptive Prototype Manifolds for Out-of-Distribution Detection

TL;DR

This work tackles two pervasive problems in prototype-based OOD detection: the Static Homogeneity Assumption, which causes prototype collisions, and the Learning-Inference Disconnect, which wastes rich training signals at inference. It introduces APEX, a two-stage repair framework comprising Adaptive Prototype Manifold (APM) and Posterior-Aware OOD Scoring (PAOS). APM dynamically allocates class-specific prototype counts using MDL principles via BIC on GMM fits, and PAOS calibrates the OOD score using prototype quality metrics (cohesion and separation) integrated through a category energy and Gibbs-based confidence. Across CIFAR-100, CIFAR-10, and ImageNet-100 benchmarks, APEX achieves state-of-the-art OOD detection, with ablations validating the necessity of both stages and demonstrating strong generalization and plug-and-play potential for PAOS with other prototype methods. The approach offers a principled, information-theoretic pathway to robust OOD detection by decoupling structural repair from inferential calibration, aligning with the Information Bottleneck perspective on sufficient representation for decision making.

Abstract

Out-of-distribution (OOD) detection is a critical task for the safe deployment of machine learning models in the real world. Existing prototype-based representation learning methods have demonstrated exceptional performance. Specifically, we identify two fundamental flaws that universally constrain these methods: the Static Homogeneity Assumption (fixed representational resources for all classes) and the Learning-Inference Disconnect (discarding rich prototype quality knowledge at inference). These flaws fundamentally limit the model's capacity and performance. To address these issues, we propose APEX (Adaptive Prototype for eXtensive OOD Detection), a novel OOD detection framework designed via a Two-Stage Repair process to optimize the learned feature manifold. APEX introduces two key innovations to address these respective flaws: (1) an Adaptive Prototype Manifold (APM), which leverages the Minimum Description Length (MDL) principle to automatically determine the optimal prototype complexity $K_c^*$ for each class, thereby fundamentally resolving prototype collision; and (2) a Posterior-Aware OOD Scoring (PAOS) mechanism, which quantifies prototype quality (cohesion and separation) to bridge the learning-inference disconnect. Comprehensive experiments on benchmarks such as CIFAR-100 validate the superiority of our method, where APEX achieves new state-of-the-art performance.

Figures (4)

• Figure 1: The Pprototype collision defect and its Mitigation: While the baseline PALM model suffers from prototype collision due to a fixed number of prototypes, our APM model effectively resolves this issue by utilizing an adaptive optimal number of prototypes $K_c^*$, forming distinct and compact class clusters.
• Figure 2: The overall architecture of our Two-Stage Repair Framework . A. Training: Adaptive Prototype Manifold. $\text{APM}$ determines the optimal prototype complexity $K_c^*$ for each class using Gaussian Mixture Model ($\text{GMM}$) and Bayesian Information Criterion ($\text{BIC}$) analysis, optimizing the hyperspherical embedding space for better structural separation. B. Inference: Posterior-Aware OOD Scoring. $\text{PAOS}$ utilizes prototype quality information (left) to calibrate the final OOD scoring function (right), which is based on the Energy Function, achieving fine-grained decision boundary refinement.
• Figure 3: APEX: Experimental analysis of model sensitivity and qualitative results. (a) Analysis of the PAOS calibration strength $\alpha$. (b) Sensitivity to the fixed prototype number $K$.
• Figure 4: Generalization Performance Analysis of the APM Model and PAOS Module.(a) Performance comparison of our APM model against baseline methods (e.g., PALM, APEX) when CIFAR-10 serves as the in-distribution dataset, highlighting the superior OOD detection capability of APM. (b) Effectiveness validation of the PAOS module as a universal enhancer, illustrating the AUROC performance improvements when integrating it with the existing prototype-based method CIDER on the CIFAR-100 benchmark.