Geometry-driven OOD Detectors Are Class-Incremental Learners

Class-Incremental Learning (CIL) seeks to acquire new classes over time without erasing prior knowledge. While recent methods leverage pre-trained models (PTMs) to curb forgetting, they largely optimize the feature extractor and overlook the crucial classification head. In this work, we advance a simple view: if each task is equipped with a classifier that has the ability to both recognize in-distribution (IND) classes and reject out-of-distribution (OOD) inputs, CIL arises naturally-inputs are accepted only by heads that deem them in-distribution and rejected otherwise. Supported by rigorous theoretical and empirical studies, we find that this ability is characterized by Inter-class Separation and Intra-class Compactness; lacking these, standard linear and cosine-similarity heads remain closed-set and fail to yield a usable OOD signal. To address this, we propose GOD (Geometry-driven OOD Detectors), which unifies IND recognition and OOD rejection in a single geometric space by replacing the learnable head with fixed Equiangular Tight Frame (ETF) anchors; an ETF loss enforces inter-class separation, and an ArcFace loss further tightens intra-class compactness. For efficiency, we further introduce a parameter-efficient hybrid architecture and an efficient inference strategy, thus reducing both parameter footprint and inference cost. Extensive experiments on multiple incremental settings and datasets show that GOD achieves state-of-the-art results. 1