Inducing Neural Collapse via Anticlasses and One-Cold Cross-Entropy Loss

While softmax cross-entropy (CE) loss is the standard objective for supervised classification, it primarily focuses on the ground-truth classes, ignoring the relationships between the nontarget, complementary classes. This leaves valuable information unexploited during optimization. In this work, we propose a novel loss function, one-cold CE (OCCE) loss, which addresses this limitation by structuring the activations of these complementary classes. Specifically, for each class, we define an anticlass, which consists of everything that is not part of the target class-this includes all complementary classes as well as out-of-distribution (OOD) samples, noise, or in general any instance that does not belong to the true class. By setting a uniform one-cold encoded distribution over the complementary classes as a target for each anticlass, we encourage the model to equally distribute activations across all nontarget classes. This approach promotes a symmetric geometric structure of classes in the final feature space, increases the degree of neural collapse (NC) during training, addresses the independence deficit problem of neural networks, and improves generalization. Our extensive evaluation shows that incorporating OCCE loss in the optimization objective consistently enhances performance across multiple settings, including classification, open-set recognition, and OOD detection.