Abstract

In Class-Incremental Learning (CIL), the main challenge is catastrophic forgetting, which is commonly mitigated using regularization, replay buffers, or architectural adaptations. In this work, we revisit this formulation in the context of modern visual foundation models. We argue that once representations are frozen and sufficiently discriminative, the fundamental task of CIL shifts from protecting model parameters to modeling class distributions in a stationary feature space. Building on this observation, we formulate incremental learning as recursive estimation of class-conditional Gaussian densities in foundation embeddings. To handle multimodality, we introduce Mixture-of-up-to-four-Gaussians models using either a full covariance matrix (MOG4-F) or a shared covariance matrix (MOG4-Shared). We validate per-feature Gaussianity rigorously using formal statistical methods (D’Agostino- Pearson and Diagonal Henze-Zirkler statistics) and quantify inter-class separability via the Bhattacharyya distance, which provides a direct connection to the Bayes error rate. Along with its simplicity, the proposed approach achieves competitive performance on CIFAR-100, ImageNet-R, and Caltech-256, while requiring significantly lower computational cost and providing a principled probabilistic interpretation.