Subspace-Guided Continual Learning: Hessian Based Stable–Plastic Decomposition for Exemplar-Free Class-Incremental Learning

Exemplar-Free Class-Incremental Learning (EFCIL) is a challenging continual learning paradigm where a model must learn new classes sequentially without access to old data, making it susceptible to catastrophic forgetting. The core difficulty lies in balancing stability (preserving old knowledge) and plasticity (acquiring new knowledge). We propose Subspace-Guided Continual Learning (SGCL), a novel method that tackles this dilemma from a geometric perspective. SGCL decomposes the feature space into two orthogonal subspaces: a stable subspace containing directions critical for previous tasks, and a plastic subspace where new knowledge can be learned with minimal interference. This decomposition is efficiently identified via the feature-space Hessian, where high-curvature eigendirections define the stable subspace. Building on this, SGCL introduces two synergistic components: 1) Subspace-Guided Regularization (SGR), which imposes curvature-weighted penalties on feature drifts within the stable subspace, and 2) Subspace-Guided Prototype Alignment (SGPA), which adaptively corrects the shift of old-class prototypes to recalibrate the classifier. Extensive experiments on standard benchmarks show that SGCL consistently achieves competitive or superior performance compared to existing state-of-the-art methods, offering a principled approach to mitigating forgetting through loss landscape analysis.