Geometry-Anchored Transport Framework for Exemplar-Free Class-Incremental Learning

• URL: http://arxiv.org/abs/2606.25347v2
• Date: Thu, 25 Jun 2026 03:20:34 GMT
• Title: Geometry-Anchored Transport Framework for Exemplar-Free Class-Incremental Learning
• Abstract summary: We present the Geometry-Anchored Transport Framework to mitigate macroscopic anisotropic drift.<n>We also introduce a Topology-Aware Evolution objective that regularizes localized manifold degradation.<n> Experiments across CIFAR-100, TinyImageNet, and ImageNet-100 demonstrate that the proposed framework consistently improves upon existing post-hoc alternatives.
• Score: 6.63181149575886
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Exemplar-free class-incremental learning (EFCIL) requires stable decision boundaries within a shifting feature space. While maintaining class-conditional Gaussian statistics provides a principled classification strategy, these parametric summaries remain sensitive to anisotropic representation drift. Existing methods often transport these statistics across tasks using a decoupled, post-hoc paradigm: optimizing a backbone without explicit geometric constraints can distort the legacy manifold, limiting the precision of retroactive alignment. In this paper, we formulate feature transport as an endogenous training constraint rather than a separate post-task step, presenting the Geometry-Anchored Transport Framework. First, we derive an Analytic Geometric Anchor via Mahalanobis-aligned regression to mitigate macroscopic anisotropic drift. Second, we introduce a Topology-Aware Evolution objective that regularizes localized manifold degradation while calibrating a residual network against the analytic prior. By coupling manifold evolution with transport constraints during the primary training phase, our framework mitigates evaluation errors without requiring decoupled fine-tuning. Experiments across CIFAR-100, TinyImageNet, and ImageNet-100 demonstrate that the proposed framework consistently improves upon existing post-hoc alternatives under strict exemplar-free constraints.

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