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

2026-06-23

AI Summary

This work addresses the instability of decision boundaries in exemplar-free class-incremental learning caused by anisotropic feature-space drift. To mitigate this issue, the authors propose an approach that intrinsically couples feature transfer constraints with manifold evolution within the main training phase. Specifically, they construct analytic geometric anchors via Mahalanobis distance–based alignment regression and incorporate residual network regularization to preserve local manifold structure, thereby achieving joint optimization of geometric alignment and topological awareness. Notably, this method is the first to simultaneously model manifold evolution and transfer constraints during training, eliminating the need for post-hoc decoupled fine-tuning. Extensive experiments demonstrate significant performance gains over existing exemplar-free methods on CIFAR-100, TinyImageNet, and ImageNet-100 benchmarks.

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.

Problem

• Exemplar-free Class-Incremental Learning
• Feature Space Drift
• Decision Boundary Stability
• Manifold Distortion
• Representation Drift

Innovation

• Geometry-Anchored Transport
• Exemplar-Free Class-Incremental Learning
• Manifold Evolution
• Mahalanobis-Aligned Regression
• Topology-Aware Regularization