Two-Way Is Better Than One: Bidirectional Alignment with Cycle Consistency for Exemplar-Free Class-Incremental Learning

Continual learning (CL) seeks models that acquire new skills without erasing prior knowledge. In exemplar-free class-incremental learning (EFCIL), this challenge is amplified because past data cannot be stored, making representation drift for old classes particularly harmful. Prototype-based EFCIL is attractive for its efficiency, yet prototypes drift as the embedding space evolves; thus, projection-based drift compensation has become a popular remedy. We show, however, that existing one-directional projections introduce systematic bias: they either retroactively distort the current feature geometry or align past classes only locally, leaving cycle inconsistencies that accumulate across tasks. We introduce bidirectional projector alignment during training: two maps, old$\to$new and new$\to$old, are trained during each new task with stop-gradient gating and a cycle-consistency objective so that transport and representation co-evolve. Analytically, we prove that the cycle loss contracts the singular spectrum toward unity in whitened space and that improved transport of class means/covariances yields smaller perturbations of classification log-odds, preserving old-class decisions and directly mitigating catastrophic forgetting. Empirically, across standard EFCIL benchmarks, our method achieves unprecedented reductions in forgetting while maintaining very high accuracy on new tasks, consistently outperforming state-of-the-art approaches.