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, projectionbased 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 BiCyc, a bidirectional projector alignment approach with a cycle-consistency objective: two maps, old→new and new→old, are optimized with stop-gradient gating 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 substantially reduces forgetting and improves accuracy in from-scratch settings, while remaining competitive in the pretrained fine-grained regime. The code is available at https://github.com/HXuSz11/BiCyc_ICLR2026 . INTRODUCTION Continual learning (CL) studies models that learn from a stream of tasks without retraining from scratch or erasing prior knowledge (Parisi et al., 2019; Lange et al., 2022; Zenke et al., 2017). A widely used protocol is class-incremental learning (CIL), where tasks introduce disjoint labels and the learner must recognize all seen classes at test time without task identifiers. While rehearsal with stored exemplars often curbs forgetting (