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

arXiv: https://arxiv.org/abs/2606.05675 · HTML: https://mlsanity.com/paper/2606.05675/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 40 references that are in the map.
- First posted on arXiv 4 Jun 2026.

## Builds on (most cited first, 30 of 31)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [Memory Aware Synapses: Learning what (not) to forget](https://mlsanity.com/paper/1711.09601/) (2017)
- [Overcoming catastrophic forgetting with hard attention to the task](https://mlsanity.com/paper/1801.01423/) (2018)
- [Learning to Learn without Forgetting by Maximizing Transfer and Minimizing Interference](https://mlsanity.com/paper/1810.11910/) (2018)
- [Progress & Compress: A scalable framework for continual learning](https://mlsanity.com/paper/1805.06370/) (2018)
- [Class-incremental learning: survey and performance evaluation on image classification](https://mlsanity.com/paper/2010.15277/) (2020)
- [Gradient Projection Memory for Continual Learning](https://mlsanity.com/paper/2103.09762/) (2021)
- [Online Continual Learning in Image Classification: An Empirical Survey](https://mlsanity.com/paper/2101.10423/) (2021)
- [Co2L: Contrastive Continual Learning](https://mlsanity.com/paper/2106.14413/) (2021)
- [Semantic Drift Compensation for Class-Incremental Learning](https://mlsanity.com/paper/2004.00440/) (2020)
- [New Insights on Reducing Abrupt Representation Change in Online Continual Learning](https://mlsanity.com/paper/2104.05025/) (2021)
- [FeTrIL: Feature Translation for Exemplar-Free Class-Incremental Learning](https://mlsanity.com/paper/2211.13131/) (2022)
- [PyCIL: A Python Toolbox for Class-Incremental Learning](https://mlsanity.com/paper/2112.12533/) (2021)
- [Flattening Sharpness for Dynamic Gradient Projection Memory Benefits Continual Learning](https://mlsanity.com/paper/2110.04593/) (2021)
- [CoSCL: Cooperation of Small Continual Learners is Stronger than a Big One](https://mlsanity.com/paper/2207.06543/) (2022)
- [Elastic Feature Consolidation for Cold Start Exemplar-Free Incremental Learning](https://mlsanity.com/paper/2402.03917/) (2024)
- [A Unified Approach to Domain Incremental Learning with Memory: Theory and Algorithm](https://mlsanity.com/paper/2310.12244/) (2023)
- [Resurrecting Old Classes with New Data for Exemplar-Free Continual Learning](https://mlsanity.com/paper/2405.19074/) (2024)
- [Exemplar-free Continual Representation Learning via Learnable Drift Compensation](https://mlsanity.com/paper/2407.08536/) (2024)
- [A Unified and General Framework for Continual Learning](https://mlsanity.com/paper/2403.13249/) (2024)
- [DualHSIC: HSIC-Bottleneck and Alignment for Continual Learning](https://mlsanity.com/paper/2305.00380/) (2023)
- [Meta-Learning with Less Forgetting on Large-Scale Non-Stationary Task Distributions](https://mlsanity.com/paper/2209.01501/) (2022)
- [Task-recency bias strikes back: Adapting covariances in Exemplar-Free Class Incremental Learning](https://mlsanity.com/paper/2409.18265/) (2024)
- [Dataset Knowledge Transfer for Class-Incremental Learning without Memory](https://mlsanity.com/paper/2110.08421/) (2021)
- [Semantic Shift Estimation via Dual-Projection and Classifier Reconstruction for Exemplar-Free Class-Incremental Learning](https://mlsanity.com/paper/2503.05423/) (2025)
- [A Normality Test for High-dimensional Data based on a Nearest Neighbor Approach](https://mlsanity.com/paper/1904.05289/) (2019)

## Built on by (most cited first, 1 of 1)

- [EchoRec: Multi-Item Prediction-Empowered Generative Recommendation via Cycle-Consistent Preference Alignment](https://mlsanity.com/paper/2608.14011/) (2026)

## Abstract (arXiv)

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; therefore, 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 BiCyc, a bidirectional projector alignment approach with a cycle-consistency objective. BiCyc jointly optimizes two maps, old-to-new and new-to-old, with stop-gradient gating so that transport and representation co-evolve. Analytically, we show that the cycle loss contracts the singular spectrum toward unity in whitened space, and that improved transport of class means and covariances yields smaller perturbations of classification log-odds, preserving old-class decisions and mitigating catastrophic forgetting. Empirically, across standard EFCIL benchmarks, BiCyc substantially reduces forgetting and improves accuracy in from-scratch settings, while remaining competitive in the pretrained fine-grained regime.