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analytic class-incremental learning

Analytic class-incremental learning is a continual machine learning paradigm where a classification model learns to recognize new categories over sequential stages by computing closed-form, analytic mathematical solutions rather than relying entirely on iterative gradient-based optimization. In this framework, knowledge from prior phases is preserved by recursively updating compact algebraic representations, such as autocorrelation matrices, eliminating the need to retain or revisit raw historical training samples. This exemplar-free approach prevents catastrophic forgetting while protecting data privacy across sequential tasks. By utilizing linear and recursive least-squares formulations, analytic class-incremental learning produces model parameters mathematically equivalent to those obtained from joint training on all past and present data simultaneously, thereby sustaining high classification accuracy across extensive incremental phases.

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ACIL: Analytic Class-Incremental Learning with Absolute Memorization and Privacy Protection

ACIL: Analytic Class-Incremental Learning with Absolute Memorization and Privacy Protection

Huiping Zhuang, Zhenyu Weng, Hongxin Wei, Renchunzi Xie, Kar-Ann Toh, Zhiping Lin

OrganizationsNanyang Technological UniversitySouth China University of TechnologyYonsei University

Why you should read this

Proposes an analytic class-incremental learning framework that mathematically matches the performance of joint training without storing historical exemplar data, eliminating catastrophic forgetting while protecting data privacy across multi-phase learning tasks.

Class-incremental learning (CIL) learns a classification model with training data of different classes arising progressively. Existing CIL either suffers from serious accuracy loss due to catastrophic forgetting, or invades data privacy by revisiting used exemplars. Inspired by linear learning formulations, we propose an analytic class-incremental learning (ACIL) with absolute memorization of past knowledge while avoiding breaching of data privacy (i.e., without storing historical data). The absolute memorization is demonstrated in the sense that class-incremental learning using ACIL given present data would give identical results to that from its joint-learning counterpart which consumes both present and historical samples. This equality is theoretically validated. Data privacy is ensured since no historical data are involved during the learning process. Empirical validations demonstrate ACIL's competitive accuracy performance with near-identical results for various incremental task settings (e.g., 5-50 phases). This also allows ACIL to outperform the state-of-the-art methods for large-phase scenarios (e.g., 25 and 50 phases).

Added

2026-09-26