Class incremental learning (CIL) trains a network on sequential tasks with
separated categories but suffers from catastrophic forgetting, where models
quickly lose previously learned knowledge when acquiring new tasks. The
generalized CIL (GCIL) aims to address the CIL problem in a more real-world
scenario, where incoming data have mixed data categories and unknown sample
size distribution, leading to intensified forgetting. Existing attempts for the
GCIL either have poor performance, or invade data privacy by saving historical
exemplars. To address this, in this paper, we propose an exemplar-free
generalized analytic class incremental learning (G-ACIL). The G-ACIL adopts
analytic learning (a gradient-free training technique), and delivers an
analytical solution (i.e., closed-form) to the GCIL scenario. This solution is
derived via decomposing the incoming data into exposed and unexposed classes,
allowing an equivalence between the incremental learning and its joint
training, i.e., the weight-invariant property. Such an equivalence is
theoretically validated through matrix analysis tools, and hence contributes
interpretability in GCIL. It is also empirically evidenced by experiments on
various datasets and settings of GCIL. The results show that the G-ACIL
exhibits leading performance with high robustness compared with existing
competitive GCIL methods. Codes will be ready at
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通过采用解析学习（一种无梯度训练技术）和生成 GCIL 场景的解析解，我们提出了一种无样本的广义解析类增量学习方法（G-ACIL），通过将传入数据分解为暴露和未暴露的类别，实现了增量学习与联合训练之间的等价性（即权重不变性），该等价性通过矩阵分析工具在理论上得到验证，在各种数据集和 GCIL 设置上的实验证明了 G-ACIL 相对于现有竞争 GCIL 方法具有卓越的性能和高鲁棒性。