Locally adaptive compensation for analytic class-incremental learning.

The task of Class-Incremental Learning (CIL) is particularly challenging due to the absence of past data, which often results in severe catastrophic forgetting and complicates the balance between stability and plasticity. Recent Analytic CIL (ACIL) methods address forgetting through closed-form updates but remain susceptible to underfitting and limited representational flexibility. To overcome these limitations, we introduce Locally Adaptive Compensation Learning (LACL), an analytic framework that enhances ACIL with a neighborhood-aware compensation mechanism. By utilizing local neighborhood representations, LACL strengthens the compensation process to improve representational robustness, thereby reducing underfitting and better managing the stability-plasticity trade-off. The entire approach is formulated in a closed-form recursive manner, maintaining both interpretability and theoretical rigor. Experiments on CIFAR-100, ImageNet-100, and ImageNet-Full demonstrate that LACL achieves state-of-the-art performance among exemplar-free methods and offers increasing advantages over prior approaches as the number of incremental phases grows. Our codes are available at https://github.com/origi6615/lacl.