CIFNet: An Analytic Neural Learning Framework for Efficient and Calibrated Class-Incremental Learning

Class-Incremental Learning (CIL) in deep neural networks is conventionally framed as an iterative gradient-based optimization problem, incurring high computational cost, hyperparameter sensitivity, and risk of catastrophic forgetting. In this work, we demonstrate that when leveraging frozen pre-trained representations, CIL can be solved as a sequence of deterministic, closed-form classifier adaptations without backpropagation or iterative convergence. We propose CIFNet, an analytic neural learning framework built upon Regularised Recursive Least-Squares (RRLS). CIFNet updates classifier weights via an exact, closed-form ridge-regression solution operating in a stationary embedding space. To counteract the structural initialisation bias that arises when newly expanded output neurons are introduced without exposure to past-class evidence, CIFNet incorporates a lightweight calibration buffer in latent space alongside density-aware oversampling, ensuring globally balanced decision boundaries without raw image storage or gradient updates. Extensive evaluations across CIFAR-100, ImageNet-100, and CORe50 show that CIFNet achieves predictive accuracy competitive with iterative CIL baselines while maintaining strictly monotonic, smooth learning trajectories free from intermediate performance collapse. Furthermore, by replacing epoch-wise backpropagation with closed-form moment accumulation, CIFNet achieves up to 20\times reduction in energy consumption. These findings establish calibrated analytic learning as an efficient, stable, and mathematically grounded paradigm for continual adaptation in neural networks.