不用反向传播，用数学公式直接更新分类器，实现高效稳定增量学习。

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.