Natural Gradient Descent for Online Continual Learning

In Online Continual Learning (OCL), a neural network sequentially learns from a non-stationary data stream in a single-pass with access only to a limited memory replay buffer. This contrasts sharply with off-line continual learning where training is multiple epoch dependent on large datasets. The main challenge faced by OCL is to overcome catastrophic forgetting of past tasks (stability) while learning new ones efficiently (plasticity). Existing methods counter forgetting via replay-based rehearsal, output level distillation, fixed regularization, or meta-learning on the current data. However, these methods have limitations: rehearsal introduces a stored sample bias; distillation operates on output-distributions without modulating parameter updates; fixed-regularization penalizes parameters irrespective of sensitivity; stream-only meta-learning lacks a feedback controlled parameter update. We propose Meta-Adaptive Network Gradient Optimization (MANGO), an OCL framework that balances stability-plasticity via gradient-gating and meta-learned regularization. Gradient-gating scales parameter updates based on sensitivity, preventing destructive updates. Meta-learned regularization adapts stability coefficients, evaluating the effect of parameter update on replay. In MANGO, replay acts as both a training signal and a forgetting evaluator. We evaluated our method on three standard OCL benchmark datasets. MANGO outperforms strong baselines, achieving state-of-the-art results with consistent performance across replay sizes. In domain incremental learning on CLEAR-10 and class incremental learning on CIFAR-100 and Tiny-ImageNet, it achieves highest accuracy among all baselines and achieves positive Backward Transfer, overcoming forgetting on CLEAR-10.

Online Continual Self-Supervised Learning (OCSSL) aims to learn representations from a continuous stream of unlabeled data, without knowledge of task boundaries and under memory constraints. Existing methods rely either on replay buffers that exploit latent space structure, or on regularization alone. We present CLIMB (Continual Learning with Intelligent Memory Bank), which combines both simultaneously. Our method introduces a hierarchical centroid-based memory, bounded in total number of stored images, combined with knowledge distillation on replayed examples to limit representation drift. The memory groups similar images into centroids, providing hard-to-discriminate examples for contrastive learning while covering the diversity of observed distributions. Experiments on Split CIFAR-100 and Split ImageNet-100, on standard benchmarks from the state-of-the-art as well as a new protocol with irregular task distributions show that CLIMB outperforms state-of-the-art OCSSL methods.

Continual Learning (CL) aims to train neural networks on a dynamic stream of tasks without forgetting previously learned knowledge. Among optimization-based approaches, C-Flat has emerged as a promising solution due to its plug-and-play nature and its ability to encourage uniformly low-loss regions for both new and old tasks. However, C-Flat requires three additional gradient computations per iteration, imposing substantial overhead on the optimization process. In this work, we propose C-Flat Turbo, a faster yet stronger optimizer that significantly reduces the training cost. We show that the gradients associated with first-order flatness contain direction-invariant components relative to the proxy-model gradients, enabling us to skip redundant gradient computations in the perturbed ascent steps. Moreover, we observe that these flatness-promoting gradients progressively stabilize across tasks, which motivates a linear scheduling strategy with an adaptive trigger to allocate larger turbo steps for later tasks. Experiments show that C-Flat Turbo is 1.0$\times$ to 1.25$\times$ faster than C-Flat across a wide range of CL methods, while achieving comparable or even improved accuracy.