A Faster Path to Continual Learning

Continual learning remains a major challenge for modern deep networks, partly because commonly used optimizers lack inherent mechanisms for continual adaptation. One such natural mechanism is fast and slow adaptation to balance stability and plasticity. This mechanism has deep roots in neuroscience and biology, but there is no consensus on how to best incorporate it in commonly used optimizers. Here, we show that this can be easily done via the VCL framework, where past posteriors are used as priors in the future. Our key idea is to incorporate slow adaptation via merging of past posteriors to slow down the drift in the knowledge as learning progresses. The merged posterior is then used as the prior in the VCL update to implement the fast-weight updates. These steps can be seamlessly implemented in the IVON optimizer, whose form and costs are nearly identical to that of Adam. We call this new optimizer the Continual IVON (CoVON) optimizer and show that it not only consistently improves over existing VCL optimizers, but also performs better than other weight-regularization strategies across domain-incremental learning, continual pre-training, and fine-tuning of large language models.

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.

Alleviating catastrophic forgetting while enabling further learning is a primary challenge in continual learning (CL). Orthogonal-based training methods have gained attention for their efficiency and strong theoretical properties, and many existing approaches enforce orthogonality through gradient projection. In this paper, we revisit orthogonality and exploit the fact that small singular values correspond to directions that are nearly orthogonal to the input space of previous tasks. Building on this principle, we introduce NESS (Null-space Estimated from Small Singular values), a CL method that applies orthogonality directly in the weight space rather than through gradient manipulation. Specifically, NESS constructs an approximate null space using the smallest singular values of each layer's input representation and parameterizes task-specific updates via a compact low-rank adaptation (LoRA-style) formulation constrained to this subspace. The subspace basis is fixed to preserve the null-space constraint, and only a single trainable matrix is learned for each task. This design ensures that the resulting updates remain approximately in the null space of previous inputs while enabling adaptation to new tasks. Our theoretical analysis and experiments on three benchmark datasets demonstrate competitive performance, low forgetting, and stable accuracy across tasks, highlighting the role of small singular values in continual learning. The code is available at https://github.com/pacman-ctm/NESS.