Fast and Slow Variational Continual Learning

Continual learning with Low-Rank Adapters (LoRA) typically mitigates forgetting by penalizing the overlap between a new update and the accumulated past weights, which discourages certain update directions without controlling how an update distributes its energy over the ones that remain. We ask whether that restriction has to be task-aware, or whether a generic one supplied by the optimizer is enough. We train a plain incremental LoRA (IncLoRA) with Muon, which orthogonalizes each update, and compare it against O-LoRA and ELLA over five seeds and three task orders on the Standard CL Benchmark and three seeds on TRACE. IncLoRA+Muon reaches the accuracy band of the dedicated methods on Standard CL and improves on every AdamW configuration on TRACE. One update-constraining mechanism is enough, whether it comes from the loss or from the optimizer; on Standard CL a second one does not help, and for the most restrictive method it costs 8.4 points of accuracy and the plasticity to fit each task. What separates the two optimizers is not the size of the update, which under Muon is 0.91 to 2.06 times that under AdamW, but how it is distributed. AdamW confines it to between 1.4 and 1.8 effective singular directions, Muon spreads it over 7.0, and the two do not overlap in any tracked run. Part of the advantage usually attributed to dedicated CL methods may therefore be explained by the geometry of the optimizer's updates.

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.

Continual learning (CL) requires models to learn tasks sequentially, yet deep neural networks often suffer from plasticity loss and poor knowledge transfer, which can impede their long-term adaptability. Drawing high-level inspiration from global neuromodulatory mechanisms in the brain, we introduce Neuromodulation and Synchronization (NeuMoSync), a novel architecture that integrates dynamic, neuron-specific modulation into deep neural networks to enhance their adaptability and plasticity. NeuMoSync extends standard neural network architectures with learnable feature vectors for each neuron that track network-wide historical context and with a module operating at a higher level of abstraction. This module synthesizes neuron-specific signals, conditioned on both current inputs and the network's evolving state, to adaptively regulate activation dynamics and synaptic plasticity. Evaluated on diverse CL benchmarks, including memorization (Random Label CIFAR-10 and Random Label MNIST), concept drift (Shuffle CIFAR-10 and Shuffle Mini-ImageNet), class-incremental learning (Class Split ImageNet and Class Split CIFAR-100), and domain-incremental learning (Permuted MNIST), NeuMoSync demonstrates strong performance in retaining plasticity and achieves improvements in both forward and backward adaptation compared with existing methods. Ablation studies validate the necessity of each component, while analysis of the learned modulatory signals reveals interpretable coordination patterns across tasks. Our work underscores the potential of integrating global coordination mechanisms into deep learning systems to advance robust, adaptive continual learning. The code is publicly available at https://github.com/RoozbehRazavi/NeuMoSync.