Plasticity loss has emerged as a critical challenge in continual learning that significantly hinders the acquisition of sequential tasks. While optimizing activation designs offers a potential solution, current fixed-form functions suffer from an inherent spectral bias towards low-frequency variations, whereas learnable variants permit unconstrained updates that induce catastrophic forgetting. To address these limitations, we propose a novel learnable wavelet activation that decomposes the activation function into low-frequency and high-frequency components to explicitly counter spectral bias. Furthermore, we employ dynamic wavelet injection to adaptively enhance plasticity for new tasks, alongside a regularization strategy to ensure the stability of previous learned knowledge. Theoretically, we provide rigorous mathematical guarantees for the proposed framework, proving the structural necessity of the hybrid wavelet architecture for efficient L2 approximation and demonstrating that the decoupled learning rate mechanism successfully restores network plasticity for high-frequency information. Additionally, we provide a formal derivation of the loss-driven injection trigger mechanism to precisely guide the injection. Extensive empirical evaluations demonstrate that our approach maintains superior trainability and generalization throughout the learning process and achieves state-of-the-art performance across diverse continual learning benchmarks.
Continual training of deep neural networks under non-stationarity often leads to a progressive loss of plasticity, eventually limiting further learning. We relate plasticity to the empirical Neural Tangent Kernel, and identify dynamical isometry (the condition that layer-wise Jacobian singular values remain close to one) as a key mechanism for preserving plasticity in continual learning. We revisit a class of networks that are almost-everywhere isometric while remaining universal Lipschitz function approximators, demonstrating that near-dynamical isometry is compatible with expressive nonlinear representations. For general architectures, we propose an efficient isometry-promoting regularization scheme and identify a novel mechanism by which it can reactivate dormant ReLU units. Building on this, we introduce AdamO, an Adam-style adaptive optimizer that decouples isometry regularization from gradient updates, analogous to AdamW. We further reinterpret prior plasticity-preserving approaches through the lens of dynamical isometry, showing that they target only a partial measure of isometry. Across supervised and reinforcement-learning continual-learning benchmarks designed to induce plasticity loss, our methods consistently match or outperform existing approaches.
In many real-world settings, data streams are nonstationary and arrive sequentially, requiring learning systems to adapt continuously without retraining from scratch. Continual learning (CL) addresses this challenge by incorporating new tasks while mitigating catastrophic forgetting, where learning new information degrades performance on previously acquired knowledge. We introduce a control-theoretic perspective on CL that explicitly regulates the evolution of forgetting, framing adaptation as a controlled process subject to long-term stability constraints. We focus on replay-based CL, where a finite memory buffer stores representative samples from prior tasks. We propose COntinual Learning with Drift-Plus-Penalty (COLD), a continual learning framework based on the Drift-Plus-Penalty (DPP) principle from stochastic optimization. To facilitate analysis, we also consider an oracle variant, COLD-ORACLE, as a reference benchmark. At each task, both methods minimize the current task loss while maintaining a virtual queue that tracks deviations from long-term stability on previously learned tasks, capturing the stability-plasticity trade-off as a regulated dynamical process. We establish stability and convergence guarantees that characterize this trade-off through a tunable control parameter. Experiments on standard benchmarks demonstrate that COLD consistently outperforms a broad range of state-of-the-art CL methods while providing competitive and controllable forgetting behavior through explicit regulation of stability and plasticity.
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.