# Sustaining Plasticity via Learnable Wavelet Activations in Continual Learning

arXiv: https://arxiv.org/abs/2608.12874 · HTML: https://mlsanity.com/paper/2608.12874/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 46 references that are in the map.
- First posted on arXiv 13 Aug 2026.

## Builds on (most cited first, 30 of 34)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks](https://mlsanity.com/paper/1901.06523/) (2019)
- [Maintaining Discrimination and Fairness in Class Incremental Learning](https://mlsanity.com/paper/1911.07053/) (2019)
- [The Dormant Neuron Phenomenon in Deep Reinforcement Learning](https://mlsanity.com/paper/2302.12902/) (2023)
- [Understanding plasticity in neural networks](https://mlsanity.com/paper/2303.01486/) (2023)
- [A Model or 603 Exemplars: Towards Memory-Efficient Class-Incremental Learning](https://mlsanity.com/paper/2205.13218/) (2022)
- [Supervised Contrastive Replay: Revisiting the Nearest Class Mean Classifier in Online Class-Incremental Continual Learning](https://mlsanity.com/paper/2103.13885/) (2021)
- [Implicit Under-Parameterization Inhibits Data-Efficient Deep Reinforcement Learning](https://mlsanity.com/paper/2010.14498/) (2020)
- [Understanding and Preventing Capacity Loss in Reinforcement Learning](https://mlsanity.com/paper/2204.09560/) (2022)
- [Wav-KAN: Wavelet Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.12832/) (2024)
- [Bigger, Regularized, Optimistic: scaling for compute and sample-efficient continuous control](https://mlsanity.com/paper/2405.16158/) (2024)
- [PyCIL: A Python Toolbox for Class-Incremental Learning](https://mlsanity.com/paper/2112.12533/) (2021)
- [Continual Backprop: Stochastic Gradient Descent with Persistent Randomness](https://mlsanity.com/paper/2108.06325/) (2021)
- [Deep Reinforcement Learning with Plasticity Injection](https://mlsanity.com/paper/2305.15555/) (2023)
- [Maintaining Plasticity in Continual Learning via Regenerative Regularization](https://mlsanity.com/paper/2308.11958/) (2023)
- [Addressing Loss of Plasticity and Catastrophic Forgetting in Continual Learning](https://mlsanity.com/paper/2404.00781/) (2024)
- [DrM: Mastering Visual Reinforcement Learning through Dormant Ratio Minimization](https://mlsanity.com/paper/2310.19668/) (2023)
- [Slow and Steady Wins the Race: Maintaining Plasticity with Hare and Tortoise Networks](https://mlsanity.com/paper/2406.02596/) (2024)
- [In value-based deep reinforcement learning, a pruned network is a good network](https://mlsanity.com/paper/2402.12479/) (2024)
- [Learning Continually by Spectral Regularization](https://mlsanity.com/paper/2406.06811/) (2024)
- [Weight Clipping for Deep Continual and Reinforcement Learning](https://mlsanity.com/paper/2407.01704/) (2024)
- [Directions of Curvature as an Explanation for Loss of Plasticity](https://mlsanity.com/paper/2312.00246/) (2023)
- [Adaptive Rational Activations to Boost Deep Reinforcement Learning](https://mlsanity.com/paper/2102.09407/) (2021)
- [Summarizing Stream Data for Memory-Constrained Online Continual Learning](https://mlsanity.com/paper/2305.16645/) (2023)
- [Rethinking the Stability-Plasticity Trade-off in Continual Learning from an Architectural Perspective](https://mlsanity.com/paper/2506.03951/) (2025)
- [Adaptive Regularization of Representation Rank as an Implicit Constraint of Bellman Equation](https://mlsanity.com/paper/2404.12754/) (2024)

## Abstract (arXiv)

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.