# On the Effectiveness of Lipschitz-Driven Rehearsal in Continual Learning

arXiv: https://arxiv.org/abs/2210.06443 · HTML: https://mlsanity.com/paper/2210.06443/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- Builds on 75 of its 105 references that are in the map.
- First posted on arXiv 12 Oct 2022.

## Builds on (most cited first, 30 of 75)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [MixMatch: A Holistic Approach to Semi-Supervised Learning](https://mlsanity.com/paper/1905.02249/) (2019)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [Memory Aware Synapses: Learning what (not) to forget](https://mlsanity.com/paper/1711.09601/) (2017)
- [Efficient Lifelong Learning with A-GEM](https://mlsanity.com/paper/1812.00420/) (2018)
- [Dark Experience for General Continual Learning: a Strong, Simple Baseline](https://mlsanity.com/paper/2004.07211/) (2020)
- [PackNet: Adding Multiple Tasks to a Single Network by Iterative Pruning](https://mlsanity.com/paper/1711.05769/) (2017)
- [Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence](https://mlsanity.com/paper/1801.10112/) (2018)
- [Large Scale Incremental Learning](https://mlsanity.com/paper/1905.13260/) (2019)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Overcoming catastrophic forgetting with hard attention to the task](https://mlsanity.com/paper/1801.01423/) (2018)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [Gradient based sample selection for online continual learning](https://mlsanity.com/paper/1903.08671/) (2019)
- [Born Again Neural Networks](https://mlsanity.com/paper/1805.04770/) (2018)
- [Learning to Learn without Forgetting by Maximizing Transfer and Minimizing Interference](https://mlsanity.com/paper/1810.11910/) (2018)
- [Progress & Compress: A scalable framework for continual learning](https://mlsanity.com/paper/1805.06370/) (2018)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)

## Built on by (most cited first, 30 of 39)

- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [Class-Incremental Learning: A Survey](https://mlsanity.com/paper/2302.03648/) (2023)
- [Consistent Prompting for Rehearsal-Free Continual Learning](https://mlsanity.com/paper/2403.08568/) (2024)
- [The Ideal Continual Learner: An Agent That Never Forgets](https://mlsanity.com/paper/2305.00316/) (2023)
- [Continual LLaVA: Continual Instruction Tuning in Large Vision-Language Models](https://mlsanity.com/paper/2411.02564/) (2024)
- [LoRA Subtraction for Drift-Resistant Space in Exemplar-Free Continual Learning](https://mlsanity.com/paper/2503.18985/) (2025)
- [Exploring Continual Learning of Diffusion Models](https://mlsanity.com/paper/2303.15342/) (2023)
- [DualHSIC: HSIC-Bottleneck and Alignment for Continual Learning](https://mlsanity.com/paper/2305.00380/) (2023)
- [FedSOL: Stabilized Orthogonal Learning with Proximal Restrictions in Federated Learning](https://mlsanity.com/paper/2308.12532/) (2023)
- [Overcoming Recency Bias of Normalization Statistics in Continual Learning: Balance and Adaptation](https://mlsanity.com/paper/2310.08855/) (2023)
- [Towards Continual Learning Desiderata via HSIC-Bottleneck Orthogonalization and Equiangular Embedding](https://mlsanity.com/paper/2401.09067/) (2024)
- [Harnessing Textual Semantic Priors for Knowledge Transfer and Refinement in CLIP-Driven Continual Learning](https://mlsanity.com/paper/2508.01579/) (2025)
- [Continual Learning with Neuromorphic Computing: Foundations, Methods, and Emerging Applications](https://mlsanity.com/paper/2410.09218/) (2024)
- [STAR: Stability-Inducing Weight Perturbation for Continual Learning](https://mlsanity.com/paper/2503.01595/) (2025)
- [Improving Replay Sample Selection and Storage for Less Forgetting in Continual Learning](https://mlsanity.com/paper/2308.01895/) (2023)
- [Budgeted Online Continual Learning by Adaptive Layer Freezing and Frequency-based Sampling](https://mlsanity.com/paper/2410.15143/) (2024)
- [When Large Multimodal Models Confront Evolving Knowledge: Challenges and Explorations](https://mlsanity.com/paper/2505.24449/) (2025)
- [Latent Spectral Regularization for Continual Learning](https://mlsanity.com/paper/2301.03345/) (2023)
- [CKAA: Cross-subspace Knowledge Alignment and Aggregation for Robust Continual Learning](https://mlsanity.com/paper/2507.09471/) (2025)
- [IMEX-Reg: Implicit-Explicit Regularization in the Function Space for Continual Learning](https://mlsanity.com/paper/2404.18161/) (2024)
- [Harnessing Neural Unit Dynamics for Effective and Scalable Class-Incremental Learning](https://mlsanity.com/paper/2406.02428/) (2024)
- [On Space Folds of ReLU Neural Networks](https://mlsanity.com/paper/2502.09954/) (2025)
- [C3D-AD: Toward Continual 3D Anomaly Detection via Kernel Attention with Learnable Advisor](https://mlsanity.com/paper/2508.01311/) (2025)
- [On the Effectiveness of Equivariant Regularization for Robust Online Continual Learning](https://mlsanity.com/paper/2305.03648/) (2023)
- [Towards Plastic and Stable Exemplar-Free Incremental Learning: A Dual-Learner Framework with Cumulative Parameter Averaging](https://mlsanity.com/paper/2310.18639/) (2023)
- [Mitigating Interference in the Knowledge Continuum through Attention-Guided Incremental Learning](https://mlsanity.com/paper/2405.13978/) (2024)
- [May the Forgetting Be with You: Alternate Replay for Learning with Noisy Labels](https://mlsanity.com/paper/2408.14284/) (2024)
- [Adapter-Enhanced Semantic Prompting for Continual Learning](https://mlsanity.com/paper/2412.11074/) (2024)
- [Flashbacks to Harmonize Stability and Plasticity in Continual Learning](https://mlsanity.com/paper/2506.00477/) (2025)
- [COLT: Enhancing Video Large Language Models with Continual Tool Usage](https://mlsanity.com/paper/2509.18754/) (2025)

## Abstract (arXiv)

Rehearsal approaches enjoy immense popularity with Continual Learning (CL) practitioners. These methods collect samples from previously encountered data distributions in a small memory buffer; subsequently, they repeatedly optimize on the latter to prevent catastrophic forgetting. This work draws attention to a hidden pitfall of this widespread practice: repeated optimization on a small pool of data inevitably leads to tight and unstable decision boundaries, which are a major hindrance to generalization. To address this issue, we propose Lipschitz-DrivEn Rehearsal (LiDER), a surrogate objective that induces smoothness in the backbone network by constraining its layer-wise Lipschitz constants w.r.t. replay examples. By means of extensive experiments, we show that applying LiDER delivers a stable performance gain to several state-of-the-art rehearsal CL methods across multiple datasets, both in the presence and absence of pre-training. Through additional ablative experiments, we highlight peculiar aspects of buffer overfitting in CL and better characterize the effect produced by LiDER. Code is available at https://github.com/aimagelab/LiDER