# Flattening Sharpness for Dynamic Gradient Projection Memory Benefits Continual Learning

arXiv: https://arxiv.org/abs/2110.04593 · HTML: https://mlsanity.com/paper/2110.04593/

## Key facts

- Cited by 72 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 54 references that are in the map.
- First posted on arXiv 9 Oct 2021.

## Builds on (most cited first, 30 of 33)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [Continual Learning with Deep Generative Replay](https://mlsanity.com/paper/1705.08690/) (2017)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [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)
- [PackNet: Adding Multiple Tasks to a Single Network by Iterative Pruning](https://mlsanity.com/paper/1711.05769/) (2017)
- [Lifelong Learning with Dynamically Expandable Networks](https://mlsanity.com/paper/1708.01547/) (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)
- [Learning to Learn without Forgetting by Maximizing Transfer and Minimizing Interference](https://mlsanity.com/paper/1810.11910/) (2018)
- [Orthogonal Gradient Descent for Continual Learning](https://mlsanity.com/paper/1910.07104/) (2019)
- [Gradient Projection Memory for Continual Learning](https://mlsanity.com/paper/2103.09762/) (2021)
- [Variational Continual Learning](https://mlsanity.com/paper/1710.10628/) (2017)
- [On Tiny Episodic Memories in Continual Learning](https://mlsanity.com/paper/1902.10486/) (2019)
- [Learn to Grow: A Continual Structure Learning Framework for Overcoming Catastrophic Forgetting](https://mlsanity.com/paper/1904.00310/) (2019)
- [Online Structured Laplace Approximations For Overcoming Catastrophic Forgetting](https://mlsanity.com/paper/1805.07810/) (2018)
- [Reinforced Continual Learning](https://mlsanity.com/paper/1805.12369/) (2018)
- [Understanding the Role of Training Regimes in Continual Learning](https://mlsanity.com/paper/2006.06958/) (2020)
- [Uncertainty-based Continual Learning with Adaptive Regularization](https://mlsanity.com/paper/1905.11614/) (2019)
- [Flipout: Efficient Pseudo-Independent Weight Perturbations on Mini-Batches](https://mlsanity.com/paper/1803.04386/) (2018)
- [Fast and Scalable Bayesian Deep Learning by Weight-Perturbation in Adam](https://mlsanity.com/paper/1806.04854/) (2018)
- [Scalable and Order-robust Continual Learning with Additive Parameter Decomposition](https://mlsanity.com/paper/1902.09432/) (2019)
- [Uncertainty-guided Continual Learning with Bayesian Neural Networks](https://mlsanity.com/paper/1906.02425/) (2019)
- [CPR: Classifier-Projection Regularization for Continual Learning](https://mlsanity.com/paper/2006.07326/) (2020)

## Built on by (most cited first, 30 of 72)

- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [Revisiting Catastrophic Forgetting in Large Language Model Tuning](https://mlsanity.com/paper/2406.04836/) (2024)
- [Continual Learning and Catastrophic Forgetting](https://mlsanity.com/paper/2403.05175/) (2024)
- [A Comprehensive Survey of Forgetting in Deep Learning Beyond Continual Learning](https://mlsanity.com/paper/2307.09218/) (2023)
- [CoSCL: Cooperation of Small Continual Learners is Stronger than a Big One](https://mlsanity.com/paper/2207.06543/) (2022)
- [Incorporating Neuro-Inspired Adaptability for Continual Learning in Artificial Intelligence](https://mlsanity.com/paper/2308.14991/) (2023)
- [Understanding Collapse in Non-Contrastive Siamese Representation Learning](https://mlsanity.com/paper/2209.15007/) (2022)
- [Make Continual Learning Stronger via C-Flat](https://mlsanity.com/paper/2404.00986/) (2024)
- [Continual Learning with Scaled Gradient Projection](https://mlsanity.com/paper/2302.01386/) (2023)
- [A Unified Approach to Domain Incremental Learning with Memory: Theory and Algorithm](https://mlsanity.com/paper/2310.12244/) (2023)
- [Visual Prompt Tuning in Null Space for Continual Learning](https://mlsanity.com/paper/2406.05658/) (2024)
- [How to Reuse and Compose Knowledge for a Lifetime of Tasks: A Survey on Continual Learning and Functional Composition](https://mlsanity.com/paper/2207.07730/) (2022)
- [Sparsity and Heterogeneous Dropout for Continual Learning in the Null Space of Neural Activations](https://mlsanity.com/paper/2203.06514/) (2022)
- [Two Complementary Perspectives to Continual Learning: Ask Not Only What to Optimize, But Also How](https://mlsanity.com/paper/2311.04898/) (2023)
- [Beyond Losses Reweighting: Empowering Multi-Task Learning via the Generalization Perspective](https://mlsanity.com/paper/2211.13723/) (2022)
- [FedSOL: Stabilized Orthogonal Learning with Proximal Restrictions in Federated Learning](https://mlsanity.com/paper/2308.12532/) (2023)
- [Layerwise Proximal Replay: A Proximal Point Method for Online Continual Learning](https://mlsanity.com/paper/2402.09542/) (2024)
- [Parameter-Efficient Continual Fine-Tuning: A Survey](https://mlsanity.com/paper/2504.13822/) (2025)
- [Towards Continual Learning Desiderata via HSIC-Bottleneck Orthogonalization and Equiangular Embedding](https://mlsanity.com/paper/2401.09067/) (2024)
- [G-MAP: General Memory-Augmented Pre-trained Language Model for Domain Tasks](https://mlsanity.com/paper/2212.03613/) (2022)
- [ZeroFlow: Overcoming Catastrophic Forgetting is Easier than You Think](https://mlsanity.com/paper/2501.01045/) (2025)
- [Incremental Task Learning with Incremental Rank Updates](https://mlsanity.com/paper/2207.09074/) (2022)
- [Continual Learning with Neuromorphic Computing: Foundations, Methods, and Emerging Applications](https://mlsanity.com/paper/2410.09218/) (2024)
- [Semi-supervised Drifted Stream Learning with Short Lookback](https://mlsanity.com/paper/2205.13066/) (2022)
- [SHELS: Exclusive Feature Sets for Novelty Detection and Continual Learning Without Class Boundaries](https://mlsanity.com/paper/2206.13720/) (2022)
- [Progressive Learning without Forgetting](https://mlsanity.com/paper/2211.15215/) (2022)
- [DiffAug: Enhance Unsupervised Contrastive Learning with Domain-Knowledge-Free Diffusion-based Data Augmentation](https://mlsanity.com/paper/2309.07909/) (2023)
- [PLAN: Proactive Low-Rank Allocation for Continual Learning](https://mlsanity.com/paper/2510.21188/) (2025)
- [Restricted Orthogonal Gradient Projection for Continual Learning](https://mlsanity.com/paper/2301.12131/) (2023)
- [Continual Learning From a Stream of APIs](https://mlsanity.com/paper/2309.00023/) (2023)

## Abstract (arXiv)

The backpropagation networks are notably susceptible to catastrophic forgetting, where networks tend to forget previously learned skills upon learning new ones. To address such the 'sensitivity-stability' dilemma, most previous efforts have been contributed to minimizing the empirical risk with different parameter regularization terms and episodic memory, but rarely exploring the usages of the weight loss landscape. In this paper, we investigate the relationship between the weight loss landscape and sensitivity-stability in the continual learning scenario, based on which, we propose a novel method, Flattening Sharpness for Dynamic Gradient Projection Memory (FS-DGPM). In particular, we introduce a soft weight to represent the importance of each basis representing past tasks in GPM, which can be adaptively learned during the learning process, so that less important bases can be dynamically released to improve the sensitivity of new skill learning. We further introduce Flattening Sharpness (FS) to reduce the generalization gap by explicitly regulating the flatness of the weight loss landscape of all seen tasks. As demonstrated empirically, our proposed method consistently outperforms baselines with the superior ability to learn new skills while alleviating forgetting effectively.