# TRGP: Trust Region Gradient Projection for Continual Learning

arXiv: https://arxiv.org/abs/2202.02931 · HTML: https://mlsanity.com/paper/2202.02931/

## Key facts

- Cited by 82 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 37 references that are in the map.
- First posted on arXiv 7 Feb 2022.

## Builds on (most cited first, 28 of 28)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (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)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Continual Learning with Deep Generative Replay](https://mlsanity.com/paper/1705.08690/) (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)
- [Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence](https://mlsanity.com/paper/1801.10112/) (2018)
- [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)
- [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)
- [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)
- [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)
- [Learning without Memorizing](https://mlsanity.com/paper/1811.08051/) (2018)
- [Overcoming Catastrophic Forgetting by Incremental Moment Matching](https://mlsanity.com/paper/1703.08475/) (2017)
- [Compacting, Picking and Growing for Unforgetting Continual Learning](https://mlsanity.com/paper/1910.06562/) (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)
- [Continual Learning of Context-dependent Processing in Neural Networks](https://mlsanity.com/paper/1810.01256/) (2018)
- [Scalable and Order-robust Continual Learning with Additive Parameter Decomposition](https://mlsanity.com/paper/1902.09432/) (2019)
- [Incremental Learning Through Deep Adaptation](https://mlsanity.com/paper/1705.04228/) (2017)
- [Efficient Continual Learning with Modular Networks and Task-Driven Priors](https://mlsanity.com/paper/2012.12631/) (2020)

## Built on by (most cited first, 30 of 82)

- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [AlphaEdit: Null-Space Constrained Knowledge Editing for Language Models](https://mlsanity.com/paper/2410.02355/) (2024)
- [InfLoRA: Interference-Free Low-Rank Adaptation for Continual Learning](https://mlsanity.com/paper/2404.00228/) (2024)
- [A Comprehensive Survey of Mixture-of-Experts: Algorithms, Theory, and Applications](https://mlsanity.com/paper/2503.07137/) (2025)
- [Continual Learning of Natural Language Processing Tasks: A Survey](https://mlsanity.com/paper/2211.12701/) (2022)
- [Theory on Forgetting and Generalization of Continual Learning](https://mlsanity.com/paper/2302.05836/) (2023)
- [A Comprehensive Survey of Forgetting in Deep Learning Beyond Continual Learning](https://mlsanity.com/paper/2307.09218/) (2023)
- [Beyond Not-Forgetting: Continual Learning with Backward Knowledge Transfer](https://mlsanity.com/paper/2211.00789/) (2022)
- [Theory on Mixture-of-Experts in Continual Learning](https://mlsanity.com/paper/2406.16437/) (2024)
- [Learn to Unlearn for Deep Neural Networks: Minimizing Unlearning Interference with Gradient Projection](https://mlsanity.com/paper/2312.04095/) (2023)
- [The Ideal Continual Learner: An Agent That Never Forgets](https://mlsanity.com/paper/2305.00316/) (2023)
- [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 Statistical Theory of Regularization-Based Continual Learning](https://mlsanity.com/paper/2406.06213/) (2024)
- [Balancing Stability and Plasticity through Advanced Null Space in Continual Learning](https://mlsanity.com/paper/2207.12061/) (2022)
- [Understanding Forgetting in Continual Learning with Linear Regression](https://mlsanity.com/paper/2405.17583/) (2024)
- [Task-Free Continual Learning via Online Discrepancy Distance Learning](https://mlsanity.com/paper/2210.06579/) (2022)
- [Lifelong Reinforcement Learning with Modulating Masks](https://mlsanity.com/paper/2212.11110/) (2022)
- [Sparsity and Heterogeneous Dropout for Continual Learning in the Null Space of Neural Activations](https://mlsanity.com/paper/2203.06514/) (2022)
- [On Fairness of Medical Image Classification with Multiple Sensitive Attributes via Learning Orthogonal Representations](https://mlsanity.com/paper/2301.01481/) (2023)
- [Two Complementary Perspectives to Continual Learning: Ask Not Only What to Optimize, But Also How](https://mlsanity.com/paper/2311.04898/) (2023)
- [Rethinking the Stability-Plasticity Trade-off in Continual Learning from an Architectural Perspective](https://mlsanity.com/paper/2506.03951/) (2025)
- [Layerwise Proximal Replay: A Proximal Point Method for Online Continual Learning](https://mlsanity.com/paper/2402.09542/) (2024)
- [Learning to Initialize: Can Meta Learning Improve Cross-task Generalization in Prompt Tuning?](https://mlsanity.com/paper/2302.08143/) (2023)
- [Class Gradient Projection For Continual Learning](https://mlsanity.com/paper/2311.14905/) (2023)
- [Continual Gradient Low-Rank Projection Fine-Tuning for LLMs](https://mlsanity.com/paper/2507.02503/) (2025)
- [Lifelong Sequence Generation with Dynamic Module Expansion and Adaptation](https://mlsanity.com/paper/2310.09886/) (2023)
- [SplitLoRA: Balancing Stability and Plasticity in Continual Learning Through Gradient Space Splitting](https://mlsanity.com/paper/2505.22370/) (2025)
- [Unlocking the Power of Rehearsal in Continual Learning: A Theoretical Perspective](https://mlsanity.com/paper/2506.00205/) (2025)
- [BrainWash: A Poisoning Attack to Forget in Continual Learning](https://mlsanity.com/paper/2311.11995/) (2023)

## Abstract (arXiv)

Catastrophic forgetting is one of the major challenges in continual learning. To address this issue, some existing methods put restrictive constraints on the optimization space of the new task for minimizing the interference to old tasks. However, this may lead to unsatisfactory performance for the new task, especially when the new task is strongly correlated with old tasks. To tackle this challenge, we propose Trust Region Gradient Projection (TRGP) for continual learning to facilitate the forward knowledge transfer based on an efficient characterization of task correlation. Particularly, we introduce a notion of `trust region' to select the most related old tasks for the new task in a layer-wise and single-shot manner, using the norm of gradient projection onto the subspace spanned by task inputs. Then, a scaled weight projection is proposed to cleverly reuse the frozen weights of the selected old tasks in the trust region through a layer-wise scaling matrix. By jointly optimizing the scaling matrices and the model, where the model is updated along the directions orthogonal to the subspaces of old tasks, TRGP can effectively prompt knowledge transfer without forgetting. Extensive experiments show that our approach achieves significant improvement over related state-of-the-art methods.