# Hessian Aware Low-Rank Perturbation for Order-Robust Continual Learning

arXiv: https://arxiv.org/abs/2311.15161 · HTML: https://mlsanity.com/paper/2311.15161/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 60 references that are in the map.
- First posted on arXiv 26 Nov 2023.

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

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [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)
- [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)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Efficient Lifelong Learning with A-GEM](https://mlsanity.com/paper/1812.00420/) (2018)
- [A Survey on Multi-Task Learning](https://mlsanity.com/paper/1707.08114/) (2017)
- [Lifelong Learning with Dynamically Expandable Networks](https://mlsanity.com/paper/1708.01547/) (2017)
- [Learning to Learn without Forgetting by Maximizing Transfer and Minimizing Interference](https://mlsanity.com/paper/1810.11910/) (2018)
- [HAWQ: Hessian AWare Quantization of Neural Networks with Mixed-Precision](https://mlsanity.com/paper/1905.03696/) (2019)
- [BatchEnsemble: An Alternative Approach to Efficient Ensemble and Lifelong Learning](https://mlsanity.com/paper/2002.06715/) (2020)
- [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)
- [Learn to Grow: A Continual Structure Learning Framework for Overcoming Catastrophic Forgetting](https://mlsanity.com/paper/1904.00310/) (2019)
- [HAWQ-V2: Hessian Aware trace-Weighted Quantization of Neural Networks](https://mlsanity.com/paper/1911.03852/) (2019)
- [Limitations of the Empirical Fisher Approximation for Natural Gradient Descent](https://mlsanity.com/paper/1905.12558/) (2019)
- [Training Networks in Null Space of Feature Covariance for Continual Learning](https://mlsanity.com/paper/2103.07113/) (2021)
- [Scalable and Order-robust Continual Learning with Additive Parameter Decomposition](https://mlsanity.com/paper/1902.09432/) (2019)
- [Functional Regularisation for Continual Learning with Gaussian Processes](https://mlsanity.com/paper/1901.11356/) (2019)
- [Continual Learning with Node-Importance based Adaptive Group Sparse Regularization](https://mlsanity.com/paper/2003.13726/) (2020)
- [Convolutional neural networks with low-rank regularization](https://mlsanity.com/paper/1511.06067/) (2015)
- [Uncertainty-guided Continual Learning with Bayesian Neural Networks](https://mlsanity.com/paper/1906.02425/) (2019)
- [Continual Learning in Low-rank Orthogonal Subspaces](https://mlsanity.com/paper/2010.11635/) (2020)
- [Stable Low-rank Tensor Decomposition for Compression of Convolutional Neural Network](https://mlsanity.com/paper/2008.05441/) (2020)
- [Efficient Feature Transformations for Discriminative and Generative Continual Learning](https://mlsanity.com/paper/2103.13558/) (2021)
- [Prototype-Sample Relation Distillation: Towards Replay-Free Continual Learning](https://mlsanity.com/paper/2303.14771/) (2023)
- [Triple Memory Networks: a Brain-Inspired Method for Continual Learning](https://mlsanity.com/paper/2003.03143/) (2020)
- [Learning Adaptive Embedding Considering Incremental Class](https://mlsanity.com/paper/2008.13351/) (2020)
- [Prototype-Guided Memory Replay for Continual Learning](https://mlsanity.com/paper/2108.12641/) (2021)

## Built on by (most cited first, 2 of 2)

- [Order-Robust Class Incremental Learning: Graph-Driven Dynamic Similarity Grouping](https://mlsanity.com/paper/2502.20032/) (2025)
- [CrispEdit: Low-Curvature Projections for Scalable Non-Destructive LLM Editing](https://mlsanity.com/paper/2602.15823/) (2026)

## Abstract (arXiv)

Continual learning aims to learn a series of tasks sequentially without forgetting the knowledge acquired from the previous ones. In this work, we propose the Hessian Aware Low-Rank Perturbation algorithm for continual learning. By modeling the parameter transitions along the sequential tasks with the weight matrix transformation, we propose to apply the low-rank approximation on the task-adaptive parameters in each layer of the neural networks. Specifically, we theoretically demonstrate the quantitative relationship between the Hessian and the proposed low-rank approximation. The approximation ranks are then globally determined according to the marginal increment of the empirical loss estimated by the layer-specific gradient and low-rank approximation error. Furthermore, we control the model capacity by pruning less important parameters to diminish the parameter growth. We conduct extensive experiments on various benchmarks, including a dataset with large-scale tasks, and compare our method against some recent state-of-the-art methods to demonstrate the effectiveness and scalability of our proposed method. Empirical results show that our method performs better on different benchmarks, especially in achieving task order robustness and handling the forgetting issue. The source code is at https://github.com/lijiaqi/HALRP.