# Beyond Not-Forgetting: Continual Learning with Backward Knowledge Transfer

arXiv: https://arxiv.org/abs/2211.00789 · HTML: https://mlsanity.com/paper/2211.00789/

## Key facts

- Cited by 59 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 49 references that are in the map.
- First posted on arXiv 1 Nov 2022.

## Builds on (most cited first, 24 of 24)

- [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)
- [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)
- [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)
- [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)
- [Orthogonal Gradient Descent for Continual Learning](https://mlsanity.com/paper/1910.07104/) (2019)
- [PathNet: Evolution Channels Gradient Descent in Super Neural Networks](https://mlsanity.com/paper/1701.08734/) (2017)
- [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)
- [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)
- [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)
- [TRGP: Trust Region Gradient Projection for Continual Learning](https://mlsanity.com/paper/2202.02931/) (2022)
- [Continual Learning of a Mixed Sequence of Similar and Dissimilar Tasks](https://mlsanity.com/paper/2112.10017/) (2021)
- [Natural continual learning: success is a journey, not (just) a destination](https://mlsanity.com/paper/2106.08085/) (2021)
- [Continual Learning with Recursive Gradient Optimization](https://mlsanity.com/paper/2201.12522/) (2022)
- [GROWN: GRow Only When Necessary for Continual Learning](https://mlsanity.com/paper/2110.00908/) (2021)

## Built on by (most cited first, 30 of 59)

- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [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)
- [The Ideal Continual Learner: An Agent That Never Forgets](https://mlsanity.com/paper/2305.00316/) (2023)
- [Learnability and Algorithm for Continual Learning](https://mlsanity.com/paper/2306.12646/) (2023)
- [Disentangling and Mitigating the Impact of Task Similarity for Continual Learning](https://mlsanity.com/paper/2405.20236/) (2024)
- [Continual Learning Using a Kernel-Based Method Over Foundation Models](https://mlsanity.com/paper/2412.15571/) (2024)
- [Optimal Task Order for Continual Learning of Multiple Tasks](https://mlsanity.com/paper/2502.03350/) (2025)
- [MINGLE: Mixture of Null-Space Gated Low-Rank Experts for Test-Time Continual Model Merging](https://mlsanity.com/paper/2505.11883/) (2025)
- [Continual Gradient Low-Rank Projection Fine-Tuning for LLMs](https://mlsanity.com/paper/2507.02503/) (2025)
- [Merge before Forget: A Single LoRA Continual Learning via Continual Merging](https://mlsanity.com/paper/2512.23017/) (2025)
- [Lifelong Sequence Generation with Dynamic Module Expansion and Adaptation](https://mlsanity.com/paper/2310.09886/) (2023)
- [Unlocking the Power of Rehearsal in Continual Learning: A Theoretical Perspective](https://mlsanity.com/paper/2506.00205/) (2025)
- [Adaptive Visual Scene Understanding: Incremental Scene Graph Generation](https://mlsanity.com/paper/2310.01636/) (2023)
- [Null-Space Filtering for Data-Free Continual Model Merging: Preserving Stability, Promoting Plasticity](https://mlsanity.com/paper/2509.21413/) (2025)
- [Sub-network Discovery and Soft-masking for Continual Learning of Mixed Tasks](https://mlsanity.com/paper/2310.09436/) (2023)
- [Persistent Backdoor Attacks under Continual Fine-Tuning of LLMs](https://mlsanity.com/paper/2512.14741/) (2025)
- [Efficient Self-supervised Continual Learning with Progressive Task-correlated Layer Freezing](https://mlsanity.com/paper/2303.07477/) (2023)
- [Merge then Realign: Simple and Effective Modality-Incremental Continual Learning for Multimodal LLMs](https://mlsanity.com/paper/2503.07663/) (2025)
- [Doubly Perturbed Task Free Continual Learning](https://mlsanity.com/paper/2312.13027/) (2023)
- [Theory of Mixture-of-Experts for Mobile Edge Computing](https://mlsanity.com/paper/2412.15690/) (2024)
- [Sequence Transferability and Task Order Selection in Continual Learning](https://mlsanity.com/paper/2502.06544/) (2025)
- [Decomposing the Basic Abilities of Large Language Models: Mitigating Cross-Task Interference in Multi-Task Instruct-Tuning](https://mlsanity.com/paper/2605.05676/) (2026)
- [Reconstruct before Query: Continual Missing Modality Learning with Decomposed Prompt Collaboration](https://mlsanity.com/paper/2403.11373/) (2024)
- [CODE-CL: Conceptor-Based Gradient Projection for Deep Continual Learning](https://mlsanity.com/paper/2411.15235/) (2024)
- [Dynamic Prototype Rehearsal for Continual ECG Arrhythmia Detection](https://mlsanity.com/paper/2501.07555/) (2025)
- [Achieving Upper Bound Accuracy of Joint Training in Continual Learning](https://mlsanity.com/paper/2502.12388/) (2025)
- [Rethinking Continual Learning with Progressive Neural Collapse](https://mlsanity.com/paper/2505.24254/) (2025)
- [Unveiling the Tapestry: the Interplay of Generalization and Forgetting in Continual Learning](https://mlsanity.com/paper/2211.11174/) (2022)
- [Chunking: Continual Learning is not just about Distribution Shift](https://mlsanity.com/paper/2310.02206/) (2023)

## Abstract (arXiv)

By learning a sequence of tasks continually, an agent in continual learning (CL) can improve the learning performance of both a new task and `old' tasks by leveraging the forward knowledge transfer and the backward knowledge transfer, respectively. However, most existing CL methods focus on addressing catastrophic forgetting in neural networks by minimizing the modification of the learnt model for old tasks. This inevitably limits the backward knowledge transfer from the new task to the old tasks, because judicious model updates could possibly improve the learning performance of the old tasks as well. To tackle this problem, we first theoretically analyze the conditions under which updating the learnt model of old tasks could be beneficial for CL and also lead to backward knowledge transfer, based on the gradient projection onto the input subspaces of old tasks. Building on the theoretical analysis, we next develop a ContinUal learning method with Backward knowlEdge tRansfer (CUBER), for a fixed capacity neural network without data replay. In particular, CUBER first characterizes the task correlation to identify the positively correlated old tasks in a layer-wise manner, and then selectively modifies the learnt model of the old tasks when learning the new task. Experimental studies show that CUBER can even achieve positive backward knowledge transfer on several existing CL benchmarks for the first time without data replay, where the related baselines still suffer from catastrophic forgetting (negative backward knowledge transfer). The superior performance of CUBER on the backward knowledge transfer also leads to higher accuracy accordingly.