# A Unified Gradient-based Framework for Task-agnostic Continual Learning-Unlearning

arXiv: https://arxiv.org/abs/2505.15178 · HTML: https://mlsanity.com/paper/2505.15178/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Machine unlearning, one of 12 directions in LLM safety and security.
- Builds on 58 of its 77 references that are in the map.
- First posted on arXiv 21 May 2025.

## Placed in

- LLM safety and security / [Machine unlearning](https://mlsanity.com/safety/machine-unlearning/)

## Builds on (most cited first, 30 of 58)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [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)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Continual Learning with Deep Generative Replay](https://mlsanity.com/paper/1705.08690/) (2017)
- [Machine Unlearning](https://mlsanity.com/paper/1912.03817/) (2019)
- [On First-Order Meta-Learning Algorithms](https://mlsanity.com/paper/1803.02999/) (2018)
- [Dark Experience for General Continual Learning: a Strong, Simple Baseline](https://mlsanity.com/paper/2004.07211/) (2020)
- [Membership Inference Attacks From First Principles](https://mlsanity.com/paper/2112.03570/) (2021)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [Eternal Sunshine of the Spotless Net: Selective Forgetting in Deep Networks](https://mlsanity.com/paper/1911.04933/) (2019)
- [Three scenarios for continual learning](https://mlsanity.com/paper/1904.07734/) (2019)
- [Learning to Learn without Forgetting by Maximizing Transfer and Minimizing Interference](https://mlsanity.com/paper/1810.11910/) (2018)
- [Making AI Forget You: Data Deletion in Machine Learning](https://mlsanity.com/paper/1907.05012/) (2019)
- [New insights and perspectives on the natural gradient method](https://mlsanity.com/paper/1412.1193/) (2014)
- [SalUn: Empowering Machine Unlearning via Gradient-based Weight Saliency in Both Image Classification and Generation](https://mlsanity.com/paper/2310.12508/) (2023)
- [Remember What You Want to Forget: Algorithms for Machine Unlearning](https://mlsanity.com/paper/2103.03279/) (2021)
- [Lookahead Optimizer: k steps forward, 1 step back](https://mlsanity.com/paper/1907.08610/) (2019)
- [Amnesiac Machine Learning](https://mlsanity.com/paper/2010.10981/) (2020)
- [Descent-to-Delete: Gradient-Based Methods for Machine Unlearning](https://mlsanity.com/paper/2007.02923/) (2020)
- [On Tiny Episodic Memories in Continual Learning](https://mlsanity.com/paper/1902.10486/) (2019)
- [Stochastic Gradient Descent as Approximate Bayesian Inference](https://mlsanity.com/paper/1704.04289/) (2017)
- [Systematic Evaluation of Privacy Risks of Machine Learning Models](https://mlsanity.com/paper/2003.10595/) (2020)
- [The Loss Surfaces of Multilayer Networks](https://mlsanity.com/paper/1412.0233/) (2014)
- [Unrolling SGD: Understanding Factors Influencing Machine Unlearning](https://mlsanity.com/paper/2109.13398/) (2021)

## Built on by (most cited first, 6 of 6)

- [SoK: Machine Unlearning for Large Language Models](https://mlsanity.com/paper/2506.09227/) (2025)
- [RePAIR: Interactive Machine Unlearning through Prompt-Aware Model Repair](https://mlsanity.com/paper/2604.12820/) (2026)
- [BID-LoRA: A Parameter-Efficient Framework for Continual Learning and Unlearning](https://mlsanity.com/paper/2604.12686/) (2026)
- [Robust Continual Unlearning against Knowledge Erosion and Forgetting Reversal](https://mlsanity.com/paper/2604.19108/) (2026)
- [The Forgetting-Retention Dilemma: Certified Unlearning Theory in Continual Learning](https://mlsanity.com/paper/2606.29832/) (2026)
- [On the Plasticity Collapse in Continual Machine Unlearning](https://mlsanity.com/paper/2608.29513/) (2026)

## Abstract (arXiv)

Recent advancements in deep models have highlighted the need for intelligent systems that combine continual learning (CL) for knowledge acquisition with machine unlearning (MU) for data removal, forming the Continual Learning-Unlearning (CLU) paradigm. While existing work treats CL and MU as separate processes, we reveal their intrinsic connection through a unified optimization framework based on Kullback-Leibler divergence minimization. This framework decomposes gradient updates for approximate CLU into four components: learning new knowledge, unlearning targeted data, preserving existing knowledge, and modulation via weight saliency. A critical challenge lies in balancing knowledge update and retention during sequential learning-unlearning cycles. To resolve this stability-plasticity dilemma, we introduce a remain-preserved manifold constraint to induce a remaining Hessian compensation for CLU iterations. A fast-slow weight adaptation mechanism is designed to efficiently approximate the second-order optimization direction, combined with adaptive weighting coefficients and a balanced weight saliency mask, proposing a unified implementation framework for gradient-based CLU. Furthermore, we pioneer task-agnostic CLU scenarios that support fine-grained unlearning at the cross-task category and random sample levels beyond the traditional task-aware setups. Experiments demonstrate that the proposed UG-CLU framework effectively coordinates incremental learning, precise unlearning, and knowledge stability across multiple datasets and model architectures, providing a theoretical foundation and methodological support for dynamic, compliant intelligent systems.