# NoT: Federated Unlearning via Weight Negation

arXiv: https://arxiv.org/abs/2503.05657 · HTML: https://mlsanity.com/paper/2503.05657/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Placed in Federated unlearning and poisoning, one of 12 directions in LLM safety and security.
- Builds on 41 of its 70 references that are in the map.
- First posted on arXiv 7 Mar 2025.

## Placed in

- LLM safety and security / [Federated unlearning and poisoning](https://mlsanity.com/safety/federated-unlearning-and-poisoning/)

## Builds on (most cited first, 30 of 41)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [How transferable are features in deep neural networks?](https://mlsanity.com/paper/1411.1792/) (2014)
- [BadNets: Identifying Vulnerabilities in the Machine Learning Model Supply Chain](https://mlsanity.com/paper/1708.06733/) (2017)
- [Exact solutions to the nonlinear dynamics of learning in deep linear neural networks](https://mlsanity.com/paper/1312.6120/) (2013)
- [Eternal Sunshine of the Spotless Net: Selective Forgetting in Deep Networks](https://mlsanity.com/paper/1911.04933/) (2019)
- [SalUn: Empowering Machine Unlearning via Gradient-based Weight Saliency in Both Image Classification and Generation](https://mlsanity.com/paper/2310.12508/) (2023)
- [Membership Inference Attacks on Machine Learning: A Survey](https://mlsanity.com/paper/2103.07853/) (2021)
- [Stochastic Gradient Descent as Approximate Bayesian Inference](https://mlsanity.com/paper/1704.04289/) (2017)
- [Unrolling SGD: Understanding Factors Influencing Machine Unlearning](https://mlsanity.com/paper/2109.13398/) (2021)
- [ReZero is All You Need: Fast Convergence at Large Depth](https://mlsanity.com/paper/2003.04887/) (2020)
- [Federated Learning for Internet of Things: A Comprehensive Survey](https://mlsanity.com/paper/2104.07914/) (2021)
- [Fast Yet Effective Machine Unlearning](https://mlsanity.com/paper/2111.08947/) (2021)
- [Model Sparsity Can Simplify Machine Unlearning](https://mlsanity.com/paper/2304.04934/) (2023)
- [Can Bad Teaching Induce Forgetting? Unlearning in Deep Networks using an Incompetent Teacher](https://mlsanity.com/paper/2205.08096/) (2022)
- [Fast Machine Unlearning Without Retraining Through Selective Synaptic Dampening](https://mlsanity.com/paper/2308.07707/) (2023)
- [Forgetting Outside the Box: Scrubbing Deep Networks of Information Accessible from Input-Output Observations](https://mlsanity.com/paper/2003.02960/) (2020)
- [Dynamical Isometry and a Mean Field Theory of CNNs: How to Train 10,000-Layer Vanilla Convolutional Neural Networks](https://mlsanity.com/paper/1806.05393/) (2018)
- [Signal Propagation in Transformers: Theoretical Perspectives and the Role of Rank Collapse](https://mlsanity.com/paper/2206.03126/) (2022)
- [Resurrecting the sigmoid in deep learning through dynamical isometry: theory and practice](https://mlsanity.com/paper/1711.04735/) (2017)
- [Federated Unlearning: How to Efficiently Erase a Client in FL?](https://mlsanity.com/paper/2207.05521/) (2022)
- [Machine Unlearning: Solutions and Challenges](https://mlsanity.com/paper/2308.07061/) (2023)
- [Universal Statistics of Fisher Information in Deep Neural Networks: Mean Field Approach](https://mlsanity.com/paper/1806.01316/) (2018)
- [Federated Unlearning with Knowledge Distillation](https://mlsanity.com/paper/2201.09441/) (2022)
- [A Survey on Federated Unlearning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/2310.20448/) (2023)
- [Federated Learning for Internet of Things: Applications, Challenges, and Opportunities](https://mlsanity.com/paper/2111.07494/) (2021)
- [VeriFi: Towards Verifiable Federated Unlearning](https://mlsanity.com/paper/2205.12709/) (2022)
- [Dynamical Isometry and a Mean Field Theory of RNNs: Gating Enables Signal Propagation in Recurrent Neural Networks](https://mlsanity.com/paper/1806.05394/) (2018)

## Built on by (most cited first, 15 of 15)

- [The Right to be Forgotten in Pruning: Unveil Machine Unlearning on Sparse Models](https://mlsanity.com/paper/2507.18725/) (2025)
- [EASE: Federated Multimodal Unlearning via Entanglement-Aware Anchor Closure](https://mlsanity.com/paper/2605.00733/) (2026)
- [CoUn: Empowering Machine Unlearning via Contrastive Learning](https://mlsanity.com/paper/2509.16391/) (2025)
- [Certified Unlearning in Decentralized Federated Learning](https://mlsanity.com/paper/2601.06436/) (2026)
- [FedCARE: Federated Unlearning with Conflict-Aware Projection and Relearning-Resistant Recovery](https://mlsanity.com/paper/2601.22589/) (2026)
- [Federated Unlearning Made Practical: Seamless Integration via Negated Pseudo-Gradients](https://mlsanity.com/paper/2504.05822/) (2025)
- [FedUP: Efficient Pruning-based Federated Unlearning for Model Poisoning Attacks](https://mlsanity.com/paper/2508.13853/) (2025)
- [Rethinking Federated Unlearning via the Lens of Memorization](https://mlsanity.com/paper/2605.24545/) (2026)
- [Lethe: Principled Dual-Stream Update for Persistent Knowledge Erasure in Federated Unlearning](https://mlsanity.com/paper/2601.22601/) (2026)
- [f-FUM: Federated Unlearning via min--max and f-divergence](https://mlsanity.com/paper/2602.06187/) (2026)
- [Computation and Communication Efficient Federated Unlearning via On-server Gradient Conflict Mitigation and Expression](https://mlsanity.com/paper/2603.13795/) (2026)
- [SoK: Unlearnability and Unlearning for Model Dememorization](https://mlsanity.com/paper/2605.11592/) (2026)
- [pFedUL: Layer-Aware Federated Unlearning for Personalized Federated Learning](https://mlsanity.com/paper/2606.16304/) (2026)
- [IREU: Identity-Related Encoder-Only Unlearning for Customized Portrait Generation](https://mlsanity.com/paper/2606.29880/) (2026)
- [Lethe: How Hard Is It to Forget? A Benchmark for Federated Unlearning in Medical Imaging](https://mlsanity.com/paper/2608.01094/) (2026)

## Abstract (arXiv)

Federated unlearning (FU) aims to remove a participant's data contributions from a trained federated learning (FL) model, ensuring privacy and regulatory compliance. Traditional FU methods often depend on auxiliary storage on either the client or server side or require direct access to the data targeted for removal-a dependency that may not be feasible if the data is no longer available. To overcome these limitations, we propose NoT, a novel and efficient FU algorithm based on weight negation (multiplying by -1), which circumvents the need for additional storage and access to the target data. We argue that effective and efficient unlearning can be achieved by perturbing model parameters away from the set of optimal parameters, yet being well-positioned for quick re-optimization. This technique, though seemingly contradictory, is theoretically grounded: we prove that the weight negation perturbation effectively disrupts inter-layer co-adaptation, inducing unlearning while preserving an approximate optimality property, thereby enabling rapid recovery. Experimental results across three datasets and three model architectures demonstrate that NoT significantly outperforms existing baselines in unlearning efficacy as well as in communication and computational efficiency.