# Rotation Control Unlearning: Quantifying and Controlling Continuous Unlearning for LLM with The Cognitive Rotation Space

arXiv: https://arxiv.org/abs/2509.25743 · HTML: https://mlsanity.com/paper/2509.25743/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Machine unlearning, one of 12 directions in LLM safety and security.
- Builds on 34 of its 50 references that are in the map.
- First posted on arXiv 30 Sep 2025.

## Placed in

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

## Builds on (most cited first, 30 of 34)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [A Survey on Large Language Model based Autonomous Agents](https://mlsanity.com/paper/2308.11432/) (2023)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Learn to Explain: Multimodal Reasoning via Thought Chains for Science Question Answering](https://mlsanity.com/paper/2209.09513/) (2022)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Machine Unlearning](https://mlsanity.com/paper/1912.03817/) (2019)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [Eternal Sunshine of the Spotless Net: Selective Forgetting in Deep Networks](https://mlsanity.com/paper/1911.04933/) (2019)
- [TOFU: A Task of Fictitious Unlearning for LLMs](https://mlsanity.com/paper/2401.06121/) (2024)
- [Negative Preference Optimization: From Catastrophic Collapse to Effective Unlearning](https://mlsanity.com/paper/2404.05868/) (2024)
- [Who's Harry Potter? Approximate Unlearning in LLMs](https://mlsanity.com/paper/2310.02238/) (2023)
- [Large Language Model Unlearning](https://mlsanity.com/paper/2310.10683/) (2023)
- [Rethinking Machine Unlearning for Large Language Models](https://mlsanity.com/paper/2402.08787/) (2024)
- [Task Arithmetic in the Tangent Space: Improved Editing of Pre-Trained Models](https://mlsanity.com/paper/2305.12827/) (2023)
- [Unlearn What You Want to Forget: Efficient Unlearning for LLMs](https://mlsanity.com/paper/2310.20150/) (2023)
- [SOUL: Unlocking the Power of Second-Order Optimization for LLM Unlearning](https://mlsanity.com/paper/2404.18239/) (2024)
- [Guardrail Baselines for Unlearning in LLMs](https://mlsanity.com/paper/2403.03329/) (2024)
- [Rethinking LLM Unlearning Objectives: A Gradient Perspective and Go Beyond](https://mlsanity.com/paper/2502.19301/) (2025)
- [On Large Language Model Continual Unlearning](https://mlsanity.com/paper/2407.10223/) (2024)
- [Exploring Criteria of Loss Reweighting to Enhance LLM Unlearning](https://mlsanity.com/paper/2505.11953/) (2025)
- [Unsupervised Out-of-Domain Detection via Pre-trained Transformers](https://mlsanity.com/paper/2106.00948/) (2021)
- [SAEs Can Improve Unlearning: Dynamic Sparse Autoencoder Guardrails for Precision Unlearning in LLMs](https://mlsanity.com/paper/2504.08192/) (2025)
- [Contrastive Learning for Prompt-Based Few-Shot Language Learners](https://mlsanity.com/paper/2205.01308/) (2022)
- [Safety Mirage: How Spurious Correlations Undermine VLM Safety Fine-Tuning and Can Be Mitigated by Machine Unlearning](https://mlsanity.com/paper/2503.11832/) (2025)
- [Pre-training Limited Memory Language Models with Internal and External Knowledge](https://mlsanity.com/paper/2505.15962/) (2025)
- [Estimating Soft Labels for Out-of-Domain Intent Detection](https://mlsanity.com/paper/2211.05561/) (2022)
- [CTRAP: Embedding Collapse Trap to Safeguard Large Language Models from Harmful Fine-Tuning](https://mlsanity.com/paper/2505.16559/) (2025)
- [UIPE: Enhancing LLM Unlearning by Removing Knowledge Related to Forgetting Targets](https://mlsanity.com/paper/2503.04693/) (2025)

## Abstract (arXiv)

As Large Language Models (LLMs) become increasingly prevalent, their security vulnerabilities have already drawn attention. Machine unlearning is introduced to seek to mitigate these risks by removing the influence of undesirable data. However, existing methods not only rely on the retained dataset to preserve model utility, but also suffer from cumulative catastrophic utility loss under continuous unlearning requests. To solve this dilemma, we propose a novel method, called Rotation Control Unlearning (RCU), which leverages the rotational salience weight of RCU to quantify and control the unlearning degree in the continuous unlearning process. The skew symmetric loss is designed to construct the existence of the cognitive rotation space, where the changes of rotational angle can simulate the continuous unlearning process. Furthermore, we design an orthogonal rotation axes regularization to enforce mutually perpendicular rotation directions for continuous unlearning requests, effectively minimizing interference and addressing cumulative catastrophic utility loss. Experiments on multiple datasets confirm that our method without retained dataset achieves SOTA performance.