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

Xiang Zhang, Kun Wei, Xu Yang, Jiahua Li, Su Yan, Cheng Deng

TL;DR

This work tackles continuous unlearning in LLMs without retaining data by reframing LoRA updates as rotations within a cognitive rotation space $R\in SO(n)$, where the update $W\gets (I+BA)W$ induces a rotation with angle $\theta$. The authors introduce a skew symmetric loss $\mathcal{L}_{Sk}$ to enforce antisymmetric updates, an orthogonal rotation axes loss $\mathcal{L}_{o}$ to ensure perpendicularity between successive unlearning steps, and an unlearning-alignment loss $\mathcal{L}_{Ua}$ to align OOD representations with the RCUs paradigm. An OOD-based rotational salience weight $\beta$ is computed via a distributional shift compensator to control the unlearning degree continuously, enabling a retain-free, monotonic control over unlearning progress. Extensive experiments on ScienceQA and TOFU demonstrate state-of-the-art unlearning performance with fewer trainable parameters than prior retainful methods, and ablations confirm the key role of the rotational losses and alignment components. The approach offers a principled, scalable path for safe, continual unlearning in large language models.

Abstract

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.

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

TL;DR

This work tackles continuous unlearning in LLMs without retaining data by reframing LoRA updates as rotations within a cognitive rotation space , where the update induces a rotation with angle . The authors introduce a skew symmetric loss to enforce antisymmetric updates, an orthogonal rotation axes loss to ensure perpendicularity between successive unlearning steps, and an unlearning-alignment loss to align OOD representations with the RCUs paradigm. An OOD-based rotational salience weight is computed via a distributional shift compensator to control the unlearning degree continuously, enabling a retain-free, monotonic control over unlearning progress. Extensive experiments on ScienceQA and TOFU demonstrate state-of-the-art unlearning performance with fewer trainable parameters than prior retainful methods, and ablations confirm the key role of the rotational losses and alignment components. The approach offers a principled, scalable path for safe, continual unlearning in large language models.

Abstract

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.

Paper Structure

This paper contains 19 sections, 28 equations, 4 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Methodology
  4. Continuous Unlearning for LLM with LoRA
  5. Unlearned Knowledge Detection
  6. Experiments
  7. Datasets
  8. Experimental Setup
  9. Experimental Results
  10. Hyperparameter Analysis
  11. Ablation Study
  12. Conclusion
  13. Appendix
  14. Proofs Of the Theorems.
  15. More Experimental Results
  16. ...and 4 more sections

Figures (4)

  • Figure 1: The overall architecture of our method is shown in the figure. In the training pipeline, the orthogonal rotation axes loss $\mathcal{L} _{o}$ is applied to the attention layers of the LLMs for training; simultaneously, the unlearning alignment loss $\mathcal{L} _{Ua}$ is used to train an OOD detector, whose output is fed into the distributional shift compensator to generate the rotational salience weight $\beta$. In the inference pipeline, given that the LoRA parameters $BA$ are proportional to the rotation angle $\theta_{R_{BA}}$ in the Cognitive Rotation Space $R_{BA}$. We control the rotation angle $\theta_{R_{BA}}$ amplitude by adjusting the scale of LoRA $BA$, and use the weight $\beta$ to dynamically load the parameters that match the required unlearning degree.
  • Figure 2: Experimental results on the ScienceQA dataset. (a)The relationship between the $\beta$ and unlearning processes (S.U.). (b) The relationship between the $\beta$ and unlearning processes (D.U.). (c) The results of C.QA.. (d)The results of O.QA..
  • Figure 3: The comparison results with other methods on the ScienceQA dataset. (a) The results of S.U.. (b) The results of D.U.. (c) The results of R.D..
  • Figure 4: The relationship between the $\beta$ process and the unlearning process. (a) The results of S.U. on the TOFU dataset. (b) The results of D.U. on the TOFU dataset.