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J Wang

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6

NeurIPS Conference 2025 Conference Paper

Elastic Robust Unlearning of Specific Knowledge in Large Language Models

  • Yize Sui
  • Jing Ren
  • Wenjing Yang
  • Ruochun Jin
  • Liyang Xu
  • Xiyao Liu
  • J Wang

LLM unlearning aims to remove sensitive or harmful information within the model, thus reducing the potential risk of generating unexpected information. However, existing Preference Optimization (PO)-based unlearning methods suffer two limitations. First, their rigid reward setting limits the effect of unlearning. Second, the lack of robustness causes unlearned information to reappear. To remedy these two weaknesses, we present a novel LLM unlearning optimization framework, namely Elastic Robust Unlearning (ERU), to efficiently and robustly remove specific knowledge from LLMs. We design the elastic reward setting instead of the rigid reward setting to enhance the unlearning performance. Meanwhile, we incorporate the refusal feature ablation into the unlearning process to trigger specific failure patterns for efficiently enhancing the robustness of the PO-based unlearning methods in multiple scenarios. Experimental results show that ERU can improve the unlearning effectiveness significantly while maintaining a high utility performance. Especially, on the WMDP-Bio benchmark, ERU shows a 9\% improvement over the second-best method, and maintains 83\% performance even under 1, 000 sample fine-tuned retraining attacks, significantly better than the baseline method.

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NeurIPS Conference 2023 Conference Paper

On the Properties of Kullback-Leibler Divergence Between Multivariate Gaussian Distributions

  • Yufeng Zhang
  • Jialu Pan
  • Li Ken Li
  • Wanwei Liu
  • Zhenbang Chen
  • Xinwang Liu
  • J Wang

Kullback-Leibler (KL) divergence is one of the most important measures to calculate the difference between probability distributions. In this paper, we theoretically study several properties of KL divergence between multivariate Gaussian distributions. Firstly, for any two $n$-dimensional Gaussian distributions $\mathcal{N}_1$ and $\mathcal{N}_2$, we prove that when $KL(\mathcal{N}_2||\mathcal{N}_1)\leq \varepsilon\ (\varepsilon>0)$ the supremum of $KL(\mathcal{N}_1||\mathcal{N}_2)$ is $(1/2)\left((-W_{0}(-e^{-(1+2\varepsilon)}))^{-1}+\log(-W_{0}(-e^{-(1+2\varepsilon)})) -1 \right)$, where $W_0$ is the principal branch of Lambert $W$ function. For small $\varepsilon$, the supremum is $\varepsilon + 2\varepsilon^{1. 5} + O(\varepsilon^2)$. This quantifies the approximate symmetry of small KL divergence between Gaussian distributions. We further derive the infimum of $KL(\mathcal{N}_1||\mathcal{N}_2)$ when $KL(\mathcal{N}_2||\mathcal{N}_1)\geq M\ (M>0)$. We give the conditions when the supremum and infimum can be attained. Secondly, for any three $n$-dimensional Gaussian distributions $\mathcal{N}_1$, $\mathcal{N}_2$, and $\mathcal{N}_3$, we theoretically show that an upper bound of $KL(\mathcal{N}_1||\mathcal{N}_3)$ is $3\varepsilon_1+3\varepsilon_2+2\sqrt{\varepsilon_1\varepsilon_2}+o(\varepsilon_1)+o(\varepsilon_2)$ when $KL(\mathcal{N}_1||\mathcal{N}_2)\leq \varepsilon_1$ and $KL(\mathcal{N}_2||\mathcal{N}_3)\leq \varepsilon_2$ ($\varepsilon_1, \varepsilon_2\ge 0$). This reveals that KL divergence between Gaussian distributions follows a relaxed triangle inequality. Note that, all these bounds in the theorems presented in this work are independent of the dimension $n$. Finally, we discuss several applications of our theories in deep learning, reinforcement learning, and sample complexity research.

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