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CE-U: Cross Entropy Unlearning

Large language models (LLMs) inadvertently memorize sensitive data from their massive pretraining corpora \cite{jang2022knowledge}. In this work, we propose CE-U (Cross Entropy Unlearning), a novel loss function designed specifically for unlearning tasks. CE-U addresses fundamental limitations of gradient ascent approaches which suffer from instability due to vanishing gradients when model confidence is high and gradient exploding when confidence is low. We also unify standard cross entropy supervision and cross entropy unlearning into a single framework. Notably, on the TOFU benchmark for unlearning \cite{maini2024tofu}, CE-U achieves state-of-the-art results on LLaMA2-7B with 1\% and 5\% forgetting, even without the use of any extra reference model or additional positive samples. Our theoretical analysis further reveals that the gradient instability issues also exist in popular reinforcement learning algorithms like DPO and GRPO, as they include a gradient ascent component. This suggests that applying CE-U principles to reinforcement learning could be a promising direction for improving stability and convergence.

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