Large Language Models often contain factually incorrect or outdated knowledge, giving rise to model editing methods for precise knowledge updates. However, current mainstream locate-then-edit approaches exhibit a progressive performance decline during sequential editing, due to inadequate mechanisms for long-term knowledge preservation. To tackle this, we model the sequential editing as a constrained stochastic programming. Given the challenges posed by the cumulative preservation error constraint and the gradually revealed editing tasks, **LyapLock** is proposed. It integrates queuing theory and Lyapunov optimization to decompose the long-term constrained programming into tractable stepwise subproblems for efficient solving. This is the first model editing framework with rigorous theoretical guarantees, achieving asymptotic optimal editing performance while meeting the constraints of long-term knowledge preservation. Experimental results show that our framework scales sequential editing capacity to over 10,000 edits while stabilizing general capabilities and boosting average editing efficacy by 11.89% over SOTA baselines. Furthermore, it can be leveraged to enhance the performance of baseline methods. Our code is released on https://github.com/caskcsg/LyapLock.

Deep semantic retrieval has achieved remarkable success in online E-commerce applications. The majority of methods aim to distinguish positive items and negative items for each query by utilizing margin loss or softmax loss. Despite their decent performance, these methods are highly sensitive to hyper-parameters, i.e., margin and temperature 𝜏, which measure the similarity of negative pairs and affect the distribution of items in metric space. How to design and choose adaptively parameters for different pairs is still an open challenge. Recently several methods have attempted to alleviate the above problem by learning each parameter through trainable/statistical methods in the recommendation. We argue that those are not suitable for retrieval scenarios, due to the agnosticism and diversity of the queries. To fully overcome this limitation, we propose a novel adaptive metric learning method that designs a simple and universal hyper-parameter-free learning method to improve the performance of retrieval. Specifically, we first propose a method that adaptive obtains the hyper-parameters by relying on the batch similarity without fixed or extra-trainable hyper-parameters. Subsequently, we adopt a symmetric metric learning method to mitigate model collapse issues. Furthermore, the proposed method is general and sheds a highlight on other fields. Extensive experiments demonstrate our method significantly outperforms previous methods on a real-world dataset, highlighting the superiority and effectiveness of our method. This method has been successfully deployed on an online E-commerce search platform and brought substantial economic benefits.