Yi Xu

Bo Xue, Yi Xu, Bolei Ma et al.

Traditional knowledge graph completion (KGC) methods rely solely on structural information and struggle with sparsity, while Large Language Models (LLMs) address these limitations through rich world knowledge and strong context modeling. Fine-tuning LLMs is effective but costly, while non-fine-tuned LLMs are efficient but suboptimal. To address this trade-off, we propose \textbf{FLAME}, a framework that extracts context-aware hidden states from intermediate layers of frozen LLMs to train data-efficient KGC classifiers. We bridge LLM-KG semantic gaps via subgraph-based entity descriptions and employ sliced mutual information (SMI) to quantify task-relevant information in representations. Experiments demonstrate that FLAME achieves 47\% improvement over non-fine-tuned LLM baselines and, to our knowledge, is the first to achieve fine-tuned performance with $188\times$ memory efficiency and $26.11\times$ speedup.

Tianxi Zhu, Yi Xu, Xiangyang Ji

An increasing number of studies have focused on stochastic first-order methods (SFOMs) under heavy-tailed gradient noises, which have been observed in the training of practical deep learning models. In this paper, we focus on two types of gradient noises: one is sub-Weibull noise, and the other is noise under the assumption that it has a bounded $p$-th central moment ($p$-BCM) with $p\in (1, 2]$. The latter is more challenging due to the occurrence of infinite variance when $p\in (1, 2)$. Under these two gradient noise assumptions, the in-expectation and high-probability convergence of SFOMs have been extensively studied in the contexts of convex optimization and standard smooth optimization. However, for weakly convex objectives-a class that includes all Lipschitz-continuous convex objectives and smooth objectives-our understanding of the in-expectation and high-probability convergence of SFOMs under these two types of noises remains incomplete. We investigate the high-probability convergence of the vanilla stochastic subgradient descent (SsGD) method under sub-Weibull noises, as well as the high-probability and in-expectation convergence of clipped SsGD under the $p$-BCM noises. Both analyses are conducted in the context of weakly convex optimization. For weakly convex objectives that may be non-convex and non-smooth, our results demonstrate that the theoretical dependence of vanilla SsGD on the failure probability and number of iterations under sub-Weibull noises does not degrade compared to the case of smooth objectives. Under $p$-BCM noises, our findings indicate that the non-smoothness and non-convexity of weakly convex objectives do not impact the theoretical dependence of clipped SGD on the failure probability relative to the smooth case; however, the sample complexity we derived is worse than a well-known lower bound for smooth optimization.