Kai Sun

Xiaokang Pan, Xingyu Li, Jin Liu et al.

STOchastic Recursive Momentum (STORM)-based algorithms have been widely developed to solve one to $K$-level ($K \geq 3$) stochastic optimization problems. Specifically, they use estimators to mitigate the biased gradient issue and achieve near-optimal convergence results. However, there is relatively little work on understanding their generalization performance, particularly evident during the transition from one to $K$-level optimization contexts. This paper provides a comprehensive generalization analysis of three representative STORM-based algorithms: STORM, COVER, and SVMR, for one, two, and $K$-level stochastic optimizations under both convex and strongly convex settings based on algorithmic stability. Firstly, we define stability for $K$-level optimizations and link it to generalization. Then, we detail the stability results for three prominent STORM-based algorithms. Finally, we derive their excess risk bounds by balancing stability results with optimization errors. Our theoretical results provide strong evidence to complete STORM-based algorithms: (1) Each estimator may decrease their stability due to variance with its estimation target. (2) Every additional level might escalate the generalization error, influenced by the stability and the variance between its cumulative stochastic gradient and the true gradient. (3) Increasing the batch size for the initial computation of estimators presents a favorable trade-off, enhancing the generalization performance.

Kai Sun, Yushi Bai, Ji Qi et al. · tsinghua

To advance the evaluation of multimodal math reasoning in large multimodal models (LMMs), this paper introduces a novel benchmark, MM-MATH. MM-MATH consists of 5,929 open-ended middle school math problems with visual contexts, with fine-grained classification across difficulty, grade level, and knowledge points. Unlike existing benchmarks relying on binary answer comparison, MM-MATH incorporates both outcome and process evaluations. Process evaluation employs LMM-as-a-judge to automatically analyze solution steps, identifying and categorizing errors into specific error types. Extensive evaluation of ten models on MM-MATH reveals significant challenges for existing LMMs, highlighting their limited utilization of visual information and struggles with higher-difficulty problems. The best-performing model achieves only 31% accuracy on MM-MATH, compared to 82% for humans. This highlights the challenging nature of our benchmark for existing models and the significant gap between the multimodal reasoning capabilities of current models and humans. Our process evaluation reveals that diagram misinterpretation is the most common error, accounting for more than half of the total error cases, underscoring the need for improved image comprehension in multimodal reasoning.

Kai Sun, Jiapu Wang, Huajie Jiang et al.

Conventional Knowledge graph completion (KGC) methods aim to infer missing information in incomplete Knowledge Graphs (KGs) by leveraging existing information, which struggle to perform effectively in scenarios involving emerging entities. Inductive KGC methods can handle the emerging entities and relations in KGs, offering greater dynamic adaptability. While existing inductive KGC methods have achieved some success, they also face challenges, such as susceptibility to noisy structural information during reasoning and difficulty in capturing long-range dependencies in reasoning paths. To address these challenges, this paper proposes the Query-Enhanced Adaptive Semantic Path Reasoning (QASPR) framework, which simultaneously captures both the structural and semantic information of KGs to enhance the inductive KGC task. Specifically, the proposed QASPR employs a query-dependent masking module to adaptively mask noisy structural information while retaining important information closely related to the targets. Additionally, QASPR introduces a global semantic scoring module that evaluates both the individual contributions and the collective impact of nodes along the reasoning path within KGs. The experimental results demonstrate that QASPR achieves state-of-the-art performance.