Zhi-Yong Liu

Siyu Cao, Lu Zhang, Ruizhe Zeng et al.

Sports videos are a challenging domain for multimodal understanding because they involve complex and dynamic human activities. Despite rapid progress in Multimodal Large Language Models (MLLMs), long-horizon reasoning in sports videos remains difficult, as answering questions requires both locating temporally sparse evidence and integrating it into reasoning. We attribute this limitation to two closely coupled factors: insufficient supervision over temporally dispersed evidence, and the lack of methods that require models to identify, localize, and justify temporal evidence. To address these gaps, we introduce SportsTime, a large-scale benchmark for long-form sports video understanding, comprising 14K+ open-ended QA pairs and 50K+ step-wise temporal evidence annotations. Building on SportsTime, we propose Chain-of-Time Reasoning (CoTR), which treats reasoning as a process of temporally grounded evidence composition. Specifically, during training, CoTR introduces a temporal-reward GRPO to encourage temporally grounded reasoning. During inference, it employs an anchor-observe-infer evidence-seeking loop to iteratively localize, verify, and compose temporal evidence before producing the final answer. Experiments demonstrate the usefulness of SportsTime as a benchmark and the effectiveness of CoTR, which consistently improves temporal compositional reasoning and step-wise grounding quality over strong MLLM baselines.

Xu Yang, Hong Qiao, Zhi-Yong Liu

We propose a weighted common subgraph (WCS) matching algorithm to find the most similar subgraphs in two labeled weighted graphs. WCS matching, as a natural generalization of the equal-sized graph matching or subgraph matching, finds wide applications in many computer vision and machine learning tasks. In this paper, the WCS matching is first formulated as a combinatorial optimization problem over the set of partial permutation matrices. Then it is approximately solved by a recently proposed combinatorial optimization framework - Graduated NonConvexity and Concavity Procedure (GNCCP). Experimental comparisons on both synthetic graphs and real world images validate its robustness against noise level, problem size, outlier number, and edge density.

Zhi-Yong Liu, Hong Qiao

In this paper we propose the Graduated NonConvexity and Graduated Concavity Procedure (GNCGCP) as a general optimization framework to approximately solve the combinatorial optimization problems on the set of partial permutation matrices. GNCGCP comprises two sub-procedures, graduated nonconvexity (GNC) which realizes a convex relaxation and graduated concavity (GC) which realizes a concave relaxation. It is proved that GNCGCP realizes exactly a type of convex-concave relaxation procedure (CCRP), but with a much simpler formulation without needing convex or concave relaxation in an explicit way. Actually, GNCGCP involves only the gradient of the objective function and is therefore very easy to use in practical applications. Two typical NP-hard problems, (sub)graph matching and quadratic assignment problem (QAP), are employed to demonstrate its simplicity and state-of-the-art performance.