Large Vision-Language Models (LVLMs) consistently require new arenas to guide their expanding boundaries, yet their capabilities with hypergraphs remain unexplored. In the real world, hypergraphs have significant practical applications in areas such as life sciences and social communities. Recent advancements in LVLMs have shown promise in understanding complex topologies, yet there remains a lack of a benchmark to delineate the capabilities of LVLMs with hypergraphs, leaving the boundaries of their abilities unclear. To fill this gap, in this paper, we introduce HyperGVL, the first benchmark to evaluate the proficiency of LVLMs in hypergraph understanding and reasoning. HyperGVL provides a comprehensive assessment of 12 advanced LVLMs across 84,000 vision-language question-answering (QA) samples spanning 12 tasks, ranging from basic component counting to complex NP-hard problem reasoning. The involved hypergraphs contain multiscale synthetic structures and real-world citation and protein networks. Moreover, we examine the effects of 12 textual and visual hypergraph representations and introduce a generalizable router WiseHyGR that improves LVLMs in hypergraph via learning adaptive representations. We believe that this work is a step forward in connecting hypergraphs with LVLMs.

Efficient fine-tuning plays a fundamental role in modern large models, with low-rank adaptation emerging as a particularly promising approach. However, the existing variants of LoRA are hampered by limited expressiveness, a tendency to overfit, and sensitivity to hyperparameter settings. This paper presents LoRA Slow Cascade Learning (LoRASC), an innovative technique designed to enhance LoRA’s expressiveness and generalization capabilities while preserving its training efficiency. Our approach augments expressiveness through a cascaded learning strategy that enables a mixture-of-low-rank adaptation, thereby increasing the model’s ability to capture complex patterns. Additionally, we introduce a slow-fast update mechanism and cascading noisy tuning to bolster generalization. The extensive experiments on various language and vision datasets, as well as robustness benchmarks, demonstrate that the proposed method not only significantly outperforms existing baselines, but also mitigates overfitting, enhances model stability, and improves OOD robustness.