We explore graph rewiring methods that optimise commute time. Recent graph rewiring approaches facilitate long-range interactions in sparse graphs, making such rewirings commute-time-optimal $\textit{on average}$. However, when an expert prior exists on which node pairs should or should not interact, a superior rewiring would favour short commute times between these privileged node pairs. We construct two synthetic datasets with known priors reflecting realistic settings, and use these to motivate two bespoke rewiring methods that incorporate the known prior. We investigate the regimes where our rewiring improves test performance on the synthetic datasets. Finally, we perform a case study on a real-world citation graph to investigate the practical implications of our work.

Two approaches have emerged to input images into large language models (LLMs). The first is to caption images into natural language. The second is to map image feature embeddings into the domain of the LLM and pass the mapped embeddings directly to the LLM. The majority of recent few-shot multimodal work reports performance using architectures that employ variations of one of these two approaches. But they overlook an important comparison between them. We design a controlled and focused experiment to compare these two approaches to few-shot visual question answering (VQA) with LLMs. Our findings indicate that for Flan-T5 XL, a 3B parameter LLM, connecting visual embeddings directly to the LLM embedding space does not guarantee improved performance over using image captions. In the zero-shot regime, we find using textual image captions is better. In the few-shot regimes, how the in-context examples are selected determines which is better.