Vision-language retrieval-augmented generation (RAG) has become an effective approach for tackling Knowledge-Based Visual Question Answering (KB-VQA), which requires external knowledge beyond the visual content presented in images. The effectiveness of Vision-language RAG systems hinges on multimodal retrieval, which is inherently challenging due to the diverse modalities and knowledge granularities in both queries and knowledge bases. Existing methods have not fully tapped into the potential interplay between these elements. We propose a multimodal RAG system featuring a coarse-to-fine, multi-step retrieval that harmonizes multiple granularities and modalities to enhance efficacy. Our system begins with a broad initial search aligning knowledge granularity for cross-modal retrieval, followed by a multimodal fusion reranking to capture the nuanced multimodal information for top entity selection. A text reranker then filters out the most relevant fine-grained section for augmented generation. Extensive experiments on the InfoSeek and Encyclopedic-VQA benchmarks show our method achieves state-of-the-art retrieval performance and highly competitive answering results, underscoring its effectiveness in advancing KB-VQA systems. Our code can be found at https://github.com/ChaoLinAViy/OMGM.

Visual reasoning is crucial for multimodal large language models (MLLMs) to address complex chart queries, yet high-quality rationale data remains scarce. Existing methods leveraged (M)LLMs for data generation, but direct prompting often yields limited precision and diversity. In this paper, we propose Chain of Functions (CoF), a novel programmatic reasoning data generation pipeline that utilizes freely-explored reasoning paths as supervision to ensure data precision and diversity. Specifically, it starts with human-free exploration among the atomic functions (e.g., maximum data and arithmetic operations) to generate diverse function chains, which are then translated into linguistic rationales and questions with only a moderate open-sourced LLM. CoF provides multiple benefits: 1) Precision: function-governed generation reduces hallucinations compared to freeform generation; 2) Diversity: enumerating function chains enables varied question taxonomies; 3) Explainability: function chains serve as built-in rationales, allowing fine-grained evaluation beyond overall accuracy; 4) Practicality: it eliminates reliance on extremely large models. Employing CoF, we construct the ChartCoF dataset, with 1.4k complex reasoning Q&A for fine-grained analysis and 50k Q&A for reasoning enhancement.Experiments show that ChartCoF improves performance for MLLMs on widely used benchmarks, and the fine-grained evaluation on ChartCoF reveals varying performance across question taxonomies and step numbers for each MLLM. Furthermore, the novel paradigm of function-governed rationale generation in CoF could inspire broader applications beyond charts. The code and data have been publicly available at https://github.com/microsoft/Chain-of-Functions.