Knowledge-intensive visual question answering (VQA) requires external knowledge beyond image content, demanding precise visual grounding and coherent integration of visual and textual information.Although multimodal retrieval-augmented generation has achieved notable advances by incorporating external knowledge bases, existing approaches largely adopt single-pass frameworks that often fail to acquire sufficient knowledge and lack mechanisms to revise misdirected reasoning.We propose PMSR (Progressive Multimodal Search and Reasoning), a framework that progressively constructs a structured reasoning trajectory to enhance both knowledge acquisition and synthesis.PMSR uses dual-scope queries conditioned on both the latest record and the trajectory to retrieve diverse knowledge from heterogeneous knowledge bases.The retrieved evidence is then synthesized into compact records via compositional reasoning.This design facilitates controlled iterative refinement, which supports more stable reasoning trajectories with reduced error propagation.Extensive experiments across six diverse benchmarks (Encyclopedic-VQA, InfoSeek, MMSearch, LiveVQA, FVQA, and OK-VQA) demonstrate that PMSR consistently improves both retrieval recall and end-to-end answer accuracy.

Cross-Domain Few-Shot Learning (CDFSL) methods typically parameterize models with task-agnostic and task-specific parameters. To adapt task-specific parameters, recent approaches have utilized fixed optimization strategies, despite their potential sub-optimality across varying domains or target tasks. To address this issue, we propose a novel adaptation mechanism called Task-Specific Preconditioned gradient descent (TSP). Our method first meta-learns Domain-Specific Preconditioners (DSPs) that capture the characteristics of each meta-training domain, which are then linearly combined using task-coefficients to form the Task-Specific Preconditioner. The preconditioner is applied to gradient descent, making the optimization adaptive to the target task. We constrain our preconditioners to be positive definite, guiding the preconditioned gradient toward the direction of steepest descent. Empirical evaluations on the Meta-Dataset show that TSP achieves state-of-the-art performance across diverse experimental scenarios.