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.

Large language models (LLMs) are commonly adapted to downstream tasks using parameter-efficient fine-tuning (PEFT) or in-context learning (ICL). Recently, ICL-driven embedding-based adaptation has been proposed as a distinct task adaptation paradigm. It derives task-specific embeddings from intermediate activations using few-shot prompts and injects them during inference. Despite its conceptual appeal, this approach has not demonstrated consistent performance gains over PEFT or ICL, and its empirical advantages have been limited in practice. We propose Soft head-selection for ICL-derived Task Embeddings (SITE), a gradient-based method that identifies task-relevant attention heads to enable effective task embedding injection. Across various types of open-ended generation, reasoning, and natural language understanding tasks, SITE significantly outperforms prior embedding-based adaptation methods and few-shot ICL, while using substantially fewer trainable parameters than PEFT. Experiments on 12 LLMs ranging from 4B to 70B parameters demonstrate the generality of our approach, and intra-task and inter-task activation patching analyses further provide new mechanistic insights by revealing strong task dependence in attention head functionality.