Retrieval-Augmented Generation (RAG) im- proves the factuality of large language models (LLMs), yet existing RAG systems often struggle with complex, multi-step reasoning that requires adaptive retrieval and continuous revision of intermediate contexts. Recent reinforcement learning (RL)-based agentic RAG methods partially alleviate this issue, but typically rely on coarse-grained action spaces and trajectory-level rewards, resulting in weak reward assignment and a bias toward short-horizon, stereotyped reasoning template. To address, we propose AGENTICRAG-R1, a RL framework that deeply integrates reasoning, retrieval, and memory via a memory stack and fine-grained action space, supported by hierarchical action-aware rewards and an information-aware trajectory rejection strategy to enable effective long-horizon learning. Experiments across a diverse set of multi-hop, open-domain, and agentic reasoning benchmarks, spanning multiple backbone model sizes, demonstrate that AGENTICRAG- R1 consistently outperforms strong baselines. Moreover, AGENTICRAG-R1 learns more robust, interpretable, and memory-aware reasoning behaviors, highlighting the effect of fine-grained action modeling and information- aware optimization for long-horizon reasoning. Our code is anonymous available at https: //github.com/jiangxinke/Harness-RL/ tree/AgenticRAG-R1-Whitebox.

Mathematical reasoning is a key capability for vision-language models (VLMs), yet current benchmarks mainly evaluate text-based or explicitly symbolic visual inputs. It remains unclear whether VLMs can reason mathematically when information must be perceived and inferred from images rather than read from explicit symbols. We introduce GSM8K-V, a benchmark transforming GSM8K into multi-image sequences with semantic equivalence preserved. By mapping text-based problems into visual form via an automated pipeline and human verification, we curate 1,319 high-quality samples. In GSM8K-V, quantities must be extracted through visual perception, and reasoning chains must be reconstructed by integrating implicit cues across scenes. Evaluation of 34 VLMs reveals a striking modality gap: while most models exceed 90% on text, the best model achieves only 59% on GSM8K-V, far below the 91% human accuracy. Notably, models enhanced for visual math reasoning show no improvement on GSM8K-V despite large gains on existing benchmarks, confirming that it evaluates a distinct capability. Error analysis shows that the primary bottleneck lies in Implicit Visual Inference Error (IVIE), where models fail to recover visual semantics that are implied rather than explicitly stated. Our code and data are released at https://github.com/ZJU-REAL/GSM8K-V.

Agentic search augments large language models (LLMs) with external knowledge through reinforcement learning. However, existing approaches suffer from blind reliance on noisy retrieval and hallucination when both parametric and external knowledge fail—reflecting a lack of calibration regarding the model’s knowledge boundary. We propose Knowledge boundary Policy Optimization (KbPO), a reinforcement learning framework that explicitly aligns retrieval decisions with quantified knowledge states. KbPO introduces: (1) a semantic stability metric to delineate reliable parametric knowledge; (2) a four-quadrant taxonomy synthesising internal certainty with retrieval quality; and (3) a quadrant-based reward mechanism incentivising calibrated behaviour. We further adopt an iterative query evolution pipeline to construct boundary-probing training samples. Experiments on ten benchmarks demonstrate that KbPO outperforms strong baselines while exhibiting reduced hallucination rates.