Reinforcement learning (RL) for multi-turn deep research agents suffers from a granularity mismatch: token-level methods incur high variance over long reasoning horizons, while sequence-level methods ignore the internal decision structure of multi-turn interactions. We introduce Block-wise Geometric Policy Optimization (BGPO), which treats each assistant turn—packaging reasoning and tool invocation into one semantically coherent unit—as an optimization-level macro-action and aggregates block-averaged log-importance ratios with equal weights across blocks. We prove that block-equal weighting minimizes a covariance-robust upper bound on ratio variance under weak inter-block coupling, with the approximation gap relative to sequence-length weighting bounded by block-length imbalance. To improve exploration efficiency, we expose human-defined rewrite operators—including decomposition, keyword extraction, synonym replacement, and HyDE—as a prompt-level exploration prior during RL rollouts. On seven knowledge-intensive QA benchmarks, our 7B system achieves an average judge score of 0.715 ± 0.010 over three training seeds, compared with 0.664 for Search-R1-7B. A controlled fixed-prior attribution study further confirms that block-level optimization independently improves answer quality, achieving 0.527/0.395 F1/EM compared with 0.482/0.350 for GRPO. Our code is publicly available at https://github.com/meiotoufa/Learning-to-Think-in-Blocks.

Information retrieval plays a crucial role in resource localization. Current dense retrievers retrieve the relevant documents within a corpus via embedding similarities, which compute similarities between dense vectors mainly depending on word co-occurrence between queries and documents, but overlook the real query intents. Thus, they often retrieve numerous irrelevant documents. Particularly in the scenarios of complex queries such as negative-constraint queries, their retrieval performance could be catastrophic. To address the issue, we propose a neuro-symbolic information retrieval method, namely NS-IR, that leverages first-order logic (FOL) to optimize the embeddings of naive natural language by considering the logical consistency between queries and documents. Specifically, we introduce two novel techniques, logic alignment and connective constraint, to re-rank candidate documents, thereby enhancing retrieval relevance. Furthermore, we construct a new dataset NegConstraint including negative-constraint queries to evaluate our NS-IR’s performance on such complex IR scenarios. Our extensive experiments demonstrate that NS-IR not only achieves superior zero-shot retrieval performance on web search and low-resource retrieval tasks, but also performs better on negative-constraint queries. Our scource code and dataset are available at https://github.com/xgl-git/NS-IR-main.