Enhancing Agentic Search via Data Synthesis on Hierarchical Constraint Satisfaction

Deep research becomes increasingly important as people seek to solve complex problems that require gathering and synthesizing information from diverse sources. A key capability in this process is agentic search, where an LLM-agent iteratively retrieves relevant information across multiple sources while performing multi-step reasoning. However, developing effective agentic search systems is challenging due to the lack of high-quality training data that reflects the complexity of real-world research tasks. To address this gap, we introduce InfoSeek, a novel data synthesis framework that conceptualizes agentic search as a Hierarchical Constraint Satisfaction Problem (HCSP), where solving a task requires satisfying layered constraints across multiple levels of sub-problems. InfoSeek employs a Diffusion–Retrospection process: in the diffusion phase, the framework expands outward from a seed webpage, generating constraints that connect to neighboring pages and forming an exploration tree; in the retrospection phase, a subtree is sampled and backtracking constraints are introduced, which are then blurred and integrated into an HCSP instance. As a generic framework, InfoSeek can be easily extended to other domains beyond web, facilitating ad-hoc optimization of deep research. To our knowledge, InfoSeek is the first publicly released framework in this area, complete with open-source code and well-curated datasets. Extensive experiments on diverse information-seeking benchmarks show that training on InfoSeek-generated data substantially improves agentic search performance, delivering significantly larger gains than traditional datasets across diverse model backends and training strategies, thereby validating the effectiveness of our approach.