Open Data Synthesis for Deep Research
Authors: Ziyi Xia
Kun Luo
Hongjin Qian
Siqi Bao
Zheng Liu
Venue: ICLR 2026 Poster (2026)
Keywords: data synthesis
agentic search
large language models
Primary area: datasets and benchmarks
TL;DR: InfoSeek is the first open-source framework with a large-scale dataset that generates complex, research-like tasks to train LLMs for stronger agentic search and deep reasoning.

Abstract: 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.

Published as a conference paper at ICLR 2026
OPEN DATA SYNTHESIS FOR DEEP RESEARCH
Ziyi Xial* Kun Luo1.2 Hongjin Qian Siqi Bao Zheng Liu
Beijing Academy of Artificial Intelligence Institute of Automation, Chinese Academy of Sciences 3 Hong Kong University of Science and Technology *Hong Kong Polytechnic University
{ziyixia85 ch i jnghj, zhengliut 02 0mm) 0mma com sbao@connect. ust.hk
ABSTRACT
Deep research becomes increasingly important as people seek solve com- plex problems that require gathering and synthesizing information from diverse sources. A key capability this process is agentic search, where an LLM LLM-agent iteratively retrieves relevant information across multiple sources while perform- ing multi-step reasoning. However, developing effective agentic search systems is challenging due to the lack of high-quality training data that reflects the com- plexity of real-world research tasks. To address this gap, we introduce InfoSeek, novel data synthesis framework that conceptualizes agentic search as a Hierar- chical Constraint Satisfaction Problem (HCSP), where solving a task requires InfoSeek satisfying layered constraints across multiple levels of sub-problent employs a Diffusson-RReroospcctiin process: in the diffusion phase, the frame- work expands outward from seed webpage, generating constraints that connect to neighboring pages and forming an exploration tree; in the retrospection phase, subtree sampled and backtracking constraints are introduced, which are then blurred and integrated into an HCSP instance. As generic framework, InfoSeek can be easily extended to other domains beyond web, facilitating ad-hoc opti- mization of deep research. To our knowledge, InfoSeek is the first publicly re- leased framework in this area, complete with open-source code and well-curated datasets. Extensive experiments on diverse information-sseeking benchmarks show that training on InfoSeck infoSeek-generateed data substantially improves agentic search performance, delivering significantly larger gains than traditional datasets across diverse model backends and training strategies, thereby validating the effective- ness of our approach. Our datasets and codes are in this repository
INTRODUCTION
Recently, large language models (LLMs) have become primary channel for information seeking. bridging human queries with vast knowledge sources (OpenAl 2023) Gemini Team 2025). Aug- menting LLMs with external retrieval, in retrieval-uummented generation (RAG) (Lewis et al.) 2020). has proven effective for factual question answering but falls short on complex tasks that re- quire iterative search, query decomposition, and multi-step reasoning over heterogeneous evidence. Addressing such challenges requires agentic capabilities such as planning, refinement, and integra- tion, which define the emerging paradigm of agentic search (Citron) 2024 OpenAl 2025), where models evolve from conversational assistants into autonomous know wewledge engines (Li et al. 2025c
Recent advances in agentic search fall into two main paradigms. The first relies on human huran-curated workflows, which are easy to implement but difficult to optimize (Li et al., 2025b Yao et al. 2023).
The second, increasingly mainstream, adopts end-to-end optimization with reinforcement learning. where models explore reasoning trajectories and improve through reward feedback (Jin et al. 2025 Song et al. 2025a Zheng et al. 2025). However, this approach critically depends on high-quality traiiing data. Such data must be sufficiently in depth incentivize deep exploration, and its answers
Equaa contribution Corresponding author

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Published as a conference paper at ICLR 2026
Table 1: Comparison of the open-source status of classical QA datasets and recent data synthesis approaches for agentic search, highlighting the nature of the problems they cover, data sources, and the availability of their constructed datasets and frameworks.
Name
Problem
Data Source
QA pairs
Trajectories
Framework
NQ
Single-hop
Wiki
300k+
HotpotQA
Multi-hop
Wiki
100k+
WebWalkerQA
Multi-hop
Web
14.3k
InForage
Multi-hop
Web
SimpleDeepSearcher
Multi-hop
871
Open
Pangu DeeeDiver
Multi-hop
Web
WebDancer
Multi-hop
Wiki& Web
200
200
WebSailor
Multi-hop
Wiki
20
WebShaper
Complex
Wiki
500
InfoSeek
HCSP
Wiki&
50k+
16.5k
Open
must be verifiable to ensure reliable rewards (Qian & Liu| 2025). As shown in Table I existing resources, such as Natural Questions (Kwiatkowski et al., 2019) and HotpotQA (Yang et al. 2018),
provide only shallow supervision, while recent synthetic datasets either remain confined to multi-
hop QA (Wu et al. 2025b) or are not publicly available (Li et al. 2025a Tao et al. 2025).
To bridge the persistent data gap, we propose InfoSeek, framework for synthesizing structurally complex and realistic data tailored to agentic search. At its core, InfoSeek formalizes challenging agentic search tasks Hierarchical Constraint Satisfaction Problem (HCSP). As illustrated in Figure an HCSP extends the classical notion of constraint satisfaction by embedding both parallel and sequential dependencies within hierarchical structure. Simple constraint satisfaction problems can be seen as flat instances where independent conditions directly narrow a candidate set, and multi- hop reasoning tasks correspond to sequential chains of dependent conditions. HCSPs generalize both by explicitly requiring the resolution of multiple layers of interdependent sub- wub-problems. By nature, such problems can be unfolded into a like structure, where internal nodes represent intermediate sub-questions, edges encode logical dependencies, and the root corresponds to the final solution.
Building on this formulation, InfoSeek employs a Diffusiin-RReroospettion process to synthesize HCSP-style questions. In the diffusion phase, the framework begins from a seed webpage and pro- gressively expands outward by following entity relations to neighboring pages, thereby building an exploration tree enriched with layered constraints. In the retrospection phase, subtrees are sampled from this exploration graph, and reverse constraints are introduced to enforce backtracking toward the seed. These constraints are blurred and integrated into well-defined HCSP instances, ensuring that each synthesized problem requires genuine multi-step reasoning and admits a unique verifiable answer. To instantiate this framework scale, leverage filtered web and Wikipedia corpora to generate a large collection of research trees and their corresponding QA pairs. The resulting dataset captures both breadth and depth, enabling the design of diverse tasks that go beyond existing benchmarks and better reflect the complexity of real-world deep research.
To examine how InfoSeck can effectively support model training, we start with supervised fine- tuning (SFT), where trajectories are filtered by rejection sampling to ensure correctness. We then apply a basic reinforcement learning setup. using GRPO with a final reward grounded in verifiable answers (Guo et al.) 2025). Even under this simple yet transparent pipeline, models trained on InfoSeek consistently surpass strong baselines. Beyond these results, the dataset's preserved meta- information, such intermediate steps and detailed retrieval labels, offers richer signals that could enable the design of more sophisticated RL objectives in future work.
In summary, this work makes the following contributions: (1) We formalize complex information-
seeking questions as Hierarchical Constraint Satisfaction Problems (HCSPs), offering a principled and unified formulation that generalizes and clearly distinguishes them from simpler multi-hop or flat CSP formulations. (2) We introduce InfoSeck, an autonomous and scalable data synthesis frame- work that concretely instantiates this definition. To knowledge, InfoSeek is the first publicly
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Figure Illustration of Hicrarchical Constraint Satisfaction Problems (HCSP), with Constraint Satisfaction Problems (CSP) and Multi-hop Problems (MHP). The left panel contrasts CSP as flat independent conditions, MHP as sequential dependencies, and HCSP as a hierarchical composition of both parallel and sequential constraints that naturally form a tree structure. The right panel fur- ther demonstrates the blurred parent node technique and the quality assurance process within the InfoSeek data synthesis framework, which together ensure increased problem difficulty, uniqueness of solutions, and reliable construction of verifiable QA pairs.
released framework in this area, enabling high-quality dataset construction with explicit control over structural complexity. (3) We build a large-scale Deep Research dataset with more than 50k QA pairs and 16.5k reasoning trajectories, fully recording the entire construction process. Through comprehensive experiments, we rigorously verify the effectiveness of InfoSeek by fine-tuning and optimizing models on the dataset, achieving consistent improvements over strong baselines.
INFOSEEK: SCALABLE DATA SYNTHESIS FRAMEWORK FOR HCSP
2.1 PRELIMINARY
As illustrated in Figure within the InfoSeek framework we provide a general and principled for- malization for complex deep research tasks, which we define as Hierarchical Constraint Satis- faction Problems (HCSPs). An HCSP captures the essential nature of deep information-sseking: the final answer not directly accessible but must be progressively uncovered by systematically satisfying hierarchy of interdependent constraints. Solving such problems requires carefully and systematically pruning the search space at each level, climinating candidates inconsistent with ac- cumulated evidence, until the eventual convergence
unique valid solution.
Formally, given a question x containing a set constraints C₁ = fcr...., c and a set of sub- questions Yz (V1..... .,. Fm }, we define hierarchical decomposition H-)) as:
m
H
S(C) n N (w:)), with N Ø = U, j=1
where U denotes the universal set. The final answer A of a hierarchical constraint satisfaction problem qu is then given by A (qg)). This formulation highlights two central characteristics of HCSPs: (1) multi-layered dependencies that intertwine both parallel and sequential reasoning, and (2) the necessity of integrating evidence across multiple levels to reach unique, verifiable answer.
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Such hierarchical pruning not only parallels algorithmic paradigms such as constraint propagation in AI, but also echoes human reasoning, where complex judgments arise from combining multiple, interdependent strands of evidence.
With the formal definition of HCSP, two types of classical problems can be defined similarly. A Constraint Satisfaction Problem (CSP) is simplified form of HCSP in which all constraints flat and independent, and the solution is given by the intersection of the satisfying sets for all constraints.
A =
S(c)) s.t. |A|= = [S(c)] 2 1 Vi,
where S(c:) denotes the set of entities that satisfy constraint c;. When n = 1, CSP reduces to the base case of a single-construint problem, which involves exactly one condition and yields a unique ground-truth answer. For example, the question "Who developed the theory of relativity?" corre- sponds to C. = {[i} with C1 "devellped the theory of relativityy", yields to A = {Albert Einstein). For 1, such in Fig. a with constraints ci "got PhD from Princeton University in
1938", C2 : "born in London", C3 "graduated from University of Cambridge". The intersection ((ci) n S(c2) S(ca) leads A {Alan Turing].
By contrast, a Multi-hop Problem (MHP) represents another special form of HCSP, where con- straints are dependent and arranged in a sequential chain, and the answer emerges only after each step is resolved in order.
A (c) = =
S5. ........00 S(c), s.t. s.t.ki1
(3)
A times
where denotes the number of reasoning hops. Take the 3-hop question illustrated in Fig.
as an example: (1) starting with = "scientist who solved the Enigma code", we obtain S(c)
{Alan Turing]; (2) using this entity, we resolve S("bitthplace of Alan Turing") [London]; (3)
finally, the problem reduces to a single-constrait query: "which country has London as its capital", yielding A {England}.
In contrast to both CSPs and MHPs, HCSPs generalize and extend these formulations by requiring structured reasoning across multiple layers of interdependent constraints, thereby more faithfully reflecting the complexity of real-world deep research tasks.
2.2 FRAMEWORK
To instantiate the formulation of HCSPs at scale, we design the InfoSeek framework, which gener- ates complex question-answer pairs through two-stage process called Diffussion-Retrospeciion The key idea is to mimic the structure of HCSPs: the diffusion phase explores outward from an initial seed iteratively construct
with interdependent entities and constraints, while the retrospec- tion phase traverses this tree in reverse to synthesize question that enforce hierarchical reasoning. This design ensures that the resulting data not only captures the layered structure of HCSPs but also provides verifiable answers grounded in factual evidence.
Constructing a Research Tree. sion of a research process: starting from a single seed entity, it gradually spreads to related entities, much like diffusion in a graph. The process results a research tree T = (V, E), where each vertex U E V represents knowledge entity (e.g., "Alan Turing", "University of Cambridge") or trivial fact (e.g., "1910s", "summer of 1925"), and each edge (v, w) E E encodes their semantic relationship (e.g., "Alan Turing graduated from the University of Cambridge").
Diffusion Stage:
The diffusion stage simulates the outward expan-
Formally, the process can expressed as:
T (1)).0) [w], FU ((r, w))),
initialization with single seed r as root,
(4)
expansion by adding w & V connected to v E V.
That is, the construction starts with a trivial tree containing only the root r, then recursively expands by sampling a new entity w related to some existing entity v and attaching it with new edge. Re- peated applications of this outward expansion grow a tree of interdependent entities and constraints, which captures the layered structure required for hierarchical reasoning.
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In essence, the diffusion stage operationalizes the idea of "spreading out" from concept into its surrounding context, systematically expanding to related entities and relationships. This outward growth not only diversifies the search space but also organizes it into structured exploration tree, ensuring that the resulting problem instances are both rich in content and faithful to the hierarchical nature of deep research. By doing so, the diffusion stage establishes well-grounded exploration space that serves as the essential foundation for the retrospection stage.
Retrospection Stage: From Research Tree to HCSP. The retrospection stage operationalizes the idea of "looking back" from the exploration tree to reconstruct question that enforces hierarchi- cal reasoning. While diffusion expands outward contracts inward by traversing the tree in reverse, turning structural dependencies and layered con- straints into a question. Each vertex of the tree associated with a question whose answer is derived from both its immediate constraints and the sub-questions induced by its descendants.
generate entities and relations, retrospection
Formally, the process can be described recursively:
Q(C,), Q. QCC. U (Q(w)) wy E internal children of v)), otherwise.
if all children of v are leaves,
where C₁ denotes the set of constraints converted from edges to leaf children of v, Q(-) is the recursive function that turns
of constraints or sub-questions into natural-language question. The first case reduces to standard CSP, while the second composes constraints with recursively defined sub-questions. Finally, for research tree T with root r, the retrospection stage produces the HCSP instance Q(r), which integrates all constraints and sub-questions across the hierarchy. In essence, retrospection transforms the exploration tree into coherent HCSP, ensuring that each synthesized question demands multi-layered reasoning and admits a unique, verifiable answer.
2.3 METHODOLOGG
Diffusion Stage. the diffusion stage, a research tree T = (V, E) is expanded outward from a seed entity At each step, the system applies one of two operations, designed to capture the breadth and depth of hierarchical dependencies.
Blurring Parent Node. Suppose vertex E V currently has only single child its constraints are insufficient to uniquely identify v. In this case, we select distinct claims {ci,..., cx from v's source page such that the corresponding candidate sets S(c,) are non-empty and incomparable:
S(c)) & S(c;), J
Each claim induces a child vertex wA with corresponding edge (u, wi). yielding an updated tree:
T = (V (wi...., wx), [(w, wi), (v, wx))).
This "blurring" process enforces that e is the unique result, and can only be resolved when all constraints from its children are jointly satisfied, thereby increasing both difficulty and verifiability.
Expanding Depth. To model deeper logical dependencies, we allow any vertex v E V with an entity to grow new child. Given relation r(c, w) extracted from v's document (e.g.. "v was discovered by w"), we attach a fresh node w & V as the child of o and update the tree as:
T = (V U (w), E U w)))
(8)
This operation lengthens the reasoning chain and ensures that solving the eventual HCSP requires multi-step logical inference.
Retrospection Stage. Once diffusion produces a tree rich in breadth and depth, retrospection tra- verses in reverse synthesize a hierarchical constraint satisfaction problem. For node v, let its leaf children [Wi...., wa} generate constraints C. {a..... ) and its internal children (wk+1,..... wr} generate sub-questions (Q(#k+1), Q(w,)), The question is then:
q. Q(C, U (Q(w,) | k I,...,n))..
At the root r, retrospection outputs the HCSP instance = Q(r), which integrates all constraints and sub-questions across the tree. The blurring steps guarantee sufficient parallel constraints, while depth expansions enforce sequential dependencies, together yielding HCSP questions that require layered reasoning and admit unique, verifiable answer.
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Table 2: Dataset statisties by reasoning vertex number, including QA pairs count, curation costs,
and average token lengths for questions and answers.
Vertices
Count
Cost ($)
Question Len (tok)
Answer Len (tok)
3,841
43.9
31.97
6.17
15,263
142.8
43.38
5.91
15,051
160.4
54.35
5.75
17,714
214.4
65.52
5.64
27
269
10.3
81.59
5.23
Total
52138
571.8
53.43
5.79
2.4
DATA QUALITY ASSURANCE
While the tree-based construction of HCSP provides a systematic framework, also introduces potential quality issues. Underdeterminatiion may occur when combining multiple constraints still leaves the answer set non-unique, creating ambiguity the solution space. Conversely, overdeter- mination arises when single constraint (or small subset) already suffices identify the unique answer, leading to premature convergence and weakening the role of hierarchical reasoning. Both phenomena compromise the intended multi-level structure HCSP, posing challenges for synthesiz- ing high-quality data. To mitigate these issues, we design two- wro-pronged quality assurance protocol.
Difficulty. We ensure that problems are sufficiently challenging and cannot be trivially solved by relying on a language model's parametric memory. Concretely, we tested Qwen2.5-32B (Group) 2025) the dataset without any retrieval context. The model achieved only 2% accuracy, firming the high difficulty of our questions. Those correctly answered samples were removed to further strengthen the dataset's challenge level.
Verifiability. We further require that every question be factually grounded. unambiguous, and solvable via the generated search trajectory. To validate this, we provide Gemini 2.5 Flash (Comanici et al. (025) API with the ground-trute supporting web pages mixed with distractor documents. The model is tasked with deriving the correct answer from this context. We filter out questions for which the model returns an incorrect answer, multiple possible answers, or no solution. This step effectively prevents underdetermined cases and ensures that each retained question admits unique, verifiable solution. Together, these quality control measures preserve the richness of hierarchical reasoning while ensuring that InfoSeek yields more reliable and effective training dataset.
Statistics: As shown Table leveraging DeepSeek-V? (Liu et al. 2024) as the operation model, constructed InfoSeek dataset comprises more than 50K samples, with the total data curation cost as $571.8, provided for reproducibility. The majority of problems fall within the 4-6 vertex range. Question length increases steadily with vertex count, from average of 31.97 tokens at vertices to 81.59 tokens at 27 vertices. While answer length remains relatively stable at around 5-6 tokens, ensuring all the questions are leading a concise and verifiable answer.
We present the full data synthesis process using InfoSeek in Algorithm
2.5 MODEL OPTIMIZATION ON INFOSEEK
To validate the effectiveness of InfoSeek, we explore multiple optimization strategies, showing that the dataset provides reliable foundation for various optimization settings.
Foundation: Parallel Querying and Evidence Refinement. Following recent advances in search-augmented reasoning (Jin et al., 2025) Chen et al., (025aa,, we design rollout template with special tokens to standardize the solution generation process. Each reasoning step begins with <think>... ... </think>, where the model reflects on gathered evidence and identifies missing in- formation. It then generates multiple, diverse queries enclosed in <search> <..e....r///eiii allowing parallel exploration that broadens coverage and accelerates discovery compared to se- quential, single-query search. Retrieved documents not directly injected; instead, they

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processed by lightweight refiner (Qwen2.5-7B-In's which extracts salient evidence and pro- duces a concise summary aligned with the query intent. The refined evidence, encapsulated within <information>... ... </ iinformattt tin>, is paired with the original queries and appended to the context. Once sufficient information has been accumulated, the model generates its final response within <answer> ... </answer>. This workflow not only enforces consistency in reasoning traces but also reduces noise from raw retrieval results.
Supervised Fine-tuning (SFT) via Rejection Sampling. Training deep research agents directly with reinforcement learning often unstable due to sparse rewards and the combinatorial nature of reasoning and search. To obtain a reliable starting point, we adopt rejection sampling to curate a high-quality dataset of executable reasoning trajectories. Specifically, teacher model (Qwen2.5- 72B) attempt tasks from the InfoSeek dataset using the workflow described above. Only trajectories that complete the task successfully and yield a demonstrably correct final answer are retained. To further ensure robustness, we use Gemini 2.5 Flash to check whether a trajectory exploits shortcuts in search or reasoning, filtering out such cases. This process yields a supervised dataset consisting exclusively of verified trajectories, allowing the model to learn effective planning, querying, and verification strategies through SFT, and serve as a good starting point for follow-up training.
Reinforcement Learning with GRPO. Starting from the SFT-trained checkpoint, we further ap- ply reinforcement learning to strengthen the model's reasoning and query formulation abilities. We employ Group Relative Policy Optimization (GRPO) (Shao et al.] 2024), which provides stable up- dates in group-based comparisons. Since the SFT phase already equips the model with a reasonable capability to solve deep research tasks in the desired format, we adopt simple binary reward: R if both the output format and the extracted answer are correct, and It 0 otherwise. This straightforward reward design leverages InfoSeek's verifiable structure, while RL fine-tuning re- inforces precision and robustness in reasoning and search. Together, these steps demonstrate that InfoSeek enables consistent optimization across different training paradigms and produces models with stronger capabilities for complex information-seekicn
3 EXPERIMENT
3.1 SETTINGS
Datasets: We evaluate on single-hop benchmarks: Natural Questions (NQ) (wiiakowski et al.,
2019). TriviaQA (TQA) (Joshi et al. 2017). PopQA (Mallen et al., 2022); and multi-hop bench-
marks: HotpotQA (HQA) Yangg et al. 2018), 2WikiMulihhoOAA (2Wiki) (Ho et al. 22020), Musique
(MSQ) (Trivedi et al., 20226), and Bamboogle (Bamb) (Press et al. 2022). Exact Match (EM) is used as the evaluation metric. For advanced deep research, we further use the complex BrowseC- omp (Wei et al. 2025) benchmark, with 830 filtered problems and the fixed 100K webpage corpus from BrowseComp-Plut (Chen et al. 2025b). following the official accuracy judgment with LLMs.
Baselines: We compare against representative RAG and agentic search methods: (1) Vanilla RAG
(one-shot top-k retrieval); (2) IRCoT (Trivedi et al.) 2022a) (retrieval with chain-of-thought): (3)
RQRAG (Chan et al.) 2024) (query rewriting and decomposition): (4) Self-RAG (Asai et al.) 2023)
(self-reflection with evidence); (5) Search-ol (Li et al. 2025b) (reasoning with search tool): (6)
Search-R1 (Jin et al., 2025) (RI. with multi-round reasoning ; (7) ZeroSearch (Sun et al., (025a) (LLMM generates "search results" directly);
(8) AutoRefine (Shi al., (025b) (special refine
loken for summaries); (9) InForage (Qian & Liu 2025) (SFT+RL with synthetic rewards).
3.2 MAIN RESULTS
In Table we present the results on classic knowledge-intensive QA benchmarks covering both single-hop and multi-hop settings, while in Table 4 we show the performance on the more challenging BrowseComp-Pins benchmark that emphasizes open-ended, search-intensive reasoning. From these experiments, we draw several crucial findings: (1) On classic QA un-
benchmarks, model trained on InfoSeck consistently outperform most baselines der basic optimization strategies such as SFT and lightweight RL. This validates the effec- tiveness of InfoSeek high-quality supervision source, demonstrating that structured, hier-
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Table 3: Performance comparison classic showledge-intensiin single-hop and multi-hop bench- marks. The best-performing results are highlighted in bold.
Single-Hop
Multi-Hop
Group
Model
Avg.
NQ
TQA
PopQA
HQA
2W
MSQ
Bamb
RAG
34.8
54.4
38.7
25.5
22.6
4.7
8.0
27.0
IRCoT
11.1
31.2
20.0
16.4
17.1
6.7
8.0
15.8
RAG-based
RQRAG
32.6
52.5
39.4
28.5
30.7
10.1
12.9
29.5
Self-RAG
36.4
38.2
23.2
15.7
11.3
3.9
5.6
19.2
Search-ol-3B
23.8
48.2
26.2
22.1
21.8
5.4
32.0
25.6
Scarch-R R13B
40.8
59.1
42.8
30.8
31.1
8.4
13.0
32.3
Agentic Search
ZeroSearch-3B
41.2
61.5
44.0
31.2
33.2
12.6
14.3
34.0
AutoRefine-3B
43.6
59.7
44.7
40.4
38.0
16.9
33.6
39.6
InForage-3B
42.1
59.7
45.2
40.9
42.8
17.2
36.0
40.6
InfoSeeker
InfoSecker-3B
41.7
56.1
46.5
44.6
50.0
20.5
39.2
42.7
archically constructed data can substitute for large-scale in-domain annotations and still gen- eralize robustly to standard QA tasks. (2) Compared the traditional RAG based methods that merely prepend retrieved passages, the agentic search approaches achieve stronger overall results, confirming the paradigm's effectiveness in integrating iterative reasoning and retrieval. Notably, InfoSeeker, despite relying only on straightforward training protocols, outperforms many carefully engineered agentic baselines with sophisticated optimization, underscoring that the quality and structure of the train- ing data can be as critical as model architec- ture training tricks. (3) On BrowseComp- Plus, InfoSeeker-3B reaches 15.3% accuracy, surpassing several closed-source systems (e.g., GPT-4.1, Sonnet 4) and vastly outperform- ing open-source baselines such as Qwen3-32B and SearchR1-32B. Considering that InfoS- eeker contains only 3B parameters, this result highlights the efficiency of our pipeline in dis- tilling deep research capabilities into compact LLMs, enabling them to tackle highly challenging, search-heavy problems at scale.
Table 4: Performance on the BrowseComp-Plnn benchmark, which assesses complex reasoning.
Model
Retriever
Acc.
Calls
Gemini 2.5 Flash
BM25
15.5
10.56
Gemini 2.5 Pro
BM25
19.0
7.44
Sonnet 4
BM25
14.3
9.95
GPT-4.1
BM25
14.6
11.22
GPT-5
BM25
55.9
23.23
Qwen3-32B
BM25
3.5
SearchR 1-32B
BM25
3.9
1.78
WebSailor-3B
BM25
4.3
5.41
InfoSecker-3B
BM25
15.3
3.3 DISCUSSION
Ablation analysis. Figure (a) presents ablation study under different optimization settings, from which we derive several key observations. (1) Models optimized with InfoSeek exhibit con- sistent and significant improvements across all benchmarks, validating the effectiveness of InfoSeek as a training resource for strengthening agentic search methods.
(2) Leveraging InfoSeek's 's SFT dataset for supervised fine-tuning yields clear gains over direct RAG baselines. This demonstrates that our SFT stage provides a strong initialization for subsequent RL training. mitigating the cold- start problem and stabilizing optimization. (3) When scaling to a larger model (InfoSeeker-7B) further performance improvements are observed, confirming the scalability of InfoSeek and its abil- ity to generalize across different model sizes.
Impact on Dataset Complexity and Scale. We argue that both the depth of search encoded in the training data and the overall dataset scale play crucial roles in shaping optimization performance. Figure b) and Figure ([(c) present the breakdown of results under varying levels complexity and scale. Specifically, when trained only on NQ and HotpotQA, the model shows little incentive to develop a true "deep search" ability: : achieves an uncompetitive performance on the BrowseComp- Plus benchmark, with limited average number of search calls. In contrast, training with InfoSeek induces progressively deeper search behaviors as more complex examples are introduced. Even using subsets restricted to fewer than five vertices yields gains in both accuracy and search calls.
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(a) Ablation Analysis Classic Knowledge-Intenet Intensive Benchmarks.
Vanilla
RAG
SFT
InfoSecker-3B
InfoSecker-7B
68
34
0
TQA
NQ
PopQA
HotpotQA
2Wiki
Bamboogle
Musique
Avg.
Acc
Calls
Acc
Calls
Failure Rate
95
8
90
NQ+HQA
<55 vertices
Full
1K
5K
18K
3
4
7+
(h) Impact on Dataset Complexity.
(c) Impact on Datasct Scale.
(d) Analysis on Dataset Complexity.
Figure 2: Overall analysis across different aspects. (a) Ablation on classic knowledge-intensive
tasks. (b) Impact of dataset complexity on BrowseComp-Plus. comparing models trained with only NQ+HQA, InfoSeek restricted fewer than five vertices, and the full InfoSeek dataset. (c) Effect of varying dataset scale for training.
(d) Data contamination analysis, where strong model directly attempts tasks, with error rates reported across samples containing different numbers vertices.
With the full InfoSeek dataset, the model achieves performance comparable to several commercial LLMs, underscoring the importance of complexity in data design. Moreover, Figure (c) shows that model performance improves as the dataset size increases, confirming the strong effect of scale. Since InfoSeek is inherently scalable, enabling the construction of more complex and larger datasets, highlights promising path for incentivizing L.MS to acquire robust agentic search capabilities.
Analysis on Dataset Complexity. To examine the intrinsic difficulty of our dataset, we evaluate the failure rate of strong baseline, Qwen2.5-72B (Group) 2025), prompted with Mlain-of-thought reasoning (Wei et al. 2022). Following prior work (Wei al. 2025), such failure rate could serve as reliable proxy for deep research difficulty. As shown in Fig. (d), the results indicate a high overall failure rate 91.6% demonstrating that our dataset remains challenging even for large models with stronger capability. Importantly, the failure rate grows with structural complexity, rising from 88. % on 3-vertex problems to 94.1 on problems with 2 vertices, confirming that our synthesis pipeline effectively scales reasoning difficulty with the number of vertices.
These findings highlight two desirable properties InfoSeck. First, the combination of hierarchi- cal constraints and real-world webpages ensures that the data cannot be trivially solved by memo- rization, thereby avoiding contamination from static parametric knowledge L.Mss. Second, the observed correlation between vertex count and failure rate validates that our construction procedure provides fine-grained control over problem complexity.
4 RELATED WORK
Agents for Reasoning and Search. A major line of work trains L.LM agents to interleave reason- ing with retrieval. RL-based methods (Song et al.) (202aa] Chen et 2025a Jin et 2025 lever- age RL to improve multi-turn search but training is computationally expensive and time- time-consuming. While (Song et al. 20256 Mei al. 2025) adding an SFT stage before RL enhances stability, they still relies on shallow datasets such as NQ (Kwiatkowski et al. 2019) and HotpotQA (Yang et al.) 2018). As result, models remain limited when tackling problems beyond a few reasoning turns.
Other approaches introduce auxiliary tokens to summarize evidence (Shi et al., 2025b Zhao et al. 2025
but context length limits continue to hinder performance on harder tasks.
Data Synthesis for Complex QA. To cultivate stronger reasoning skills, recent work has explored
synthetic QA data from web pages or navigation tasks (Wu et al. 22225;; | Shi et al., (225a /Wu et al. 2025al (un et al. 2025b). These efforts show improvement in results but largely remain at the

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multi-hop level, falling short of Deep Research complexity. WebSailor (Li al. 2025a synthesizes high-uncertainty web navigation tasks to train specialized agents, and WebShaper (Tao et al. 2025) adopts formalization-driven approach where reasoning graph is defined before the corresponding question is generated. Those works shows eminent results of training on their synthesized data with high quality and complexity. While both of them publicly release their trained models and infer- ence code, the detailed data-construction pipelines are not public, and only small example datasets available. With this backdrop, InfoSeek offers the first open-source framework for synthesiz- ing hierarchical constraint satisfaction problems with controllable complexity, together with large scale open-sourced QA dataset, thereby enabling scalable training for complex information-seekiin agents.
5 CONCLUSION
In this work, we introduced InfoSeek, framework for synthesizing structurally complex and real- istic data for agentic search by formalizing information-seeking as Hierarchical Constraint Satisfac- tion Problems (HCSPs). Through wnffusionnRRerospeene like QA pairs with explicitly controllable structural complexity, instantiated on large-scale web and Wikipedia corpora to produce over 50k QA pairs and 16.5k reasoning trajectories, together with fully open-source pipeline. Experiments with both supervised fine-tuning and reinforcement learn- ing demonstrate consistent and substantial improvements utility and robustness of our synthesized data. Additional analyses on ablation, complexity, and scale further validate its stability, generality, and scalability across diverse tasks. Overall, InfoSeek establishes a principled foundation for complex information-seeking research and delivers the first publicly available, large-scale open resource of its kind, offering the community a reproducible and extensible platform for ad advancing next-generation agentic search systems.
process, InfoSeek generates research-
strong baselines, underscoring the
ACKNOWLEDGEMENT
This work was supported by National Natural Science Foundation of China No. 62502049.
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ETHICS STATEMENT
This work focuses on curating task-specific datasets using two primary sources: the Wikipedia cor- pus and web pages that are publicly available without registration payment. While we strive to ensure quality, such data may inevitably contain information bias. To mitigate this, we prioritize content from authoritative sources, such official news websites, though residual bias is unavoid- able. We also note that employing Wikipedia and open web pages for dataset construction is widely adopted and accepted practice in the development and optimization of large language models.
With respect to copyright, Wikipedia content is released under open licenses, and for major web sources (e.g., news websites) we have inspected their terms of use and ensured compliance. How- ever, it is infeasible to exhaustively review all potential licenses. To further comply with ethical standards, we retain the ability to modify, delete, or recover specific data samples any copyright violations, privacy concerns, biases are detected, reported, or formally requested.
REPRODUCIBILITY STATEMENT
The source code, prompts, and constructed datasets in this paper are available at this anonymous repositor) Benchmarks, hyperparameters, and optimization settings are documented the main paper and Appendix. Our model training and evaluation experiments were conducted 8 8xH100 GPUs, while data production can be ran on CPU only machines.
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A THE USE OF LLMs
The authors of this paper used large language models (LLMs) solely writing assistant for check- ing and refining spelling, grammar, and phrasing. All core ideas and research content were devel- oped by the authors, and LLMs did not contribute the academic analysis substantive writing.
B APPENDIX
B.1 IMPLEMENTATION DETAILS
In this section, we introduce the detailed training pipeline and implementation details of InfoS- eeker. Training deep research agents is non-trivial, partieularly for small scale LLMs. The key challenges lie in the scarcity of high-quality, complex data, and the lack of a clear, reproducible training pipeline. To address this, we construct the InfoSeek-50K dataset and design a two-stage training pipeline, enabling us to train a 3B LLM (Qwen2.5-3B-Ins)) (Group 2025) that approaches the performance of proprietary models.
Since small L.Mss are inherently weaker, we begin with knowledge distillation from larger teacher model. Specifically, we distill trajectories from Qwen2.5-72B-Ins. (Group 2025) executing re- search workflows, which are then used for SFT of Qwen2.5-3B-Inst (Group 2025). Concretely, we utilize 50K InfoSeek samples (For training advanced agentic search capability) and 5K NQ & HQA samples (For preserving general multi-hop QA capability), each rolled out twice. After filter- ing incorrect executions, we obtain 24K valid trajectories, implying that the teacher model achieves 21.8% accuracy under our carefully designed workflow. Importantly, we deliberately retain "short- cut" cases among the correct trajectories, as preserving diverse solution strategies offers valuable learning signals for small LLMs during the early stages of training. Figure 3 provide statistics for the constructed SFT Trajectory data from Research Tree data.
Following distillation, we use the filtered 24K trajectories to fine-tune Qwen2.5-3B-Ins. model for 2 epochs, with a learning rate of le-5, weight decay of 0.01, and a context length of 16,384. In addition, adopt the public Search-R1 training pipeline, the first fully open-source RL framework for agentic search, which allows us to enforce consistent data processing, sampling strategy, and optimization procedures across all models. Training single 8x H100 node completes in 2 hours, yielding InfoSeeker-3B-. 3B-ST. Take it as the starting point, we then perform reinforcement learning using GRPO on selected 18k InfoSeck subset. Training conducted with batch size of 256, maximum of 10 turns, rollout size of 5, temperature 0.8, and search engine restricted to the top-5 retrieved contents.
B.2 EVALUATION DETAILS
For both single-hop and multi-hop QA tasks (NQ, TQA, PopQA, HQA, 2Wiki, MSQ, and Bamb), we employ Wikipedia-25 as the corpus. segmented into chunks of 512 tokens. Document re- trieval is performed using BGE-M3 (Chen et al. 2023). with the top-5 documents selected. For the BrowseComp-Pile
benchmark, we utilize the T0OK web page corpus provided by the official release (Chen et al. 2025b). with BM25 (Robertson al. 2009) serving as the retrieval method. We control the same RL configuration for all RL trained baselines: GRPO as the optimization algorithm, with identical rollout size (5), maximum conversation length (10 turns), sampling temperature (0.8), and a shared search environment as described above. Training schedules, stopping criteria, and trajectory truncation rules are matched across models to eliminate confounding factors and ensure that any performance differences arise purely from data quality and algorithmic choice, not training discrepancies.
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Algorithm 1: InfoSeek: Diffusion- DiffusioonRRtrospeciion Synthesis
Input: Knowledge base K. (filtered Web & Wikipedia), nodes N, max depth D
Output: Research tree T = (V, and HCSP question q
Diffusion (Outward Expansion):;
Sample seed entity K; set V < (r), (r), Ø, depth(()) 0.;
while |V| < N and maX.gv depth(e) <
Select a vertex v to expand (e.g.. highest uncertainty or (egree-1).;
if underconstrained at (e.g. single child or weak constraints) then // Blur Parent Node Extract l distinet claims (ci....,ck] from page(u) s.t. S(ci) # @ and S(c,) S(cs)) = Ø for
+ j-i
For each ci, create child wx & V and add (v, wx) to E; set depth(ws)) + depth(u).;
else
// Expand Depth
Sample relation r(v, w) from page(v) that induces dependency; create w & V and add edge (v, w) to E; set depth(w) + depth(v) +1;
Set T (V,
Retrospection (Backward Composition to HCSP);
Function Compose (E)
Let leaf children of be {wi....,
.......,,,, we with edges (u, w)) and convert them constraints
C. .c...... Ck
Let internal children be (u.41...., J.
if n = then return (CC,)
// CSP at m3
else return (Cv U {Compose(u;) j k ,I..,.,,,
Set Crmpose(r):;
Quality Controls (Optional Filtering):
if parametric-only LM correctly answers then discard (T, if retrieval LM fails ground-truth pages mixed with distractors then discard (T, .)) // enforce veri E Fiability:
// enforce difficulty:
return T.q
B.3
CASE STUDY AND FURTHER STATISTICS
Case Domonstration Figure illustrates an example of 5-vertices question from InfoSeek dataset. The root "Calothamnus quadrifidus subsp. obtusus" contains two leaf children, leading to two corre- sponding constraints, and one internal children "Alex George", forming a sub-question with another constraint. While figure 5 demonstrates the tree-layer structure of 6-vertices question. Solving needs to figure out the director "Joseph Kane" from two constraints, then infer toward the root vertex "Git Along Little Dogies" with other constraints. These examples with layered representation highlights how InfoSeck encodes multi-hop reasoning across interconnected entities and facts.
Success Case Study To better illustrate the rollout process, we present a case study from BrowseComp benchmark. Table 5 shows the question and key rollout steps. The question seeks a fungal species matching multiple parallel constraints, including its description in the 1780s, five unaccepted synonyms, edibility in certain Asian countries, specific chemical profiles, and DNA- based classification distancing it from superficially similar species. In the first round, the model decomposes the query into three searches targeting subsets of clues (description/synonymss edibil- ity/chemistry, and specific compounds). This yields Spondylus Linnaeus" as a partial match for synonyms but fails edibility, chemistry, and fungal traits, highlighting the need for holistic in- tegration. In the second round, the model refines searches by combining overlooked constraints, converging on Coprinus comatus". final thinking step synthesizes the evidence, confirming the 1780 description, synonyms, Asian edibility, exact chemical match, and taxonomic notes, and out- put the answer. This question's 's underlying structure aligns with our defined HCSP structure, and solving it correctly highlights the effectiveness of training on the InfoSeek dataset.
In order to better understand the deficiency of our constructed dataset and InfoSeeker which trained on it, we manually analyzed sampled set of error trajectories from the
Failure Case Study
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Statistics of Rejection Sampling Trajectory Data (Filtered)
A: Distribution of Total Token Lengths
B: Distribution of Reasoning Steps (<think> counts)
350
Mean: 1376
2000
1750
250
frequency
200
Count
1250
1000
750
50
250
Teken Longth
Number of <think> Tags
C: Distribution of <search> Tool Calls
D: Distribution of Final Answer Token Lengths
2000
Mean: 5.0
1750
700
1500
Court
frequency
500
1000
400
500
200
2.5
5.0
7.5
10.0
12.5
15.0
17.5
Number <search>> Calls
Token Length <answer> Content
Figure 3: Statistics for SFT trajectory data.
BrowseComp-Plus evaluation set. Through careful error attribution, we identified three major cate- gories failure modes:
Reasoning errors (23.1%) the agent's 's exploration direction becomes biased early in the rea- soning process, causing subsequent steps to accumulate little no meaningful information gain. The example in Table illustrates this issue. The question asks for the name of the thesis author and provides only direct clue: the author shares last name with nobleman who served in a powerful European kingdom. Additional clues concern the author's university and supervisor. The correct reasoning path should involve identifying potential noblemen, universities founded in the mid-20th century, authors of theses on nanotechnology. and supervisors matching the given constraints. However, after the first round of search, the model incorrectly assumes that the Uni- versity of Seinburrgh-fuuddee in the 16th century, not the 20th-is the relevant institution. This initial mistake sends the model down an incorrect reasoning path, ultimately leading failure.
Incomplete reasoning (30.8%) the agent produces an answer before fully exploring all con- straints implied by the HCSP structure. An example is provided in Table 7 According to the question, the first layer contains six distinct constraints. The model must answer all three sub- questions in order to obtain the correct final answer. However, shown in the trajectory, the model divides the problem into four sub-questions, grouping the first three constraints into a sin- gle, overly broad sub-query. This vague query leads to unilateral evidence from the retriever, which cannot simultaneously satisfy all three constraints. As a result, the model produces a com- pletely incorrect final answer.
Retrieval errors (46.2%) the retrieved evidence does not contain the required information. In Table 88, the question asks for the name food shop and provides clues related to locations in both Mexico and California. Although the model attempts multiple queries, useful information
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Question: "What subspecies flowering plant that formally described botanist cco collaborated with Celia Rosser on 'The Banksias' project, has Linear, rough and scaly leaves with relatively short stamen bundles, and was originally described George Bentham in 1867?"
"root":
"id":: "A",
"entity": "Calotharnus quadrifidus subsp. obtusus",
"clains": [
("target_id"; "8", "clain": "A was formally described by B in 2810"),
("target_id" id"; "C", "clain": "A has linear, rough and scaly leaves with relatively short stanen bundles"),
("target_id") id"; "D", "clain": "A originally described by George Benthan in 1867")
1, "children":
"id": "B", "entity"; "Alex George", "clains";
("target_id"; "E", "claim"; "B collaborated with Celia Rosser 'The Banksias' project")
}, "children": [ "id"; "E", "entity": "Celia Rosser", "claims": [J, "children":
"id": "C", "entity"; "None", "clains": [], "children":
"id": "D", "entity": "None", "clains": [). "children":
Figure 4: Example of 5-vertices question in InfoSeek
is returned by the search engine. For example, the detail "7.8 km from McDonald's in Polanco" is not helpful for text-based retriever, though it could be informative if a map-based search were available.
B.4 DATASET LICENSE
The code and data accompanying this work released under the Apache License, Version 2.0. This permits use, modification, and distribution for research and commercial purposes, provided that proper attribution is given and the terms of the license are followed.
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Question: "What is Western film directed by who also directed John Wayne in nuttiple films and who directed many novies starring Roy Rogers? Additionally, this film known 'Serenade the West' in the United Kingdom and was written by Dorrell and Stuart E, McGowan."
"root":
"id": "A",
"entity": "Git Alang Little Dogies (film)",
"question":
"clains":
("target id"; "B", "clain": "A was directed by B"),
("target_id": "D", "clain": "A is known as 'Serenade the West' the UK"), "ttarge_id"; "F", "clain": "A was written by Dorretl and Stuart E. McGowan")
}, "chitdren":
"id"; "B", "entity": "Joseph Kane", "clains"; ""ttarget_id": "C", "claim": "B directed C in multiple filns"), ("target_id"; "E", "claim": directed multiple films starring E")
1, "children";
("id": "c", "entity": "John wayne", "clains": [], "children": (]),
("id": "g", "entity"; "Roy Rogers", "clains": [], "children": []]
"id": "D", "entity": "None", "clains": [], "children":
"id": "F" "entity": "None", "clains": [), "children":
}
Figure Example a 6-vertices question in InfoSeek
18

---

Published as a conference paper at ICLR 2026
Table 5: Successful Case study on a BrowseComp sample. Only the key contents are preserved.
Question: A species described and named for the first time in the 1780s by naturalist who delved into other areas of study. The species has, up December 2023, five unaccepted synonyms, including its original name. DNA studies confirm that the species isn't closely related to some species that share the same particular trait, as other characteristics are better for its classification. It's categorized as edible in certain Asian countries. Among its chemical characteristies, this species has flavanols and bioflavonoids (mainly Epicatechin, Catechin, and Amentoflavone) in range of concentrations of 0.330 mg/100g d.w 0.490 mg/100g d.w. What's the name the species? Ground Truth Answer:
Coprinus comatus
<think> To identify the species, need to find a species that was described in the 1780s, has five unac- cepted synonyms, and is edible in certain Asian countries. Additionally, it has specific chemical character- istics of flavanols and bioflavonoids. including Epicatechin, Catechin, and Amentoflavone. </think> <search> 1. Species described in 1780s with five unaccepted synonyms. 2. Edible species in Asian countries with flavanols and bioflavonoids. 3. Species with Epicatechin, Catechin, and Amentoflavone in Asian countries. </ </search>
iinformations
[Current Query]: Species described in 1780s with five unaccepted synonyms.
Species Spondylus Linnaeus, 1758 has a significant number of unaccepted synonyms... [SNIPPET]
[Current Query]:
Edible species in Asian countries with flavanols and bioflavonoids.
The documents provide information on the consumption of edible species in Asian countries, particularly focusing on jellyfish and insects
The documents do not provide specific information about a species with flavanols and bioflavonoids
Asian countries, but they do provide context on the consumption of edible species in the region.
[SNIPPET]
[Current Query]: Species with Epicatechin, Catechin, and Amentoflavone in Asian countries.
The documents provide information on the presence of various bioactive compounds in different species ... Further investigation may be needed to identify the specific species in question. </informat ion>
<think> Based the information provided, the species Spondylus Linnacus, 1758, has significant number of unaccepted synonyms and is described the 1780s. However, the information about the species being edible in certain Asian countries and having specific chemical characteristics of flavanols and bioflavonoids is not directly linked to Spondylus. I need to search for species that fits all the criteria.
</think>
<search> 1. Species deseribed in 1780s with five unaccepted synonyms and edible in Asian countries 2. Edible species Asian countries with flavanols and bioflavonoids and described 1780s 3. Species with Epicatechin, Catechin, and Amentoflavone in Asian countries and described in 1780s </ search>
<informat montiio>> ion>
[Current Queryl: Species described in 1 1780s with five unaccepted synonyms and edible in Asian countries. Coprinus comatus, also known as shaggy mane, chicken drumstick mushroom, or lawyer's wig, was first named Agaricus comatus by Otto Friedrich Müller in 1780. Christiaan Hendrik Persoon later changed the name to Coprinus comatus in 1797. This species is edible in Asian countries and is often culti- vated for consumption this species has flavanols and bioflavonoids (mainly Epicatechin, Catechin, and Amentoflavone) in range of concentrations of 0.330 mg/100g d.w to 0.490 mg/100g d.w. The species has five unaccepted synonyms, including its original name.
[SNIPPET]
[Current Query]: Edible species in Asian countries with flavanols and bioflavonoids and described in 1780s.
Coprinus comatus, also known as shaggy mane, chicken drumstick mushroom, or lawyer's wig, is species of mushroom...
[SNIPPET]
[Current Query]: Species with Epicatechin, Catechin, and Amentoflavone in Asian countries and described in 1780s.
The species in question is categorized as edible in certain Asian countries and has been described and named for the first time in the 1780s...
</informat ion>
<think> Based on the information provided, the species that fits all the criteria is Coprinus comatus, also known as shaggy mane, chicken drumstick mushroom, lawyer's wig. It was first named Agaricus co- matus by Otto Friedrich Müller 780 and later transferred to the Coprinus genus by Christiaan Hendrik Persoon in 1797... It is categorized as edible in certain Asian countries and has specific chemical charac- teristics of flavanols and bioflavonoids, including Epicatechin, Catechin, and Amentoflavone. </think> <answer> Coprinus comatus </answer>
19

---

Published as a conference paper at ICLR 2026
Table 6: Failure Case study of reasoning error.
Question: This thesis which focuses on nanotechnology. was presented by an author who shares the same last name a nobleman who served in the military in once-powerful kingdom in Europe. It was submitted in the early 21st century academic work finds the progressive process of engineering to very powerful according to an article published in the 21st century at the same university of the author. Can you provide the full name of the author of this thesis?
university founded in the mid-20th century. The main supervisor of this
Ground Truth Answer: Martyna Laszez
<think>
name of the author, I need to identify author's last name, which shared with a nobleman who served in powerful European kingdom. The thesis was presented in the early 21st century and submitted to university founded in the mid-20th century. The supervisor of the thesis found the progressive process of engineering to be very powerful, which might be key detail to identify the author. </think>
find
<search>
1. nobleman who served in powerful European kingdom and shares last name with nanotechnology author
2. university founded in the mid-20th century and nanotechnology thesis submitted in early 2 2 century
3. supervisor of a nanotechnology thesis university founded in the mid-20th century and found engi- necring progress powerful
</search>
<information>.. s/informations
<think>
The information provided does not directly identify the author of the thesis. The key details are the univer- sity (University of Edinburgh) and the supervisor's statement about the progressive process of engineering. need to search for the specific author of the nanotechnology thesis at the University of Edinburgh in the early 21st century.
</think>
<search>
1. nanotechnology thesis University of Edinburgh early 21st century
2. author nanotechnology thesis at University of Edinburgh early s1 century
3. University of Edinburgh nanotechnology thesis supervisor found engineering progress powerful </ search>
<informati on> formati on> <think>
I need to refine the search to find the specific author of the nanotechnology thesis the University of Ed- inburgh in the early 21 century. The supervisor's statement about the progressive process of engincering might he a key detail to identify the author. will try to search for the author's name directly, focusing on the university and the supervisor's 's statement.
</think>
<search>>
1. author of nanotechnology thesis at University of Edinburgh in early 21st century and supervisor found engineering progress powerful
2. University of Edinburgh nanotechnology thesis author carly 21 century
3. nanotechnology thesis at University of Edinburgh early 2 2 century and supervisor statement on engi-
neering progress
</search>
<information>.. </information>
<think>
The information provided does dircetly identify the author of the thesis. The supervisor's statement about the progressive process of engineering key detail, but it does not provide a specific name. need to search for the author's 's name directly, focusing on the university and the supervisor's 's statement. I will try to search for the author's 's name using the supervisor's statement and the university's 's name again.
</think>
(The wrong direction made the model kept trying until reaching round limit)
20

---

Published as a conference paper at ICLR 2026
Table Failure Case study of incomplete reasoning.
Question: Can you name the movie based the following details? This movie released between 2005 and 2020 (exclusive at the endpoints). One of the actors plays the role of fun-filled and carefree character in the movie. One had guys in several scenes and protects the protagonist in one scene. According to a film review blog between 2011 and 2016 (exclusive at the endpoints), one of the characters delivers excellent comic timing in her role ditzy uranslator. The director of this film born between 1970 and 1980 (exclusive at the endpoints). One of the actors this movie made their film debut before 1999 (exclusive at the endpoints).
characters has very few dialogues the film hut takes down the
Ground Truth Answer: Singh Is Bliing
<think>
To find the movie based on the given details, I need to identify the movie that matches all the provided criteria. will start by searching for a movie released between 2005 2020, with character who plays fun-filled and carefree role, and another character who takes down bad guys and protects the protagonist. will also look for character with excellent comic timing and director born between 1970 and 1980, and actor who made their debut before 1999.
</think>
<search>
1. Movie released between 2005 and 2020 with filledeeed character and character who takes down bad guys
2. Movie with a character delivering excellent comic timing as a ditzy translator between 2011 I and 2016
3. Movie directed by director born between 1970 and 1980
4. Movie with actor who made their debut before 1999
< seaarch>
<information>
</informat: intiiiioon
<think>
Based on the information provided, the movie that matches criteria "Rango." was released between 2005 and 2020, and the character played by Isla Fisher is a fun-filled and carefree character. The character who takes down bad guys and protects the protagonist is played by Jack Black. The character with excellent comic timing
ditzy translator is played by Isla Fisher, who was horn before 1999. The director of the movie, Gore Verbinski, was born hetween 1970 and 1980. However, need verify if the movie indeed "Rango" and the details about the character and director are correct.
</ </think>
<search>
1. Movie details Rango (2005)
2. Isla Fisher's character in Rango
3. Jack Black's character in Rango
4. Gore Verbinski's 's directorial debut
< / search>
<information>
</informat ion>
<think>
Based on the information provided, the movie that matches the criteria "Rango." was released between 2005 and 2020, and the character played by Isla Fisher is a fun-filled and carefree character. The character who takes down bad guys and protects the protagonist is played by Jack Black. The character with excellent comic timing a ditzy translator played by Isla Fisher, who born before 1999. The director of the movie, Gore Verbinski, was born between 1970 and 1980. The details about movie and the characters are consistent with the provided information.
</think>
Kanswer> Rango </answer>
21

---

Published as a conference paper at ICLR 2026
Table 8: Failure Case study of retrieval emrors.
Question:
am looking for a specialty food shop that has at least one location in both Mexico and Califor- nia of December 1, 2023. One of the locations in Mexico is 7.8- d--lolmmeter walk from a McDonald's located at Anillo Perif. 137, Polanco. Polanco Secc, Miguel Hidalgo. 11510 Ciudad de México, CDMX, Mexico as of December 2023. The location California located within market that held a Thanks- giving Floral Arrangement Class event in November 2023 as December 1, 2023. What is the name of the specialty food shop?
Ground Truth Answer: Churrería EI Moro
<think>
find the specialty food shop, need to identify the location in Mexico and then find the corresponding location in California. I will start by searching for the location in Mcxico and then look for the correspond- ing location in California.
</think>
<search>
1. Specialty food shop in Mexico 7.8 km from McDonald's in Polanco, Mexico City 2. Specialty food shop California market that held Thanksgiving Floral Arrangement Class in November 2023
</search>
<information>
</informat: ion>
<think>
Based on the information found, Northgate Market in California held a Thanksgiving Floral Arrangement Class event in November 2023. However, the information does not directly mention a specialty food shop that is 7.8 kilometers from a McDonald's in Polanco, Mexico City. need to search for a specialty food shop that is located in both Mexico and California and has location 7.8 kilometers from McDonald's in Mexico City.
</ //thnnk>
<sea rch>
1. Specialty food shop in Mexico and California, 7.8 km from McDonald's in Polanco, Mexico City
2. Specialty food shop in Mexico and California, near a McDonald's Polanco, Mexico City
3. Specialty food shop in Mexico and California, with a location in Polanco, Mexico City seaerchhh
<information
</informat
<think>
The search results have provided information about shopping malls and specialty food shops in Mexico City, but of the sources have explicitly mentioned specialty food shop that is 7.8 kilometers from McDonald's in Polanco, Mexico City. The information about Northgate Market California is related Thankssiving event, but does not directly connect to specialty food shop in Mcxico. I need to search for a specialty food shop that is located in both Mexico and California and has location 7.8 kilometers from a McDonald's 's in Mexico City.
</think> <search>
1. Specialty food shop in Mexico and California, 7.8 km from McDonald's in Polanco, Mexico City, 2023
2. Specialty food shop in Mexico and California, near McDonald's Polanco, Mcxico City, 2023
3. Specialty food shop in Mexico and California, with a location in Polanco, Mexico City, 2023
< search>
<information>
/inforrmtiinn
(The model kept trying by adding some keywords after the three search queries until reaching round limit)
22


Reviews:
[{"review_id": "Krk7JhPchj", "reviewer": "Reviewer_8YAE", "summary": "Developing effective agentic search systems is difficult due to a lack of complex, realistic training data. InfoSeek formalizes complex search tasks as Hierarchical Constraint Satisfaction Problems (HCSP), which require satisfying layered constraints across multiple sub-problems. It uses a Diffusion-Retrospection process. First, it \"diffuses\" outward from a seed webpage to build an exploration tree of entities and constraints. Second, it \"retrospects\" by traversing the tree in reverse to synthesize a complex question that requires hierarchical reasoning.", "questions": "1. Could we discuss the main areas where the gap between BM25 and GPT-5 lies?\n2. How robust is the HCSP data in handling irrelevant information or unexpected search paths? Why is InfoSeek better at generalizing to more complex Agentic Search benchmarks compared to traditional Multi-hop QA (Question Answering) datasets?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. This framework effectively captures the layered dependencies (both parallel and sequential) of real-world research, moving beyond simpler multi-hop or flat constraint problems.\n2. This is the first publicly released framework in this area, complete with open-source code and a large-scale dataset (50k+ QA pairs). This provides a valuable, reproducible, and extensible resource for the research community.\n3. Training on InfoSeek-generated data substantially improves agentic search performance. Notably, a 3B parameter model (InfoSeeker-3B) trained on this data achieves impressive results, surpassing several strong closed-source systems (like GPT-4.1 and Sonnet 4) on the complex BrowseComp-Plus benchmark. This highlights the framework's efficiency in distilling deep research capabilities into smaller models.", "weaknesses": "1. The restrictiveness of synthetic data models is a potential drawback.\n2. The authors indirectly prove the training's effectiveness via result improvement, but a quantitative analysis of the InfoSeeker agent's runtime error modes is missing.\n3. I feel that the InfoSeek dataset is still not hard enough.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "YzvWB7mNrF", "reviewer": "Reviewer_vAbD", "summary": "The paper proposes InfoSeek, a data-synthesis framework that casts agentic search as a Hierarchical Constraint Satisfaction Problem (HCSP) and generates training data via a Diffusion–Retrospection process. It releases ~50k QA pairs and 16.5k trajectories, adds quality controls for difficulty/verifiability, and shows consistent gains on multiple QA and deep-research benchmarks.", "questions": "See weaknesses above.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "* The Diffusion–Retrospection design yields controllable structural complexity and unique, verifiable answers.\n* Releases >50k QA pairs and 16.5k trajectories, with code, prompts, and datasets, enhancing reproducibility.\n* Analyses show benefits from structural complexity and dataset size, and failure-rate increases with more vertices, supporting the HCSP design.", "weaknesses": "### Major Weaknesses\n\n1. **Staleness/mischaracterization of related work availability.** In Related Work, the paper claims that “more advanced pipelines such as WebSailor and WebShaper … are not publicly available.” However,  by July 2025 both WebSailor and WebShaper have been open-sourced. ([WebSailor](https://huggingface.co/Alibaba-NLP/WebSailor-3B/tree/main) [WebShaper](https://huggingface.co/datasets/Alibaba-NLP/WebShaper)) In both functionality (agentic web research with structured planning/verification) and scale (released models/data/resources), WebSailor-3B is highly comparable to InfoSeeker-3B. Therefore, this statement is outdated, and the author should include WebSailor in the comparison. Such an oversight should not appear in a submission dated September 24, 2025.\n2. **Limited evaluation diagnostics.** While headline scores improve, the paper lacks detailed error analysis, significance testing, and human evaluation of reasoning traces/interpretability, making it hard to judge where improvements come from and whether behaviors are stable.\n3. **Novelty vs. prior formalisms.** HCSP is compelling, but the paper could better differentiate it theoretically from existing hierarchical/multi-step reasoning formalisms beyond illustrative examples; stronger connections (or guarantees) would clarify the leap over multi-hop task formalizations.\n\n### Minor Weaknesses\n\n1. **Limited model scope.** Experiments focus almost exclusively on a **3B** model variant, leaving unclear whether the gains hold at larger or smaller scales and how results trade off with compute/latency. Evaluating additional sizes (e.g., 7–8B/32B) or providing scaling curves would strengthen generality claims.\n2. **Ablation granularity.** The paper does not isolate the impact of blurring vs. depth expansion operations separately; a targeted ablation could validate each component’s necessity.\n3. **Reward design sparsity.** RL uses a binary reward (format + answer). More informative rewards (e.g., step-level correctness, retrieval quality) might further stabilize learning; an ablation would help.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "JfpOEUz0NE", "reviewer": "Reviewer_28z3", "summary": "The paper introduces InfoSeek, a framework for synthesizing high-quality, complex training data to enhance agentic search systems driven by LLMs. The core innovation is the formalization of deep research tasks as a Hierarchical Constraint Satisfaction Problem (HCSP). The HCSP structure guides the data synthesis process by systematically decomposing a complex query into a tree of sub-goals (the hierarchy) and enforcing logical rules and dependencies between intermediate facts (the constraints). This process ensures that the generated search trajectories and final answers are logically consistent, fully verifiable, and structurally complex, effectively addressing the critical lack of high-fidelity training data for multi-step reasoning agents. The resulting dataset is shown to significantly improve agent performance on complex search benchmarks.", "questions": "How does the framework ensure that the LLM, when generating the search trajectory (intermediate queries and reasoning steps), truly learns the HCSP's structural constraints and dependencies rather than just learning to parrot a factually-correct final answer? Is there a metric or auxiliary loss (beyond final accuracy) that specifically penalizes the agent for generating logically inconsistent or redundant intermediate queries, thereby transferring the HCSP's formal rigor into the agent's operational logic?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The hierarchical component of HCSP is perfectly suited to model the multi-step nature of agentic search. It provides a formal mechanism for structurally decomposing a high-level goal into mandatory, verifiable sub-goals, directly addressing the challenge of long-horizon planning and complex reasoning. By explicitly defining the variables, domains, and constraints within the HCSP, the authors gain granular control over the difficulty and scope of the synthetic tasks. This allows for the systematic generation of highly diverse training examples (e.g., tasks requiring 3, 5, or 7 dependencies), which is crucial for robust agent fine-tuning.\n\n2. Models trained on InfoSeek data, even with simple training protocols (supervised fine-tuning and basic reinforcement learning), consistently surpass strong baselines, including many more carefully engineered agentic baselines with sophisticated optimization. Ablation studies confirm that optimizing models with InfoSeek data yields clear and significant gains. Furthermore, analyses on dataset complexity and scale validate that performance improves as more complex (higher \"vertex count\") and larger subsets of the InfoSeek data are used, which supports the effectiveness of the HCSP formulation.", "weaknesses": "1. HCSP excels at tasks with hard constraints (e.g., \"Find all companies with Revenue > $1B AND P/E < 15\"). However, it exhibits poor solution coverage for high-value, real-world business problems that rely on subjective judgment, synthesis of abstract concepts, or probabilistic forecasting. For instance, an agent tasked with formulating a strategic recommendation such as \"Which market segment should a B2B SaaS company enter next?\" requires weighing conflicting qualitative data (e.g., \"market sentiment\", \"brand alignment\", \"regulatory risk outlook\") where the \"constraints\" are fuzzy, constantly changing, and lack a binary, verifiable truth state. The HCSP framework, being optimized for explicit logic, struggles to formally represent and generate high-quality training data for solutions that are fundamentally open-ended and context-dependent.\n\n2. The HCSP primarily models the structure of a correct solution. It provides limited intrinsic coverage of effective search heuristics, resource management, information filtering, or error recovery processes that define a high-quality agentic trajectory. The agent is trained on what a valid answer is, not necessarily how to robustly find it in a noisy, real-world environment.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "1K1Pb1EyNh", "reviewer": "Reviewer_NXXo", "summary": "This paper introduces **InfoSeek**, a novel data synthesis framework that formulates agentic search as a **Hierarchical Constraint Satisfaction Problem (HCSP)**. Through a **Diffusion–Retrospection** process, InfoSeek constructs over **50K QA pairs** and **16.5K reasoning trajectories**, achieving substantial improvements across multiple benchmarks, including **BrowseComp-Plus**, thereby validating the approach’s effectiveness.", "questions": "* Can the HCSP formulation be generalized to multimodal or retrieval-augmented settings?\n* Did the authors explore continuous reward functions (e.g., confidence-weighted accuracy) during RL training?", "limitations": "", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 4, "strengths": "* Clear and principled theoretical formulation via HCSP (Eqs. (1)–(3)).\n* Well-designed synthesis algorithm producing layered, verifiable data (Algorithm 1).\n* Large, high-quality dataset (Table 2) with controlled complexity.\n* Strong experimental results: InfoSeeker-3B achieves **15.3%** on BrowseComp-Plus, outperforming GPT-4.1 and Search-R1-32B.\n* Open-sourced code and data ensure transparency and reproducibility.", "weaknesses": "* **Limited baseline details:** RL-based baselines (e.g., Search-R1, InForage) lack hyperparameter disclosure.\n  → *Recommendation:* Provide full training details for reproducibility.\n* **Insufficient failure analysis:** While accuracy improvements are notable, deeper case-level error analysis is needed.\n  → *Recommendation:* Include failure taxonomy or qualitative examples.\n* **Heuristic ambiguity:** The implementation of “blur parent” and “depth expansion” lacks concrete examples.\n  → *Recommendation:* Add illustrative instances in the appendix.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)