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Co-adaptive Rule Routing and Constraining for Structured Knowledge Retrieval

Zhisheng Qi, Haoyu Han, Jiaxi Li, Bing He, Huiyuan Chen, Franck Dernoncourt, Ryan A. Rossi, Mahantesh M. Halappanavar, Jin Lu, Yu Zhang, Tianming Liu, Yu Wang

arXiv:2610.14465v1cs.IRcs.AI

TL;DR

Structured retrieval often lacks the query–rule labels needed to select an appropriate reasoning constraint. CoRE jointly learns routing and rule-constrained retrieval from retrieval feedback, achieving the strongest average performance among evaluated methods and showing complementary benefits from adapting both components.

  • Problem

    Reasoning-constrained retrieval often lacks query–rule supervision because the rule connecting a query to supporting evidence is hidden and must be inferred.

    Source: §1 · p. 2, §3 · p. 3

  • Method

    CoRE treats rules as latent and alternates retrieval-feedback reinforcement learning for routing with contrastive training of retrievers on router-assigned queries.

    Source: §1 · p. 2

  • Results

    CoRE achieves the strongest average performance and consistently outperforms existing baselines, while ablations confirm the complementary importance of router optimization and retriever adaptation.

    Source: §1 · p. 2, §6 · p. 9

  • Takeaways & Limitations

    Learned routing distributions provide insights for automatic rule mining and refinement.

    Source: §1 · p. 2

    The formulation assumes query–evidence pairs but not query–rule supervision, leaving each query’s reasoning rule latent.

    Source: §3 · p. 3

Abstract

from arXiv · show

Structured knowledge retrieval acquires task-relevant evidence from structured knowledge sources for downstream tasks. Existing methods rely on unconstrained retrieval or predefined query-rule supervision, such as author-paper rules for scientific discovery and anatomy-drug rules for precision medicine. Such supervision is rarely available in practice. We propose Co-Adaptive Rule Routing and Constraining Retrieval (CoRE), which jointly learns which reasoning rule to assign to each query and how to retrieve evidence under that rule, without predefined query-rule pairs. A routing agent selects a rule, and its corresponding retriever traverses the knowledge base and ranks evidence that satisfies the rule's constraints. Because routing and retrieval are interdependent, CoRE alternates between reinforcement learning for the routing policy and contrastive learning for the rule-constrained retriever. The selected rules provide supervision for retriever training, while retrieval performance rewards the routing policy. This closed-loop process enables both components to co-adapt without explicit query-rule supervision. Experiments on STaRK-QA datasets across scientific discovery, biomedical reasoning, and e-commerce knowledge management demonstrate CoRE's effectiveness. Ablations show the benefit of co-adapting the router and retriever. Generation-based routing transfers across datasets and benefits from multi-domain pretraining followed by target-specific fine-tuning. Analysis of rule usage across queries also informs automatic rule refinement and discovery.

1 INTRODUCTION

Structured knowledge retrieval must follow reasoning constraints, but the rule appropriate to each query is often hidden and query–rule supervision is rarely available. CoRE learns query-to-rule routing and rule-constrained retrieval together from downstream retrieval feedback.

1 INTRODUCTION

  • Structured retrieval uses explicit constraints such as relation types, meta-paths, or symbolic attributes across scientific, biomedical, and enterprise applications.The introduction illustrates clinical treatment reasoning with Symptom →Diagnosis →Treatment and scientific discovery with Paper →Author →Paper.Source: §1 · p. 1
  • Figure 1 illustrates a clinical query guided by Anatomy →Disease and depicts improved retrieval from co-adapting the router and retriever.The example frames rule selection as knowledge a doctor gradually acquires through clinical experience.Source: Figure 1 · p. 2
  • Existing reasoning-constrained methods rely on heuristics or LLM knowledge to construct query–rule supervision, which can introduce construction bias and miss query-specific rationale.The underlying reasoning rule for each query often remains hidden in practice.Source: §1 · p. 2
  • CoRE treats rule selection as latent and jointly adapts a routing agent and rule-constrained retrievers without query–rule supervision.Retrieval performance rewards the router, while its assignments supervise retriever training.Source: §1 · p. 2

2 RELATED WORK

Prior work ranges from structured queries and agentic exploration to retrieval guided by predefined reasoning structures. CoRE instead learns both the structural rule to use and retrieval under that rule from downstream feedback.

Structured Knowledge Retrieval

  • Structured retrieval methods increasingly adapt structural signals, but typically generate or optimize the structural strategy separately from the retriever.Examples include MFAR’s structured-field score aggregation and MoR’s planning graph with textual matching.Source: §2 · p. 3

Reasoning-Constrained and Agentic Graph Retrieval

  • Agentic graph methods learn traversal decisions but require the LLM to perform low-level graph exploration; CoRE separates rule selection from evidence retrieval.Its router selects a schema-valid rule, and a specialized retriever executes it and ranks reachable evidence without gold paths or query–rule labels.Source: §2 · p. 3

Co-Adaptation of Agents and Tools

  • CoRE brings co-adaptation to structured retrieval: router assignments train specialized retrievers, and retriever performance rewards the router.This places the method among approaches that adapt interacting agents and tools through feedback loops.Source: §2 · p. 3

3 NOTATION AND PROBLEM FORMULATION

The paper represents a structured knowledge base as entities and relations, and recurring multi-step retrieval patterns as ordered reasoning constraint rules. It learns from query–evidence pairs while leaving each query’s connecting rule latent.

Notation

  • A structured knowledge base G = (E, R) contains entities and relations, each associated with types and descriptive attributes.The paper’s examples include paper abstracts and protein–protein interaction descriptions.Source: §3 · p. 3
  • Reasoning constraint rules are ordered sequences of steps that guide retrieval through entity or relation types.Examples include Author→Paper→Venue for scientific literature search and Drug→Target→Disease for biomedical diagnosis.Source: §3 · p. 3

Problem Formulation

  • The objective is to learn a retrieval model that retrieves ground-truth supporting evidence from the structured knowledge base for each query.Supporting evidence may be an answer entity, multiple entities, or an entity-relation subgraph.Source: §3 · p. 3
  • The formulation assumes query–evidence pairs but not query–rule supervision; the reasoning rule connecting each query to its evidence remains latent.The rule is to be inferred automatically.Source: §3 · p. 3

4 FRAMEWORK

CoRE addresses missing query–rule labels by jointly learning a rule-routing policy and specialized retrievers. Its alternating loop lets retriever outcomes refine routing and updated assignments provide new retriever supervision.

4 FRAMEWORK

  • CoRE models the reasoning rule as latent and couples rule routing with rule-conditioned retrieval because each component supplies the other’s training signal.The router assigns queries for retriever training, while retriever performance rewards router refinement.Source: §4 · p. 4

4.1 AGENTIC RULE ROUTING MODULE

  • The routing module maps a query representation to a rule-selection distribution using either a classifier or a conditional generation decoder.The paper combines BERT or LLM encoders with classifier decoders, and also tests an LLM generation decoder.Source: §4.1 · p. 5

4.2 RULE-CONSTRAINING RETRIEVAL MODULE

  • The rule-constrained retriever traverses only candidates reachable under the selected rule, then scores each path using query–entity BM25 features and a rule embedding.Its score combines query relevance along the traversal path with the semantics of the selected rule.Source: §4.2 · p. 5

4.3 ALTERNATIVE OPTIMIZATION

  • Alternating optimization trains each assigned-rule retriever with routing fixed, then updates routing from reciprocal-rank retrieval rewards.Classifier policies evaluate candidate rules, while generation policies sample rule rollouts for reward-based updates.Source: §4.3 · p. 6

4.4 INFERENCE

  • At inference, the router selects the most probable rule, and its retriever ranks constrained candidates and returns the highest-ranked evidence for downstream execution.The selected evidence set is passed to the downstream task.Source: §4.4 · p. 6

5 EXPERIMENT

Across STaRK-QA experiments, CoRE outperforms baseline retrieval methods, and its router and retriever benefit from joint adaptation. Generation-based routing transfers across datasets, while alternate optimization shows progressively changing retrieval performance and rule assignments.

5 EXPERIMENT

  • The evaluation compares CoRE with existing structured retrieval methods, tests router and retriever adaptation, examines generation-based transfer, and tracks alternate optimization dynamics.Experiments use three STaRK-QA datasets and report Hits@1, Hits@5, Recall@20, and MRR.Source: §5 · p. 7, §5.1 · p. 7

5.1 EXPERIMENTAL SETUP

  • Training uses query–evidence pairs with latent query-rule assignments across 6 AMAZON rules, 8 MAG rules, and 65 PRIME rules; all variants use three alternate optimization rounds.The variants are CoRE-BERT-C, CoRE-LLM-C, and CoRE-LLM-G.Source: §5.1 · p. 7

5.2 Q1-MAIN RESULTS

  • Across AMAZON, MAG, and PRIME, all CoRE variants outperform textual, graph-based, and agentic graph baselines; CoRE-BERT-C leads average performance and outperforms MoR among hybrid methods.CoRE-BERT-C achieves the strongest average performance among evaluated methods.Source: §5.2 · pp. 7–8, §5.1 · p. 7

5.3 Q2-ABLATION STUDY OF CO-ADAPTING ROUTER AND RETRIEVER

  • Removing either router adaptation or retriever adaptation reduces performance; the retriever-adaptation removal hurts most on PRIME, followed by MAG and AMAZON.With router adaptation removed, fixed pre-trained or zero-shot policies underperform despite continued retriever training.Source: §5.3 · p. 8

5.4 Q3-TRANSFERABILITY OF GENERATION-BASED RULE ROUTING

  • All transferred CoRE-LLM-G routers outperform zero-shot Qwen, and multi-domain pretraining followed by target-specific fine-tuning performs best among generation-based routing settings.Joint pretraining alone beats the unadapted Qwen router but remains slightly below dataset-specific training.Source: §5.4 · pp. 8–9, Figure 3 · p. 8, Figure 4 · p. 9

5.5 Q4-ALTERNATE OPTIMIZATION DYNAMICS

  • On MAG, router training raises H@1 from about 21% to 58%, and the resulting assignments lift the next retriever update above 62% across three alternating rounds.The router shifts probability among candidate rules, initially favoring IAP and PAP and later assigning more probability to PAP and PP.Source: §5.5 · p. 9, Figure 5 · p. 9

6 CONCLUSION

CoRE jointly learns rule routing and rule-constrained retrieval without explicit query-rule supervision. The conclusion reports stronger performance than existing baselines, complementary benefits from adapting both components, and iterative co-adaptation that motivates automatic rule refinement.

6 CONCLUSION

  • CoRE jointly learns rule routing and rule-constrained retrieval without explicit query-rule supervision, using alternating bi-level optimization driven by retrieval feedback.The conclusion says ablations confirm the complementary importance of routing-agent optimization and retriever adaptation.Source: §6 · p. 9
  • The paper reports that routing and retrieval progressively co-adapt through iterative feedback, motivating rule refinement guided by high-reward routing patterns.Such patterns can guide generation and adjustment of reasoning rules.Source: §6 · p. 9
  • The authors report using generative AI for manuscript review, language polishing, and figure-generation code, and provide code and datasets for reproducing reported results.The repository includes implementation, preprocessing, training, evaluation, configuration, and reproduction scripts.Source: AI USE STATEMENT · p. 10, REPRODUCIBILITY · p. 10

D Different Training Strategies for Classification Router Agents . . . . . . . . . . . . . . 17

  • Appendix headings list extended ablations, inference-time efficiency comparisons, and generation-based router prompts with dataset-specific candidate rules.The listed materials also include training strategies for classification router agents.Source: D Different Training Strategies for… · p. 13

A EXPERIMENT SETTING DETAILS

The experimental setup builds schema-derived rule sets and rule-specific candidate pools, then trains routers and retrievers in alternating rounds. Router rewards come from ground-truth evidence ranks under each rule-constrained retriever.

Rule Space and Candidate Retrieval

  • Dataset schemas yield 6 AMAZON, 8 MAG, and 65 PRIME rules; each query-rule traversal supplies up to 200 candidates for ranking.Each rule has a 384-dimensional embedding, and inference uses only the selected rule's retriever.Source: A EXPERIMENT SETTING DETAILS · p. 14

Rule-constraining Retrievers

  • Rule-specific retrievers project candidate features and rule embeddings into hidden representations, score candidates, and train with pairwise ranking against up to 200 negatives.Training uses AdamW and retains the checkpoint with the best validation Hit@1.Source: A EXPERIMENT SETTING DETAILS · p. 14

Router Training

  • Router reward is reciprocal rank of ground-truth evidence under each rule's retriever, with the best correct-answer rank used for queries with multiple correct entities.Generation-based routing uses GRPO with eight rule-selection trajectories per query; its reward combines format correctness and downstream retrieval quality.Source: A EXPERIMENT SETTING DETAILS · pp. 14–15

Routing Variants

  • BERT-C trains on the highest-reward rule, LLM-C uses the full rule-wise reward vector with entropy regularization, and LLM-G generates a rule identifier from query and rule descriptions.For the verified PRIME configuration, LLM-G is warm-started with filtered teacher demonstrations before GRPO.Source: A EXPERIMENT SETTING DETAILS · pp. 14–15

Bi-Level Training and Evaluation

  • Each of three bi-level rounds updates retrievers with the current assignments, freezes them for router updates from retrieval ranks, and carries both components forward rather than reinitializing them.Evaluation selects one rule per query; experiments use four NVIDIA H200 NVL GPUs, with discriminative routers and retrievers trained on one GPU per run.Source: A EXPERIMENT SETTING DETAILS · p. 15

B ORACLE RULE DISTRIBUTION ANALYSIS

Oracle utility varies by query rather than concentrating in one universally effective rule, and ties reveal substantial overlap among rules. This unevenness suggests that oracle utility and uniqueness can guide rule-space refinement.

B ORACLE RULE DISTRIBUTION ANALYSIS

  • Oracle credit is query-dependent: MAG spreads it across several paths, Amazon balances it across its smaller rule set, and PRIME concentrates it in a subset of its 65 rules.Many PRIME rules are rarely oracle-selected; some receive credit only through ties and are never uniquely optimal.Source: B ORACLE RULE DISTRIBUTION ANALYSIS · p. 15
  • Tied-optimal cases account for substantial oracle credit, indicating overlapping retrieval behavior among rules, especially for several MAG and Amazon rules.In PRIME, some rules receive credit exclusively through ties, suggesting little distinctive retrieval capability under the current experts and reward.Source: B ORACLE RULE DISTRIBUTION ANALYSIS · p. 15
  • Rules with consistent unique oracle credit capture specialized patterns, while rarely optimal or only tied-optimal rules are candidates for consolidation, pruning, or merging.The analysis proposes oracle utility and uniqueness as guides for automatic refinement of the candidate rule space.Source: B ORACLE RULE DISTRIBUTION ANALYSIS · p. 15
  • Each dataset’s Figure 6 bars split rule-wise fractional oracle frequency into uniquely optimal and tied-optimal credit, with total credit summing to 100%.Each rule in a k-way tie receives 1/k credit; the datasets have 8, 6, and 65 candidate rules for MAG, Amazon, and PRIME, respectively.Source: B ORACLE RULE DISTRIBUTION ANALYSIS · p. 15, Figure 6 · p. 16

C CASE STUDY

On MAG, semantic routing can diverge from retrieval utility because a plausible rule may not match retriever capabilities, or the router may misground a structural constraint. CoRE uses retrieval outcomes to jointly adapt routing and retriever specialization.

C CASE STUDY

  • On MAG, GPT-5’s semantic rule choices often mismatch the downstream oracle; the iapf→iap mismatch alone occurs in 190 queries.The more common pattern is semantic–retriever misalignment, where a plausible interpretation is not realized effectively by its retriever.Source: C CASE STUDY · p. 16, Figure 7 · p. 17
  • For a query with institution and topical constraints, iapf retrieves no valid path, while the broader iap rule retrieves both ground-truth papers at ranks 2 and 4.The added field branch retrieves field nodes whose paper sets do not overlap with the institution-derived candidates containing the answers.Source: C CASE STUDY · p. 16, Figure 7 · p. 17
  • For “Seiberg–Witten theory,” GPT-5 treats the field anchor as ordinary text and ranks the answer 110th with p; fp grounds the field and raises it to rank 7.This is a router grounding error: the structural constraint is both semantically justified and useful for retrieval.Source: C CASE STUDY · p. 16, Figure 7 · p. 17
  • CoRE makes retrieval performance reward routing while updated routing decisions supervise retriever specialization, aligning rule selection with downstream retrieval effectiveness.The case study contrasts this feedback loop with static LLM-induced query–rule labels based only on query and rule descriptions.Source: C CASE STUDY · p. 16

D DIFFERENT TRAINING STRATEGIES FOR CLASSIFICATION ROUTER AGENTS

Across the router-training and extended-ablation studies, retrieval-feedback adaptation outperforms supervised routing targets and stronger zero-shot routers. The comparisons examine training signals and routing quality with a fixed trained retriever.

D DIFFERENT TRAINING STRATEGIES FOR CLASSIFICATION ROUTER AGENTS

  • Hard-label SFT trains on only the highest-reward rule, whereas soft-label SFT preserves relative rule-level retrieval utility and RLFT directly maximizes expected retrieval utility.RLFT uses advantages to reinforce above-average rules and suppress lower-reward ones.Source: D DIFFERENT TRAINING STRATEGIES FOR… · p. 17
  • RLFT improves consistently over soft-label SFT and hard-label SFT across all retrieval metrics.Figure 8 compares these three router-training strategies averaged over AMAZON, MAG, and PRIME.Source: Figure 8 · p. 17, D DIFFERENT TRAINING STRATEGIES FOR… · p. 17

E EXTENDED ABLATION STUDY

  • The extended ablation fixes the CoRE-LLM-G retriever and substitutes zero-shot Qwen3B, GPT-5-mini, and GPT-5 routers to isolate routing effects.Results are averaged over AMAZON, MAG, and PRIME.Source: E EXTENDED ABLATION STUDY · p. 18, §E.1 · p. 18

E.1 FIXING THE RETRIEVER, VARYING THE ROUTER

  • CoRE-LLM-G remains above even GPT-5 on every retrieval metric when all routers use the same trained retriever.Stronger zero-shot LLMs improve routing progressively, but their gains stop short of the retrieval-feedback-trained router.Source: Figure 9 · p. 18, §E.1 · p. 18
  • The remaining gap indicates that stronger off-the-shelf models alone do not explain CoRE’s gains; routing decisions must align with downstream retrieval behavior through feedback.The fixed-retriever comparison pairs each router with the same trained retrievers.Source: §E.1 · p. 18

E.2 FIXING THE ROUTER, VARYING THE RETRIEVER

The study finds that rule constraints produce the largest qualitative gain over unconstrained retrieval, while trained retrievers improve ranking within the constrained candidate space. Routing and retrieval remain complementary, and CoRE-LLM-G is best overall.

E.2 FIXING THE ROUTER, VARYING THE RETRIEVER

  • Rule-constraining retrieval consistently improves over unconstrained BM25, and CoRE-LLM-G remains best overall across datasets.Figure 10 compares average Hit@1 across router–retriever combinations.Source: Figure 10 · p. 18
  • For every router, retrieval improves from BM25-last to BM25-avg and then to the trained retriever under the selected rule constraint.The router narrows the search space, while the retriever ranks candidates using relevance signals along the traversal path.Source: §E.2 · pp. 18–19
  • Gains from improving the retriever are generally smaller than those from imposing a rule constraint, making routing the dominant improvement over unconstrained retrieval.The trained retriever still helps after the structural region is identified by the rule.Source: §E.2 · p. 19
  • Router and retriever improvements are complementary, but even the strongest decoupled combination does not match CoRE-LLM-G.Co-adaptation aligns routing decisions with retriever specialization rather than simply scaling either component alone.Source: §E.2 · p. 19

F INFERENCE TIME EFFICIENCY COMPARISON

On MAG, CoRE is reported to reduce inference cost relative to step-wise graph exploration, while generation-based routing selects among schema-level traversal rules supplied as candidates.

F INFERENCE TIME EFFICIENCY COMPARISON

  • CoRE substantially reduces mean inference time per question versus step-wise agentic graph exploration, especially with classifier routing, with routing/generation and retrieval/tool costs separated.The comparison uses 1,000 MAG questions and reports mean inference time per question.Source: Figure 11 · p. 19, F INFERENCE TIME EFFICIENCY COMPARISON · p. 19

G.1 GENERATION ROUTING AGENT PROMPTS

  • The generation prompt maps each query and candidate schema-level traversal path to one rule, favoring the simplest complete match and accepting only a provided rule key.Source: §G.1 · p. 20

G.2 DATASET-SPECIFIC CANDIDATE RULES

  • The candidate-rule appendix enumerates dataset-specific schema traversal rules, with PRIME's larger set arranged in a multi-page table.Source: §G.2 · p. 20

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