Path-finding over knowledge graphs has become an effective way to ground LLM reasoning on multi-hop questions. However, biomedical QA introduces two distinct challenges that general-domain methods are not designed for: (i) queries do not expose intermediate reasoning and can be answered through multiple valid pathways, and (ii) biomedical knowledge graphs are densely connected, so path-finding methods easily take wrong turns. To address these challenges, we propose AdaPath, a path-finding framework that retrieves query-adaptive meta-paths from Path-Bank, which captures both query semantics and biomedical knowledge graph structure. AdaPath provides the missing cues in biomedical queries while effectively pruning dense knowledge graph neighborhoods during multi-hop reasoning. We further release BioStrat-QA, a biomedical KGQA benchmark that stratifies multi-hop queries by how much intermediate reasoning they expose. Across biomedical KGQA benchmarks, AdaPath consistently outperforms baselines, sustaining meaningful path-finding even when multi-hop queries expose less surface information. The source code is available at https://github.com/Jun-Hyeong-Kim/AdaPath.
Large language models are increasingly used for knowledge graph question answering (KGQA), but can fail to correctly ground answers in the underlying graph. Current approaches to LLM-based KGQA either rely on full semantic parsing into executable queries such as SPARQL, which is brittle in practice due to complex schemas or incompleteness of real-world KGs, or on LLM-reasoning and answer generation over KGs, which can be more robust but lacks formal guarantees. In this work, we study a complementary setting in which \emph{candidate} answers are generated by an LLM-based system and subsequently verified using lightweight symbolic constraints derived from the question. We introduce \emph{Constrained Entity Selection under Partial Knowledge (CES-PK)}, a problem formulation that focuses on eliminating invalid answers and providing symbolic support for valid ones without requiring construction of executable logical forms. To account for incomplete KGs, we employ a three-valued constraint semantics (\emph{satisfied, violated, unknown}) that avoids incorrect rejections under open-world assumptions. To demonstrate the effects of our method, we instantiate this framework over the Hetionet biomedical knowledge graph and evaluate the impact of type, relation, and exclusion constraints. Experiments show that precision improves by filtering invalid candidates, while recall is preserved due to retaining candidates whose constraints are not explicitly violated. Satisfied constraints provide additional positive symbolic evidence to rank remaining candidates.
Knowledge graph question answering (KGQA) requires navigating from topic entities to an answer several relations away. Recent methods prompt a frontier LLM to explore the graph through a retrieval tool, but their reliance on frontier-scale inference makes them costly to deploy. We present Search-on-Graph-R1 (\sogrone{}), which internalizes this navigation into a compact 8B model through supervised fine-tuning (SFT) followed by reinforcement learning (RL). Our central idea is to scaffold a frontier teacher with each question's gold SPARQL query, so the teacher traverses a known answer-bearing path with a live \texttt{Search} tool rather than having to discover the path itself. Since every call executes against a live Freebase server, the resulting trajectories are grounded in the knowledge graph by construction. On WebQSP, CWQ, and GrailQA, \sogrone{} at 8B surpasses every frozen frontier-LLM system in our comparison and posts the strongest results on CWQ of any system we compare against. It does so using no auxiliary module at inference and no LLM judge during training. Isolating each training stage shows that SFT and RL contribute complementary gains, our approach transfers across model families, and RL learns to reach answers in fewer \texttt{Search} calls than its SFT initialization.
Multi-hop Question Answering over Knowledge Graphs faces a critical challenge: traditional retrieve-then-read pipelines break differentiability, preventing the retriever from learning to bridge the semantic gap where intermediate nodes lack lexical overlap with the query. To address this, we propose RSF-GLLM, a framework decoupling differentiable graph reasoning from answer generation. Our Recurrent Soft-Flow (RSF) module employs a GRU-guided query updater to propagate continuous relevance scores, utilizing a dynamic gating mechanism to traverse semantically dissimilar bridge nodes via structural cues. We introduce flow sparsity regularization to theoretically guarantee convergence from soft probabilities to discrete reasoning paths. These paths are extracted and textualized to fine-tune a Large Language Model (LLM), ensuring generation is grounded in factual topology. Experiments on WebQSP and CWQ demonstrate that RSF-GLLM achieves competitive performance with superior inference efficiency compared to LLM based computationally expensive approaches.
Knowledge graph question answering (KGQA) aims to answer natural-language questions by reasoning over structured facts. Existing multi-hop KGQA methods mainly rely on topic-centered expansion, which faces two key challenges: the search space rapidly grows with noisy mixed-type paths, and retrieved paths may fail to satisfy the semantic constraints of complex questions. To address these challenges, we propose OPI, an ontology-guided evidence path inference framework for multi-hop KGQA. OPI introduces a relation-centric ontology graph to capture the head-tail type constraints of relations, providing a compact interface for answer-side constraints. Based on this ontology graph, OPI first introduces a bidirectional retrieval mechanism by mapping the predicted answer type to compatible final-hop relations and combining topic-side prefix expansion with answer-side final-hop matching, thereby suppressing noisy mixed-type expansion. OPI further adopts an iterative refinement strategy to reassess retrieved paths and candidate answers under the question context, filtering type-compatible but question-irrelevant evidence for more reliable answer prediction. Experiments on WebQSP, CWQ, and MetaQA show that OPI substantially reduces the search space, improves Hit@1/F1 by 4.6/5.0 points on WebQSP and 8.9/3.3 points on CWQ over the strongest prior results, and achieves near-saturated Hit@1 on MetaQA with the retrieval module alone.
Large language models excel at complex reasoning, yet evaluating their intermediate steps remains challenging. Although process reward models provide step-wise supervision, they often suffer from a risk compensation effect, where incorrect steps are offset by later correct ones, assigning high rewards to flawed reasoning paths. This issue is further exacerbated in knowledge graph (KG) reasoning, as there may exist multiple paths between the start and end entities in the KGs, and a risky step can make the reasoning path flawed. Those limitations are problematic in risk-sensitive tasks such as medical and legal KG reasoning. To address the issues, we propose a Schema-aware Cumulative Process Reward Model (SCPRM) that evaluates reasoning paths by conditioning on the reasoning prefix , and incorporating schema distance between current reasoning step and the implicit target parsed from the query, which provides cumulative and future rewards to guide the path explorations. We further integrate SCPRM into Monte Carlo Tree Search (MCTS) as SCPRM-MCTS to conduct multi-hop reasoning on KGs for question answering (QA) tasks. Across medical and legal KGQA and CWQ, SCPRM-MCTS improves the performance of Hits@k by an average of 1.18% over strong baselines, demonstrating more accurate and risk-sensitive reasoning evaluation.