Large pretrained language models and neural reasoning systems have advanced many natural language tasks, yet they remain challenged by knowledge-intensive queries that require precise, structured multi-hop inference. Knowledge graphs provide a compact symbolic substrate for factual grounding, but integrating graph structure with neural models is nontrivial: naively embedding graph facts into prompts leads to inefficiency and fragility, while purely symbolic or search-heavy approaches can be costly in retrievals and lack gradient-based refinement. We introduce NeuroSymActive, a modular framework that combines a differentiable neural-symbolic reasoning layer with an active, value-guided exploration controller for Knowledge Graph Question Answering. The method couples soft-unification style symbolic modules with a neural path evaluator and a Monte-Carlo style exploration policy that prioritizes high-value path expansions. Empirical results on standard KGQA benchmarks show that NeuroSymActive attains strong answer accuracy while reducing the number of expensive graph lookups and model calls compared to common retrieval-augmented baselines.
Figures & tables
Figure 1: Architectural overview of the NeuroSymActive framework for knowledge graph question answering. The framework operates via a coupled dual-loop optimization process across three main stages: Stage 1: Uncertainty-Aware Active Retrieval , which utilizes a Bayesian head to model heteroscedastic uncertainty in hop prediction and a neural entropy predictor ηθ to estimate information gain ( IG ). This stage selectively invokes a Human Oracle via the QUERY_HUMAN action when uncertainty U(st) exceeds the threshold τhop . Stage 2: Differentiable Neural-Symbolic Fusion , where a hybrid Knowledge Adapter merges continuous path embeddings ( zfneural ) with soft symbolic plausibility scores ( zfsym ) derived from a Differentiable Inductive Logic Layer (DILL) . Rule confidences wρ are updated via gradient signals from active supervision stored in the human replay buffer Dhuman . Stage 3: Differentiable MCTS with Active Exploration , which implements a relaxed Monte Carlo Tree Search. It employs Progressive Widening governed by predictive uncertainty and treats human intervention as explicit nodes with value Vhuman(s) . The search is fully differentiable via Gumbel-Softmax relaxations, allowing end-to-end joint training of the policy πϕ , value vψ , and symbolic weights through a composite multi-objective loss Ltotal .
Method
WebQSP (Hits@1)
CWQ (Hits@1)
KV-Mem [ 65 ]
46.7
18.4
EmbedKGQA [ 66 ]
66.6
45.9
NSM [ 67 ]
68.7
47.6
KGT5 [ 68 ]
56.1
36.5
GraftNet [ 53 ]
66.4
–
PullNet [ 52 ]
68.1
–
Table 1: Performance comparison between NeuroSymActive, LightPROF and representative baselines on WebQSP and CWQ. Bold indicates the best reported result.
Table 3: Effect of structure-encoder design on NeuroSymActive.
Dataset
Retrieval (%)
Reasoning (%)
Generation (%)
WebQSP
31.2
42.8
26.0
CWQ
48.5
32.4
19.1
Table 4: Error mode distribution across datasets. Percentages denote proportions of incorrect predictions.
Figure 2: Reduction in error rates for each failure mode as annotation budget increases. Confidence intervals obtained by bootstrapping.
Figure 3: Composition of residual errors under strong active supervision. Components include KG incompleteness, question ambiguity, and entropy-predictor bias.
Component
Observed trace / output
Question
Which films starring Bruce Willis were directed by a filmmaker born in Germany?
Ground truth
[“Die Hard”, “The Fifth Element”]
Reasoning (selected steps)
Anchor extraction found “Bruce Willis”. Hop prediction indicated three hops. During exploration, uncertainty rose for a candidate relation (director nationality) and the system invoked QueryHuman ; human feedback confirmed relevance. The differentiable logic layer pruned implausible paths and prioritized validated relation links. The adapter produced a compact soft prompt; the LLM generated the final answer based on the pruned subgraph.
Final answer
[“Die Hard”, “The Fifth Element”] (correct)
Table 5: Illustrative case: NeuroSymActive reasoning trace for a complex WebQSP query.
Backbone (Framework)
WebQSP
CWQ
Gain
(Hits@1)
(Hits@1)
(avg)
LLaMa2-7B
61.4
31.5
+19.1
LLaMa2-7B (LightPROF)
71.2
48.5
LLaMa2-7B (NeuroSymActive)
76.3
54.8
LLaMa3-8B
66.8
48.9
+17.0
LLaMa3-8B (LightPROF)
83.8
59.3
Table 6: Performance comparison of different LLM backbones integrated with the LightPROF and NeuroSymActive frameworks.
Method
Time (H:M)
Tokens used
NPR
NeuroSymActive (LLaMa3-8B)
1:05:30
338,200
207
StructGPT (ChatGPT)
1:42:12
24,750,610
6400
Table 7: Efficiency comparison on WebQSP: NeuroSymActive vs. StructGPT. NPR = average tokens per request.
Error mode
Question
System output
Analysis
Retrieval
What language is spoken in the country where the film “Inception” was produced?
English (incorrect)
Hop-depth underestimated; a depth-query before retrieval would prevent this omission.
Reasoning
Which actor starred in both “Titanic” and “The Revenant”?
Johnny Depp (incorrect)
Correct path present but misranked by the value estimator; relation relevance verification does not fully resolve path-ranking ambiguity.
Generation
Who directed the sequel to “The Matrix”?
The Wachowskis, James Cameron (incorrect)
Correct supporting path was provided; generation introduced a spurious director due to prompt ambiguity and entity-linking noise.
Table 8: Representative failure cases by error mode. Suggested human-query opportunities are noted where applicable.
β
Hits@1 (%)
Query Rate
Δ Accuracy
0.1
87.1
2.8
baseline
0.5
86.9
1.6
−0.2
1.0
86.4
1.0
−0.7
2.0
84.2
0.6
−2.9
5.0
81.5
0.4
−5.6
10.0
78.3
0.3
−8.8
Table 9: Sensitivity to human-cost penalty β on WebQSP. “Query rate” denotes average human invocations per question.
Temperature τ
Hits@1 (%)
Training iterations to convergence
2.0
82.4
18,500
1.0
84.7
12,200
0.5
86.2
9,800
0.1
87.1
8,400
STE (hard)
85.3
11,600
Table 10: Influence of Gumbel temperature τ on WebQSP performance and training stability.
(λ1,λ2,λ3)
WebQSP
CWQ
(0.3,0.5,0.2)
87.1
62.5
(0.0,0.5,0.2)
84.5
58.9
(0.3,0.0,0.2)
83.2
57.4
(0.3,0.5,0.0)
85.8
60.1
(0.5,0.3,0.2)
86.3
61.2
(0.2,0.6,0.2)
86.7
61.8
Table 11: Ablation over multi-objective weights λ1:3 . Default is (0.3,0.5,0.2) .
Query strategy
Avg. queries per question
Hits@1 (%)
Efficiency (%↑ / query)
Random sampling
3.0
82.4
2.8
Fixed-interval
2.0
84.1
3.2
Uncertainty-only ( τhuman=0.9 )
0.8
83.6
6.5
Uncertainty-only ( τhuman=0.7 )
1.2
86.4
5.2
Uncertainty-only ( τhuman=0.5 )
2.1
87.0
3.1
Adaptive (NeuroSymActive)
1.2
87.1
5.8
Table 12: Annotation economy on WebQSP. See text for interpretation.
Figure 4: Accuracy versus annotation cost as controlled by uncertainty threshold τhuman . The adaptive strategy is marked.
Figure 5: Marginal information gain across successive human queries within episodes. Shaded area denotes variance across queries.
Supervision mode
Hits@1 (%)
Total queries (K)
Efficiency ( ×10−3 )
Unsupervised (no human)
80.9
0
—
Passive (fixed schedule)
84.1
9.5
3.4
Active (random selection)
85.3
7.1
6.2
Active (uncertainty-only)
86.4
5.7
9.6
Active (information-gain)
87.1
5.2
11.9
Fully supervised
88.3
23.8
3.1
Table 13: Comparison of supervision paradigms on WebQSP. Efficiency is accuracy gain per query normalized by annotation count.
Figure 6: Accuracy under varying annotation budgets. NeuroSymActive outperforms uncertainty-agnostic baselines across budgets.
Figure 7: Normalized loss-term magnitudes across training iterations. Shaded bands show seed-wise variation.
Figure 8: Evolution of rule confidences in DILL, grouped by rule category. Solid lines denote means; shading indicates distribution density.
Loss component
Final value
CV
Gradient norm
Lanswer
0.847
0.08
2.34
Lexplore
0.623
0.12
1.89
Lsymbolic
0.291
0.09
3.12
Lactive
0.445
0.11
1.56
Table 14: Convergence statistics for loss components. CV denotes coefficient of variation over the final 1,000 iterations.
(k,α)
Hits@1 (%)
Avg. nodes
Avg. depth
Branching factor
Rollout time (ms)
(1.5, 0.4)
85.2
24.3
2.8
4.2
12.4
(2.5, 0.5)
87.1
38.7
3.4
5.9
18.6
(4.0, 0.6)
87.4
67.2
4.2
7.8
31.2
Fixed k=3
84.6
45.1
3.1
6.2
22.3
Table 15: Progressive widening sensitivity on WebQSP. Tree statistics averaged over 500 evaluation queries.
Figure 9: Distribution of node expansions by tree depth and query hop count. Human query nodes marked separately.
Figure 10: Effective branching factor versus visit count, stratified by uncertainty quartiles; dashed line shows the non-adaptive baseline.
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 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 Search calls than its SFT initialization.
Jia Ao Sun, Hao Yu, Fengran Mo +4
Université de Montréal · Mila – Québec AI Institute · McGill University +2
Question answering (QA) is a core challenge in AI, particularly for complex queries requiring multi-hop reasoning across documents, or symbolic operations like aggregation or exhaustive listing. Retrieval-augmented generation has become the dominant approach to QA, with recent graph-based variants addressing part of these issues by organizing knowledge to better support compositional questions. However, most textual graph-based RAG methods still lack the structure needed for symbolic operations useful to answer complex questions reliably. This motivates symbolic graph-based approaches, which extract knowledge graphs (KGs) whose relations are logic predicates that enable SQL-like querying. Yet these pipelines typically use LLMs for KG extraction, which can introduce consistency issues, where extracted facts may violate commonsense ontology constraints. We propose a neuro-symbolic framework for ontology-grounded KG construction combining open-domain extraction, embedding-based canonicalization of types and predicates, and targeted LLM-based correction of ontology violations. By deferring corrections to a post-extraction stage, our method avoids repeated LLM calls, substantially reducing token usage while improving KG consistency and preserving downstream QA quality. Finally, we show that the extracted KGs are well suited for symbolic querying by measuring the occurrence of SPARQL graph patterns.
Lorenzo Loconte, Timothy Hospedales, Cristina Cornelio
University of Edinburgh, UK · Samsung AI Center, Cambridge, UK
Knowledge Graphs (KGs) are widely used to mitigate the limitations of Large Language Models (LLMs), such as outdated knowledge and hallucinations. Existing LLM-KG integration frameworks typically rely on predefined operators to retrieve factual knowledge from KGs and inject it into prompts for answer generation. This paradigm faces two critical bottlenecks: 1) Inflexibility: The predefined operators are limited in scope and thus lack sufficient compositional expressiveness to fully capture the complex semantics required by KG questions. 2) Unscalability: Direct injection of factual knowledge into prompts limits scalability in handling large-scale factual knowledge. To address these two bottlenecks, we propose Code-on-Graph (CoG), a programmatic reasoning framework for LLM-KG integration. Specifically, given the factual knowledge retrieved at each reasoning step, CoG first identifies the corresponding KG schemas and represents these schemas as Python classes, which serve as abstract interfaces to the retrieved facts. It then generates executable code grounded in these classes, with the retrieved facts instantiated as objects of the corresponding classes during execution. This design enables flexible code-based reasoning while avoiding the direct injection of large-scale factual knowledge into prompts. Experiments on WebQSP, CWQ, and GrailQA demonstrate that CoG outperforms prior state-of-the-art models by up to 10.5%.
Weiwei Ding, Zixuan Li, Long Bai +7
1Key Laboratory of AI Safety, Institute of Computing Technology, Chinese Academy of Sciences · 2Shandong University · 3Shandong University-Weihai Research Institute of Industrial Technology