EoG: Query-Aligned Graph Enrichment

• Enrich-on-Graph (EoG) is a knowledge graph question answering framework that transforms vanilla KGs into enriched, query-aligned graphs to bridge focus and structure mismatches.
• It employs a three-stage pipeline—Parsing, Pruning, and Enriching—to normalize queries and graph representations, enabling efficient evidence extraction and robust reasoning.
• EoG leverages large language models for both structural and feature enrichment, achieving measurable improvements in relevance, semantic richness, and overall KGQA performance.

Searching arXiv for the exact Enrich-on-Graph paper and closely related EoG usages to ground the article in current papers. Enrich-on-Graph (EoG) is a knowledge graph question answering framework that uses LLMs to transform a vanilla knowledge graph into a query-aligned enriched graph before final reasoning. It is introduced as a flexible framework that “leverages LLMs' prior knowledge to enrich KGs, bridge the semantic gap between graphs and queries,” with the stated goals of efficient evidence extraction, precise and robust reasoning, low computational costs, scalability, and adaptability across methods (Li et al., 25 Sep 2025). In the paper’s formulation, the central difficulty of LLM-based KGQA is not only multi-hop inference, but the mismatch between a natural-language query and the structure and focus of a vanilla KG.

1. Problem setting and semantic gap

EoG is defined for KGQA over a knowledge graph

$$G = \left\{ \left( e_s, r, e_o \right) \mid e_s, e_o \in E, r \in R \right\},$$

where $E$ is the entity set and $R$ is the relation set. For a complex query $q$, the task is to produce the correct answer $a^*$ using a KGQA method $M_\theta$:

$a^* = M_\theta(q, G).$

The framework attributes factual errors and hallucinations in knowledge-intensive reasoning to a “semantic gap between the natural-language query and the vanilla KG” (Li et al., 25 Sep 2025).

The paper decomposes this semantic gap into focus mismatch and structure mismatch. Focus mismatch arises because a query has a clear semantic target, whereas a KG neighborhood around a queried entity typically contains many irrelevant facts. Structure mismatch arises because the graph may encode the relevant evidence through a longer, schema-heavy, or semantically awkward path that does not align with the user’s linguistic formulation. The Astrid Fischel Volio example is used to show both issues: the query focuses on office holder, jurisdiction, and currency, while the vanilla KG may also surface unrelated facts such as birthday or education, and the relevant path may require an unintuitive chain through managed roles, office jurisdiction, and monetary value rather than a short conceptual chain directly matching the query (Li et al., 25 Sep 2025).

This diagnosis distinguishes EoG from methods that only improve reasoning over a fixed graph representation. The framework’s premise is that prior systems typically try to align query and graph during reasoning, whereas EoG aligns them by modifying the graph representation itself. A plausible implication is that the framework treats graph construction and graph conditioning as first-class reasoning components rather than purely preparatory retrieval steps.

2. Three-stage query-graph alignment pipeline

EoG is organized into three stages: Parsing, Pruning, and Enriching (Li et al., 25 Sep 2025). The first stage converts both the question and the graph into comparable query-like forms. The original question $q$ is decomposed into a set

$Q=\{q,q_1,q_2,\ldots\},$

where compound queries encode more global semantic focus and unit queries encode more local focus. The appendix prompt described in the paper explicitly asks for recursive decomposition until unit queries “can be directly answered without further reasoning or decomposition” (Li et al., 25 Sep 2025).

Graph parsing performs an analogous normalization on the KG side. Each triple $t=(e_s,r,e_o)$ is transformed by the LLM into a graph query $E$0, producing a quadruple

$E$1

Across the graph, these graph queries form $E$2. The stated purpose is to move the original query fragments $E$3 and the graph-side representations $E$4 into the same linguistic space, so that semantic comparison and alignment become easier (Li et al., 25 Sep 2025).

The second stage, focus-aware multi-channel pruning, addresses focus mismatch by scoring triples through three masked retrieval channels. For a triple $E$5, EoG creates head-masked, tail-masked, and both-masked forms. The pruning score is given in the paper as

$E$6

and the accompanying explanation states that, for each triple, semantic similarities are summed across all query fragments $E$7 and all masked channels $E$8, after which the top-$E$9 triples are retained (Li et al., 25 Sep 2025). In the reported implementation, the retriever is based on sentence-transformers and the pruning depth is set to top $R$0 (Li et al., 25 Sep 2025).

The third stage, enriching, operates on the pruned graph $R$1. For each parsed query $R$2, the LLM filters relevant graph queries $R$3 and integrates them into query-aware quadruples of the form

$R$4

The final question-answering stage then reasons over the enriched graph rather than the vanilla KG (Li et al., 25 Sep 2025). The framework therefore does not treat enrichment as a prompt-only augmentation; it treats enrichment as graph-level transformation.

3. Structural and feature enrichment mechanisms

The core enriching stage is designed to address structure mismatch. The paper specifies three structure-driven principles—similarity, symmetry, and transitivity—through which the LLM generates new graph content (Li et al., 25 Sep 2025).

Under similarity, a triple

$R$5

is rewritten with a semantically different but query-better-aligned relation $R$6. This is used when the original KG relation is technically correct but semantically awkward relative to the wording of the query. Under symmetry, the viewpoint is reversed:

$R$7

with $R$8 expressing the reverse relation. Under transitivity, two-hop evidence

$R$9

can yield a shortcut

$q$0

where $q$1 semantically composes the intermediate relations. The paper presents transitivity as especially important for collapsing long schema-heavy paths into semantically direct edges (Li et al., 25 Sep 2025).

EoG also performs feature enrichment to reduce entity ambiguity and add semantic background that is often absent from a vanilla KG neighborhood. The canonical example is

$q$2

which makes latent type information explicit. The feature-enrich prompt described in the appendix uses ontology-style relations including Hypernym_isA, Hypernym_locateAt, Hypernym_mannerOf, Induction_belongTo, Inclusion_isPartOf, Inclusion_madeOf, Inclusion_derivedFrom, and Inclusion_hasContext, with examples such as $q$3 and $q$4 (Li et al., 25 Sep 2025).

The paper is explicit that the enriched information is attached as new triples in the graph representation, not merely as natural-language explanation. This suggests that the framework should be interpreted not as generic KG completion, but as query-conditioned graph rewriting oriented toward downstream reasoning.

4. Alignment objective and graph quality metrics

The paper formalizes the desired query-aligned graph as

$q$5

Its theoretical claim is that maximizing this expected posterior is equivalent to maximizing the mutual information between query and graph:

$q$6

The derivation proceeds by rewriting the posterior in terms of conditional and joint probabilities and arrives at

$q$7

which is used as the conceptual justification for the alignment objective (Li et al., 25 Sep 2025).

To evaluate the quality of the resulting query-specific graphs, the paper proposes three metrics: Relevance, Semantic Richness, and Redundancy. Relevance is defined as

$q$8

where $q$9 and $a^*$0 are embeddings of the query and triple, respectively. Semantic Richness is defined as

$a^*$1

with $a^*$2 instantiated by a semantic scoring model such as KG-BERT. Redundancy measures pairwise semantic overlap among relations between the same head-tail pair:

$a^*$3

The constraint $a^*$4 and the definition of $a^*$5 restrict this to relations attached to fixed entity pairs (Li et al., 25 Sep 2025).

The paper further states that Relevance and Semantic Richness are positively correlated with the optimization objective $a^*$6. Empirically, on WebQSP and CWQ, EoG reportedly achieves relevance above 0.6, semantic richness around 0.5, and redundancy around 0.2, with the lowest redundancy among the compared methods. At the module level, Prune improves relevance by over 0.25; Structural Enrich and Feature Enrich each improve semantic richness by over 0.1; combining them improves semantic richness by over 0.26; and Feature Enrich reduces redundancy to below 0.1 (Li et al., 25 Sep 2025).

5. Empirical performance, ablations, and efficiency

The main evaluation is conducted on the Freebase-based WebQSP and CWQ benchmarks, with appendix results on GrailQA and QALD10-en (Li et al., 25 Sep 2025). On CWQ, EoG reports Hit@1 = 70.8 and F1 = 65.1. On WebQSP, it reports Hit@1 = 85.0 and F1 = 74.1. The paper highlights that, relative to RoG, EoG is higher on CWQ by +8.2 Hit@1 and +8.9 F1, while on WebQSP it is slightly lower on Hit@1 but higher on F1 by +3.3 (Li et al., 25 Sep 2025). Appendix results further report 85.5 Hit@1, 79.6 F1 on GrailQA and 62.3 Hit@1 on QALD10-en (Li et al., 25 Sep 2025).

Ablation results indicate that both pruning and enriching are essential. On CWQ, the full system achieves 70.8 / 65.1, compared with 58.8 / 50.9 without enrich and 55.6 / 47.9 without both prune and enrich. Removing only Structural Enrich gives 68.3 / 61.5, while removing only Feature Enrich gives 70.2 / 64.2 (Li et al., 25 Sep 2025). The paper summarizes these results by stating that Structural Enrich alone improves WebQSP Hit@1/F1 by 3.8%/9.7% and CWQ by 19.4%/26.1% over the no-enrich setting, with Feature Enrich giving similarly strong gains (Li et al., 25 Sep 2025).

The framework is also presented as plug-and-play. The Enrich module improves several existing methods: RoG + Enrich rises from 62.2/55.4 to 75.4/68.7 on CWQ and from 86.4/70.8 to 91.5/77.1 on WebQSP; ToG + Enrich improves from 67.6 to 70.7 on CWQ Hit@1 and from 82.6 to 89.4 on WebQSP Hit@1; DoG + Enrich improves from 56.0 to 60.5 on CWQ Hit@1 and from 91.0 to 92.5 on WebQSP Hit@1; and KG-CoT + Enrich improves from 62.3/52.7 to 63.7/65.7 on CWQ (Li et al., 25 Sep 2025).

Efficiency is a prominent systems claim. On CWQ, EoG uses 4 calls, 6,213.6 tokens, and cost $a^*$7, compared with 9.2 calls, 11,468.5 tokens, and $a^*$8 for ToG, and 5.7 calls, 37,919.7 tokens, and $a^*$9 for DoG. On WebQSP, EoG uses 4 calls and 6,802.1 tokens, compared with 8.8 calls and 10,189.4 tokens for ToG (Li et al., 25 Sep 2025). The paper states that pruning yields 92.8% token reduction, and reports that without pruning and without enrich the token count rises to roughly 63k–67k tokens (Li et al., 25 Sep 2025).

The reported failure analysis isolates three error sources in 100 random WebQSP samples: Identify errors (8), Structural enrich errors (1), and Feature enrich errors (2). The paper characterizes identification of which graph components should be enriched as the largest remaining weakness (Li et al., 25 Sep 2025).

6. Relation to graph-enrichment research and terminological scope

Within graph learning more broadly, EoG belongs to a family of methods that enrich graphs by changing the information available to downstream reasoning, but it does so through explicit query-conditioned graph transformation. Related work illustrates several distinct enrichment regimes. Ego-GNN augments message passing with per-node ego-graph adjacencies in order to expose closed triangles and transitivity (Sandfelder et al., 2021). IGEL preprocesses ego-networks into sparse distance-degree histograms that enrich node representations beyond 1-WL expressivity (Alvarez-Gonzalez et al., 2022). OEPG injects instance-adaptive global-aware ego-semantic descriptors into local graph convolution as new virtual/global neighbor nodes (Yang et al., 2022). Edge augments a sparse KG with textual nodes derived from external text and constrains learning through graph alignment between the original and augmented graphs (Rezayi et al., 2021). GraphER, in a retrieval-augmented generation setting, enriches data objects offline with metadata that induces structural, conceptual, or contextual proximity graphs over retrieved candidates (Miao et al., 26 Mar 2026). Compared with these methods, Enrich-on-Graph is distinctive in making query-graph alignment the organizing principle and in enriching the graph itself before final KGQA reasoning (Li et al., 25 Sep 2025).

The acronym EoG is not unique across the literature. In unrelated frameworks, it denotes “Explanations over Graphs” for graph-guided LLM investigations via local reasoning and belief propagation (Jha et al., 25 Jan 2026), and “Explore-on-Graph” for reinforcement-learning-based autonomous exploration of knowledge graphs in KGQA (Yan et al., 25 Feb 2026). In the 2025 KGQA framework discussed here, however, EoG specifically means Enrich-on-Graph (Li et al., 25 Sep 2025).

The framework’s defining claim is therefore narrow and specific: errors in LLM-based KGQA often originate in the mismatch between unstructured queries and vanilla graph structure, and this mismatch can be reduced by parsing the query and graph into aligned forms, pruning off-focus triples, and enriching the remaining graph with semantically aligned structural and ontological content (Li et al., 25 Sep 2025). In that sense, EoG is best understood as a query-conditioned graph transformation layer that precedes reasoning, rather than as a new standalone reasoning architecture.