Multi-L KG: A Multi-Level Graph Framework

• The paper introduces Multi-L KG as a framework integrating multiple representation layers beyond basic triples to encode richer semantic and structural information.
• It employs methodologies such as shared embedding spaces, local/non-local coupling, and contextual qualifiers to enhance graph reasoning and link prediction.
• Empirical evaluations demonstrate that Multi-L KG architectures improve performance in tasks like link prediction and recommendation by leveraging multiple informational levels.

Multi-information Level Knowledge Graph (Multi-L KG) is best understood as an umbrella concept for knowledge graph systems that integrate multiple representational strata—rather than treating a KG as only a flat set of triples. In the literature, the term itself is not universal, but closely related formulations recur: a shared embedding space over lexical tokens and entity symbols, local and non-local graph scopes, contextual or view-specific fact layers, event and commonsense abstractions, and cross-level reasoning or validation loops. A concise formulation appears in KG-BiLM, which frames a knowledge graph as $\mathcal{G}=(\mathcal{E},\mathcal{R},\mathcal{T})$ with $$\mathcal{T}\subseteq \mathcal{E}\times \mathcal{R}\times \mathcal{E}$$, then turns this into a representation layer where lexical semantics, entity/relation identity, local relational context, subgraph semantics, global graph connectivity, and reasoning-oriented objectives are encoded in one shared space (Chen et al., 4 Jun 2025). Related work generalizes the same idea to multi-view reasoning, contextual fact modeling, and unified construction across entity facts, event structures, and commonsense regularities (Xi et al., 2022, Xu et al., 2024, Zhang et al., 14 Mar 2025).

1. Conceptual foundations

A Multi-L KG departs from the classical triple-only view by assuming that a fact may require additional representational levels beyond $(h,r,t)$. One influential contextual formulation defines a contextual KG as

$$\mathcal{CKG} = \{\mathcal{E}, \mathcal{R}, \mathcal{Q}, \mathcal{EC}, \mathcal{RC}\},$$

where each factual unit is a quadruple $(h,r,t,rc)\in\mathcal{Q}$ and each entity may be paired with entity context $(e,ec)$; the intended contexts include temporal validity, geographic location, quantitative data, provenance information, confidence level, event-specific detail, and supplementary information (Xu et al., 2024). This suggests that Multi-L KG is not merely a richer embedding scheme, but also a richer fact model.

A second line of formalization treats “levels” as views over a shared entity set. ROMA defines a multi-view KG as

$$\mathcal{G} = \{ \mathcal{G}_{\vartheta} \}_{\vartheta \in \Theta}, \qquad \mathcal{G}_{\vartheta}=(\mathcal{V},\mathcal{R}_{\vartheta}),$$

so that facts are organized by view constraints rather than only by relation type. Exact-match, wildcard, and equal-match view constraints then become part of query semantics, making the level or view dimension a first-class reasoning variable (Xi et al., 2022). This formulation is especially close to Multi-L KG when “level” is interpreted as contextual layer.

A third formulation is progressive rather than contextual. GKG-LLM defines a Generalized Knowledge Graph as a unified construction target spanning traditional KG with <entity, relation, entity>, Event Knowledge Graph with <event, relation, event>, and Commonsense Knowledge Graph with <commonsense, relation, commonsense>. In that reading, Multi-L KG denotes a stack from concrete factual entities to dynamic event relations to abstract commonsense regularities (Zhang et al., 14 Mar 2025). This suggests that Multi-L KG can be a hierarchy of semantic abstraction, not only a hierarchy of graph scope.

2. Information levels commonly represented

Across the cited work, the most stable interpretation of Multi-L KG is a composition of several recurring information levels.

Level	Representative formulation	Typical content
Symbolic factual	$\mathcal{G}=(\mathcal{E},\mathcal{R},\mathcal{T})$	entities, relations, triples
Textual-semantic	shared token/entity space	names, descriptions, lexical context
Local structural	one-hop, triple-local, neighborhood	adjacent facts, bounded propagation
Mesoscopic	subgraph or cluster level	subgraphs, clusters, non-local neighborhoods
Global/topological	view set or full connectivity	global graph structure, overlaying views
Contextual/qualifier	$(h,r,t,rc)$ and $(e,ec)$	time, location, provenance, confidence
Abstraction/domain	KG/EKG/CKG or molecular/disease/cognitive	event, commonsense, cross-domain layers

KG-BiLM articulates this decomposition most explicitly. It identifies token-level text semantics, entity/relation semantics in a shared vocabulary $$\mathcal{T}\subseteq \mathcal{E}\times \mathcal{R}\times \mathcal{E}$$0, triple-local and neighborhood information, subgraph structure via contrastive views, global graph connectivity through graph-aware attention masking, and a reasoning-signal level supplied by masked reconstruction and contrastive discrimination (Chen et al., 4 Jun 2025). In that account, “multi-level” is not metaphorical; it is the simultaneous encoding of several granularities in one $$\mathcal{T}\subseteq \mathcal{E}\times \mathcal{R}\times \mathcal{E}$$1-dimensional space.

KGIC gives an orthogonal decomposition tailored to recommendation: signal-level multiplicity between the collaborative filtering part and the KG part, scope-level multiplicity between local and non-local graphs, depth-level multiplicity across graph layers $$\mathcal{T}\subseteq \mathcal{E}\times \mathcal{R}\times \mathcal{E}$$2, and objective-level multiplicity through intra-graph and inter-graph contrastive supervision (Zou et al., 2022). This broadens Multi-L KG from a representational notion to a design principle for balancing heterogeneous supervisory sources.

Several papers extend the same idea to domain and abstraction layers. MultiCNKG explicitly integrates three layers—Genetic Layer (GO), Disease Layer (DO), and Cognitive Neuroscience Layer (CNKG)—and states that the resulting graph supports pathways from genes $$\mathcal{T}\subseteq \mathcal{E}\times \mathcal{R}\times \mathcal{E}$$3 diseases $$\mathcal{T}\subseteq \mathcal{E}\times \mathcal{R}\times \mathcal{E}$$4 cognitive functions (Sarabadani et al., 8 Oct 2025). GKG-LLM organizes knowledge as factual, event, and commonsense levels (Zhang et al., 14 Mar 2025). LEC-KG, although it does not use the term Multi-L KG, combines textual semantics from source documents, ontology/schema constraints, a hierarchical relation space, graph-structural plausibility from embeddings, explicit evidence spans, and iterative cross-module feedback (Zeng et al., 2 Feb 2026). Taken together, these works imply that Multi-L KG may refer either to levels of graph structure or to levels of semantic abstraction.

3. Architectural patterns

One major architectural pattern is the shared-space sequence interface. KG-BiLM linearizes triples, subgraphs, entity descriptions, relation names, and natural-language tokens into one sequence, then uses Bidirectional Knowledge Attention, Knowledge-Masked Prediction, and Contrastive Graph Semantic Aggregation to integrate lexical and structural information (Chen et al., 4 Jun 2025). Retrieval-Augmented LLM for Extreme Multi-Label Knowledge Graph Link Prediction follows a related sequence-based strategy: the core query, selected one-hop triples, relation labels, and entity descriptions are serialized into BERT input, but the retrieval policy is adapted to graph statistics such as average one-hop degree and disconnected triples (Lin et al., 2024).

A second pattern is the local/global or local/non-local coupled graph architecture. KGIC constructs local and non-local graphs for both users and items, preserves layer-wise representations by concatenation, and coordinates levels through intra-graph and inter-graph interactive contrastive learning (Zou et al., 2022). CKGC-CKD defines local KGs $$\mathcal{T}\subseteq \mathcal{E}\times \mathcal{R}\times \mathcal{E}$$5 together with a fused global KG

$$\mathcal{T}\subseteq \mathcal{E}\times \mathcal{R}\times \mathcal{E}$$6

then couples local and global models by message passing over alignment edges and mutual knowledge distillation (Zhang et al., 2023). In both cases, Multi-L KG is realized as explicit coexistence of local and global graph levels rather than by collapsing everything into one graph.

A third pattern is the context-aware or view-aware reasoner. ROMA uses separate relation and view decoders over a multi-view KG, with a joint score

$$\mathcal{T}\subseteq \mathcal{E}\times \mathcal{R}\times \mathcal{E}$$7

so a candidate answer must be simultaneously plausible in relation space and compatible in view space (Xi et al., 2022). Context Graph adopts a related idea at the fact level by extending triple scoring from $$\mathcal{T}\subseteq \mathcal{E}\times \mathcal{R}\times \mathcal{E}$$8 to $$\mathcal{T}\subseteq \mathcal{E}\times \mathcal{R}\times \mathcal{E}$$9, where head context, relation context, and tail context enter the scoring process (Xu et al., 2024). These models operationalize Multi-L KG as joint reasoning over symbolic relations and contextual qualifiers.

A fourth pattern is the LLM-guided construction-and-validation loop. LEC-KG uses hierarchical coarse-to-fine extraction, evidence-guided Chain-of-Thought feedback, semantic initialization for unseen entities, and RotatE-based structural validation in a bidirectional LLM–KGE loop (Zeng et al., 2 Feb 2026). MultiCNKG uses GPT-4 and BioGPT for entity alignment, semantic similarity computation, and graph augmentation across biomedical-cognitive layers (Sarabadani et al., 8 Oct 2025). LLHKG applies one lightweight LLM for hyper-relation extraction and another for semantic and format correction, targeting hyper-relational statements that contain qualified information (Zhu et al., 21 Apr 2026). In these systems, Multi-L KG is a construction methodology in which text, schema, structure, and evidence continually constrain one another.

4. Learning objectives and reasoning mechanisms

Multi-L KG systems typically do not rely on a single objective. KG-BiLM combines a reconstruction-style objective with a contrastive subgraph objective. Its masked prediction loss is

$(h,r,t)$0

and its contrastive graph semantic aggregation loss is an InfoNCE-style objective over pooled subgraph views. The paper supports the joint form

$(h,r,t)$1

with $(h,r,t)$2 left implicit in the provided text (Chen et al., 4 Jun 2025). This is characteristic of a Multi-L KG encoder: one term preserves local recoverability, another preserves mesoscopic or global discriminability.

KGIC uses a different but structurally analogous multi-objective design. Its full optimization is

$(h,r,t)$3

where $(h,r,t)$4 aligns CF-rooted and KG-derived levels within each graph and $(h,r,t)$5 aligns local and non-local graphs layer by layer (Zou et al., 2022). The important point is not the specific loss family, but the separation of objectives by information level.

CKGC-CKD adds a further mechanism: posterior-level transfer between graph levels. Its local and global models exchange knowledge through KL-based mutual distillation,

$(h,r,t)$6

alongside a knowledge representation loss and an inference-time ensemble score

$(h,r,t)$7

This shows that Multi-L KG can be coupled not only by shared graph structure, but also by agreement between predictive distributions (Zhang et al., 2023).

Context- and validation-oriented systems introduce yet another mechanism: thresholded routing over uncertainty. LEC-KG scores a candidate triple $(h,r,t)$8 with RotatE,

$(h,r,t)$9

then routes it by dynamic thresholds:

$$\mathcal{CKG} = \{\mathcal{E}, \mathcal{R}, \mathcal{Q}, \mathcal{EC}, \mathcal{RC}\},$$0

with percentile-based updates of $$\mathcal{CKG} = \{\mathcal{E}, \mathcal{R}, \mathcal{Q}, \mathcal{EC}, \mathcal{RC}\},$$1 and $$\mathcal{CKG} = \{\mathcal{E}, \mathcal{R}, \mathcal{Q}, \mathcal{EC}, \mathcal{RC}\},$$2 (Zeng et al., 2 Feb 2026). In this setting, Multi-L KG is inseparable from multi-stage validation: schema validity, text evidence support, and structural plausibility jointly determine acceptance.

5. Empirical regimes and applications

The strongest empirical support for Multi-L KG appears where multiple information strata are genuinely available. KG-BiLM is most effective on semantically enriched and large-scale graphs: on Wikidata5M it reports MRR $$\mathcal{CKG} = \{\mathcal{E}, \mathcal{R}, \mathcal{Q}, \mathcal{EC}, \mathcal{RC}\},$$3, Hits@1 $$\mathcal{CKG} = \{\mathcal{E}, \mathcal{R}, \mathcal{Q}, \mathcal{EC}, \mathcal{RC}\},$$4, Hits@3 $$\mathcal{CKG} = \{\mathcal{E}, \mathcal{R}, \mathcal{Q}, \mathcal{EC}, \mathcal{RC}\},$$5, and Hits@10 $$\mathcal{CKG} = \{\mathcal{E}, \mathcal{R}, \mathcal{Q}, \mathcal{EC}, \mathcal{RC}\},$$6, and in zero-shot link prediction on Wikidata5M it reports MRR $$\mathcal{CKG} = \{\mathcal{E}, \mathcal{R}, \mathcal{Q}, \mathcal{EC}, \mathcal{RC}\},$$7, Hits@1 $$\mathcal{CKG} = \{\mathcal{E}, \mathcal{R}, \mathcal{Q}, \mathcal{EC}, \mathcal{RC}\},$$8, Hits@3 $$\mathcal{CKG} = \{\mathcal{E}, \mathcal{R}, \mathcal{Q}, \mathcal{EC}, \mathcal{RC}\},$$9, and Hits@10 $(h,r,t,rc)\in\mathcal{Q}$0 (Chen et al., 4 Jun 2025). KG-FIT reports Hits@10 improvements of 14.4%, 13.5%, and 11.9% over state-of-the-art PLM-based methods on FB15K-237, YAGO3-10, and PrimeKG, respectively, and also improves over the structure-based base models upon which it is built by 12.6%, 6.7%, and 17.7% (Jiang et al., 2024). These results align with the claim that higher-level semantics become most valuable when local graph structure alone is insufficient.

In reasoning settings, explicit level or context modeling also yields measurable gains. ROMA is evaluated on multi-view KGs with millions of facts and dozens of views, and the paper reports that all view-aware methods significantly outperform the view-agnostic baseline, while ROMA generalizes to unseen query structures and shows reasonable HIT@5 on unobserved future views (Xi et al., 2022). Context Graph reports that contextual information improves both KG completion and KG question answering; on KGC, average improvements over base models on FB15k-237 include $(h,r,t,rc)\in\mathcal{Q}$1 MRR and $(h,r,t,rc)\in\mathcal{Q}$2 Hits@1, and on KGQA it reports Exact Match scores of 54.7 on QALD10-en and 78.8 on WikiWebQuestion (Xu et al., 2024). The empirical pattern is consistent: level-aware modeling is most useful when queries depend on qualifiers, view consistency, or external evidence.

Construction-oriented systems show similar behavior in open-world and long-tail regimes. LEC-KG, on temporally split Chinese SDG reports, reports Micro-F1 36.79 and Macro-F1 21.63, improving over the strongest baseline by +11.25 Micro-F1 and +11.44 Macro-F1, with tail-relation F1 rising from 6.7 to 13.3 (Zeng et al., 2 Feb 2026). GKG-LLM, trained on 15 sub-tasks across 29 datasets, reports an overall average of 67.90, compared with 60.41 for Integrated-SFT, and an average OOD performance of 50.52, 5.40% higher than the second-best model in that setting (Zhang et al., 14 Mar 2025). MultiCNKG reports Precision 85.20, Recall 87.30, Coverage 92.18, Graph Consistency 82.50, Novelty Detection 40.28, and Expert Validation 89.50, while supporting cross-level biomedical-cognitive link prediction with TransE MRR 0.411 and RotatE MRR 0.395 (Sarabadani et al., 8 Oct 2025).

Application domains are correspondingly broad. KGIC applies Multi-L KG ideas to recommendation under sparse user-item supervision (Zou et al., 2022). AliNet applies them to entity alignment by combining one-hop and two-hop neighborhoods with gated fusion (Sun et al., 2019). CKGC-CKD applies them to multilingual completion via local/global co-learning (Zhang et al., 2023). LEC-KG and LLHKG apply them to domain-specific construction and hyper-relational extraction (Zeng et al., 2 Feb 2026, Zhu et al., 21 Apr 2026). MultiCNKG applies them to molecular, disease, and cognitive integration (Sarabadani et al., 8 Oct 2025). The term therefore describes not one task, but a family of graph systems whose common property is coordinated multi-level representation.

6. Limitations, misconceptions, and open problems

A first misconception is that Multi-L KG names a single standardized formalism. The literature does not support that reading. Several papers are explicitly described as compatible with the idea rather than using the term itself; the nearest native labels are “multi-level interactive contrastive learning,” “multi-view KG,” “contextual KG,” “Generalized Knowledge Graph,” and “hyper-relational KG” (Zou et al., 2022, Xi et al., 2022, Xu et al., 2024, Zhang et al., 14 Mar 2025, Zhu et al., 21 Apr 2026). Multi-L KG is therefore best treated as an editorial umbrella over related representational strategies.

A second misconception is that adding more levels always improves performance. Multiple papers report the opposite. KGIC finds that deeper propagation can introduce noise, with best depth at $(h,r,t,rc)\in\mathcal{Q}$3 on Book-Crossing and $(h,r,t,rc)\in\mathcal{Q}$4 on MovieLens-1M and Last.FM, and that removing the non-local graph hurts most but deeper expansion quickly becomes noisy (Zou et al., 2022). AliNet shows that $(h,r,t,rc)\in\mathcal{Q}$5 hops is optimal, while $(h,r,t,rc)\in\mathcal{Q}$6 and $(h,r,t,rc)\in\mathcal{Q}$7 reduce Hits@1, and that naïve multi-hop mixing is harmful because distant neighbors are noisy (Sun et al., 2019). This suggests that Multi-L KG is not defined by maximal layering, but by controlled layering.

A third limitation concerns dependence on semantic side information. KG-BiLM is strongest on semantically enriched graphs but trails specialized path-based methods on structure-only FB15k-237, which the paper attributes to relation-cardinality sensitivity and semantic sparsity dependence (Chen et al., 4 Jun 2025). KG-FIT similarly does not dominate lexical-heavy WN18RR, and the authors state that hierarchy quality and LLM bias can affect results (Jiang et al., 2024). Multi-L KG methods are therefore most attractive when multiple information levels are genuinely present and reliable.

Construction-oriented systems raise further issues: provenance, hallucination, and procedural underspecification. LEC-KG notes cold-start instability, schema redesign cost, and the absence of a single differentiable end-to-end objective, while its evidence retrieval remains exact-match and precision-oriented (Zeng et al., 2 Feb 2026). MultiCNKG omits exact prompts, alignment thresholds, ontology mapping rules, and several experimental details, and its reporting contains formatting inconsistencies (Sarabadani et al., 8 Oct 2025). LLHKG emphasizes prompt optimization and correction modules but does not provide explicit loss functions or graph-aware evaluation beyond BERTScore (Zhu et al., 21 Apr 2026). A plausible implication is that a stronger Multi-L KG framework would need explicit provenance, confidence modeling, and more formal cross-level constraints.

Finally, reasoning coverage remains incomplete. ROMA supports projection and intersection but not negation or union in the provided formulation (Xi et al., 2022). Context Graph uses an LLM-judged stopping criterion for whether sufficient information has been retrieved (Xu et al., 2024). CKGC-CKD assumes pre-existing seed alignments and may degrade when alignments are sparse or noisy (Zhang et al., 2023). GKG-LLM unifies construction tasks effectively, but does not yet provide an explicit cross-level graph schema linking entities, events, and commonsense abstractions into one fully formal object (Zhang et al., 14 Mar 2025). The literature therefore suggests that Multi-L KG is already a productive technical direction, but not yet a closed or fully standardized theory.