Higher-Order Knowledge Representations for Agentic Scientific Reasoning

TL;DR

This work tackles the inadequacy of traditional pairwise graphs for capturing higher-order interactions in scientific reasoning. It introduces a hypergraph-based representation built from a corpus of ~1,100 biocomposite scaffold papers, producing a global structure with 161,172 nodes and 320,201 hyperedges that exhibits a scale-free topology with a power-law exponent of about $1.23$ and a dense conceptual core around hubs like scaffolds and biocompatibility. By equipping a multi-agent framework with hypergraph traversal tools, the authors demonstrate grounded mechanistic reasoning and hypothesis generation, exemplified by bridging cerium oxide to PCL via chitosan and other intermediates, while preserving provenance and reducing combinatorial explosion. The results show that hypergraphs retain high-order co-occurrence patterns, enable robust cross-domain inferences, and act as a verifiable guardrail for teacherless agentic discovery, with practical implications for accelerated materials design and interdisciplinary science. The methodology provides a scalable, auditable substrate for conversation-driven scientific inquiry that leverages higher-order structure rather than relying solely on unstructured text-based prompts.

Abstract

Scientific inquiry requires systems-level reasoning that integrates heterogeneous experimental data, cross-domain knowledge, and mechanistic evidence into coherent explanations. While Large Language Models (LLMs) offer inferential capabilities, they often depend on retrieval-augmented contexts that lack structural depth. Traditional Knowledge Graphs (KGs) attempt to bridge this gap, yet their pairwise constraints fail to capture the irreducible higher-order interactions that govern emergent physical behavior. To address this, we introduce a methodology for constructing hypergraph-based knowledge representations that faithfully encode multi-entity relationships. Applied to a corpus of ~1,100 manuscripts on biocomposite scaffolds, our framework constructs a global hypergraph of 161,172 nodes and 320,201 hyperedges, revealing a scale-free topology (power law exponent ~1.23) organized around highly connected conceptual hubs. This representation prevents the combinatorial explosion typical of pairwise expansions and explicitly preserves the co-occurrence context of scientific formulations. We further demonstrate that equipping agentic systems with hypergraph traversal tools, specifically using node-intersection constraints, enables them to bridge semantically distant concepts. By exploiting these higher-order pathways, the system successfully generates grounded mechanistic hypotheses for novel composite materials, such as linking cerium oxide to PCL scaffolds via chitosan intermediates. This work establishes a "teacherless" agentic reasoning system where hypergraph topology acts as a verifiable guardrail, accelerating scientific discovery by uncovering relationships obscured by traditional graph methods.

Figures (12)

• Figure 1: Comparison between traditional pairwise graph representations and hypergraph representations for higher-order relationships. While traditional graphs decompose multi-entity interactions into implied pairwise edges, hypergraphs preserve co-occurrence relationships as a single higher-order hyperedge, enabling more faithful representation of multiway associations. The example illustrates equal co-authorship, where decomposing a three-author contribution into pairwise connections distorts the equality of all coauthors and obscures the true relational structure underlying the paper.
• Figure 2: High-order multi-entity networks organized along two conceptual axes. The horizontal axis contrasts living-agent systems (left) with material systems (right), and the vertical axis separates macro-organizational structure (top) from micro-level mechanistic interactions (bottom). The four quadrants illustrate: (a) social networks, where roles and relationships create multiway associations; (b) biological emergence, such as neural processing and swarm behavior driven by local interaction rules. Reprinted with permission from Reference liu_open_2024 Licensed under CC-BY; (c) structural hierarchy in materials, where nested architectures across length scales cooperatively determine performance. As demonstrated in studies of mussel byssal threads and bamboo culms, structural hierarchy enables disparate materials to achieve exceptional strength and robustness. Reprinted with permission from Reference libonati_advanced_2017cao_nature-inspired_2018 Licensed under CC-BY; and (d) compositional hierarchy, exemplified in chemistry where molecular bonding, electron delocalization, and reaction networks intrinsically involve simultaneous interactions among multiple atoms, electrons, and reactants rather than isolated pairwise relationships. Reprinted with permission from Reference nazli_tuning_2023szczepanik_electron_2019 Licensed under CC-BY
• Figure 3: Subgraphs of the Biocomposite Scaffold hypergraph generated with 100, 200, 500, and 1000 hyperedges. Increasing hyperedge count produces a clear core–periphery structure, with peripheral clusters integrating into a dense, highly shared central node set. Radial overlap among hyperedges at higher edge counts reflects strong multiway co-occurrence patterns in the underlying scientific corpus.
• Figure 4: Randomly sampled hypergraph substructures from the gloabl Biocompatible Scaffold hypergraph illustrating the evolution of higher-order topology as the number of hyperedges increases. (a) A single hyperedge showing the higher-order relationship engineered for, which jointly connects the nodes biomaterials, diagnostics, and therapeutics. Although metadata is omitted for clarity, this hyperedge specifies node directionality, where biomaterials points to both diagnostics and therapeutics through the edge engineered for. (b) A random sample of 20 hyperedges from the global hypergraph. We observe one clustering event where the pairwise hyperedge nHACG composite - has enhanced - biocompatibility overlaps with halloysite - demonstrated high - biocompatibility from the node biocompatibility. (c) A random sample of 50 hyperedges, showing more complex regional organization and richer connectivity patterns. As additional edges and nodes are introduced, hyperedge arrangements become increasingly structured, highlighting emergent topological behavior and concept clustering within the corpus.
• Figure 5: Node degree statistics and power-law behavior in the scientific hypergraph. The left panel shows the empirical degree distribution, where most nodes have low degree and a small subset form highly connected hubs. The middle panel depicts a log–log degree–frequency plot with a fitted power-law trend (y = 1.23, R² = 0.755), indicating heavy-tailed, scale-free connectivity. The right panel shows the complementary cumulative distribution function (CCDF), where the linear tail in log–log space further supports power-law scaling and reveals a small number of dominant semantic hubs within the corpus.