Higher-Order Knowledge Representations for Agentic Scientific Reasoning

Abstract: Scientific inquiry requires systems-level reasoning that integrates heterogeneous experimental data, cross-domain knowledge, and mechanistic evidence into coherent explanations. While 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.

• The paper introduces a hypergraph approach that captures multi-entity interactions to overcome the limits of traditional pairwise knowledge graphs.
• A dual-pass strategy combined with embedding-based deduplication processes 1,100 manuscripts to produce a hypergraph with 161,172 nodes and 320,201 hyperedges.
• The methodology empowers a multi-agent framework to generate mechanistic hypotheses, enhancing scientific reasoning in complex composite material studies.

Higher-Order Knowledge Representations for Agentic Scientific Reasoning

Abstract

The paper "Higher-Order Knowledge Representations for Agentic Scientific Reasoning" introduces a novel methodology for constructing hypergraph-based knowledge representations intended to advance agentic scientific reasoning. Traditional knowledge graphs typically rely on pairwise constraints, failing to encapsulate the complex higher-order interactions characteristic of emergent physical behavior. By employing hypergraphs, the authors aim to preserve multi-entity relationships, thereby overcoming the limitations of existing knowledge graph architectures. Specifically, the methodology has been applied to analyze a corpus of approximately 1,100 manuscripts on biocomposite scaffolds, resulting in a hypergraph consisting of 161,172 nodes and 320,201 hyperedges, exhibiting a scale-free topology organized around highly connected hubs.

Introduction

LLMs have shown remarkable proficiency in natural language processing and generation. However, the implicit encoding of knowledge in their parametric structure poses challenges for knowledge verification and updating. Retrieval-augmented generation methods only inject unstructured text, which lacks explicit relational semantics. Traditional knowledge graphs offer some structural semantics but fail to represent higher-order relationships essential for complex scientific reasoning.

Figure 1: Comparison between traditional pairwise graph representations and hypergraph representations for higher-order relationships.

The proposed solution involves constructing hypergraph-based knowledge representations that capture multi-entity interactions more faithfully than standard pairwise graphs. This approach prevents combinatorial explosion typical of pairwise expansions and maintains the co-occurrence context of scientific formulations.

Methodology

Hypergraph Construction

The methodology involves preprocessing document corpus into manageable chunks, followed by extraction of multi-entity interactions using a dual-pass strategy. Each document yields a subgraph, featuring hyperedges that encapsulate n-ary relationships, which are subsequently integrated into a global hypergraph. The resultant hypergraph encompasses relationships that support the discovery of recurring motifs, communities, and mechanistic patterns directly encoded in the corpus.

Figure 2: High-order multi-entity networks organized along two conceptual axes.

To address semantic variations across documents, embedding-based deduplication is employed. High-degree nodes are retained as canonical representations of concepts, ensuring central, well-established terms dominate the hypergraph structure.

Agentic Reasoning

A multi-agent framework is employed to conduct inference over the hypergraph. Agents collaborate by exploiting higher-order pathways to generate mechanistic hypotheses for novel composite materials. The GraphAgent identifies candidate paths for mechanistic chains, which are then refined into concrete hypotheses by specialized reasoning agents.

Results and Discussion

Structure of the Hypergraph

The hypergraph exhibits a scale-free topology, characterized by a small set of dominant conceptual hubs. The empirical node degree distribution indicates extreme hubs, confirming the presence of highly connected nodes shaping the corpus structure.

Figure 3: Subgraphs of the Biocomposite Scaffold hypergraph generated with varying hyperedge counts, illustrating core-periphery structure.

In-depth analysis reveals substantial redundancy and overlap among hyperedges, underscoring the efficiency of hypergraph representation.

Practical Implications

The induced subhypergraphs from the complete hypergraph offer insights into how scientific knowledge is structurally organized. Multi-agent reasoning fosters the exploration of latent relationships that span broader scientific domains, enriching mechanistic conclusions derived from the hypergraph.

Speculative Future Developments

The methodology sets the stage for potential advancements in LLM integration with complex data structures. Anticipated implementations include enhanced data retrieval augmented by hypergraph contexts and improved multi-domain reasoning capability.

Figure 4: Node degree statistics and power-law behavior in the scientific hypergraph.

Conclusion

This paper establishes hypergraphs as a superior representation model for encoding complex scientific relationships, transcending traditional binarized graphs. By leveraging hypergraph structures in agentic reasoning frameworks, the authors demonstrate an innovative approach to accelerating scientific discovery through robust, intricate reasoning mechanisms supported by higher-order knowledge representations.

The explored framework not only accommodates a large corpus efficiently but also opens pathways to integrate LLMs with hypergraph-based reasoning, presenting an avenue towards evolving AI systems endowed with robust structural semantics essential for advanced scientific inquiry.