# Higher-Order Knowledge Representations for Agentic Scientific Reasoning

arXiv: https://arxiv.org/abs/2601.04878 · HTML: https://mlsanity.com/paper/2601.04878/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge- and tool-augmented reasoning, one of 17 directions in LLM reasoning.
- Builds on 32 of its 98 references that are in the map.
- First posted on arXiv 8 Jan 2026.

## Placed in

- LLM reasoning / [Knowledge- and tool-augmented reasoning](https://mlsanity.com/lr/knowledge-and-tool-augmented-reasoning/)
- LLM agents and tool use / [Web, search, and research agents](https://mlsanity.com/agents/web-search-and-research-agents/)

## Builds on (most cited first, 30 of 32)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation](https://mlsanity.com/paper/2308.08155/) (2023)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [When Not to Trust Language Models: Investigating Effectiveness of Parametric and Non-Parametric Memories](https://mlsanity.com/paper/2212.10511/) (2022)
- [How Can We Know What Language Models Know?](https://mlsanity.com/paper/1911.12543/) (2019)
- [Unifying Large Language Models and Knowledge Graphs: A Roadmap](https://mlsanity.com/paper/2306.08302/) (2023)
- [Structured Prompting: Scaling In-Context Learning to 1,000 Examples](https://mlsanity.com/paper/2212.06713/) (2022)
- [MemLLM: Finetuning LLMs to Use An Explicit Read-Write Memory](https://mlsanity.com/paper/2404.11672/) (2024)
- [WikiBigEdit: Understanding the Limits of Lifelong Knowledge Editing in LLMs](https://mlsanity.com/paper/2503.05683/) (2025)
- [Thinking Like an Expert:Multimodal Hypergraph-of-Thought (HoT) Reasoning to boost Foundation Modals](https://mlsanity.com/paper/2308.06207/) (2023)
- [OG-RAG: Ontology-Grounded Retrieval-Augmented Generation For Large Language Models](https://mlsanity.com/paper/2412.15235/) (2024)
- [Hyper-RAG: Combating LLM Hallucinations using Hypergraph-Driven Retrieval-Augmented Generation](https://mlsanity.com/paper/2504.08758/) (2025)
- [Let's Ask GNN: Empowering Large Language Model for Graph In-Context Learning](https://mlsanity.com/paper/2410.07074/) (2024)
- [Sparks: Multi-Agent Artificial Intelligence Model Discovers Protein Design Principles](https://mlsanity.com/paper/2504.19017/) (2025)
- [Hypergraph Transformer: Weakly-supervised Multi-hop Reasoning for Knowledge-based Visual Question Answering](https://mlsanity.com/paper/2204.10448/) (2022)
- [Mirror: A Universal Framework for Various Information Extraction Tasks](https://mlsanity.com/paper/2311.05419/) (2023)
- [Are Large Language Models In-Context Graph Learners?](https://mlsanity.com/paper/2502.13562/) (2025)
- [Text2NKG: Fine-Grained N-ary Relation Extraction for N-ary relational Knowledge Graph Construction](https://mlsanity.com/paper/2310.05185/) (2023)
- [Beyond Graphs: Can Large Language Models Comprehend Hypergraphs?](https://mlsanity.com/paper/2410.10083/) (2024)
- [In-situ graph reasoning and knowledge expansion using Graph-PReFLexOR](https://mlsanity.com/paper/2501.08120/) (2025)
- [HyperG: Hypergraph-Enhanced LLMs for Structured Knowledge](https://mlsanity.com/paper/2502.18125/) (2025)
- [LLMs as Repositories of Factual Knowledge: Limitations and Solutions](https://mlsanity.com/paper/2501.12774/) (2025)
- [Inside-Out: Hidden Factual Knowledge in LLMs](https://mlsanity.com/paper/2503.15299/) (2025)
- [From Graphs to Hypergraphs: Hypergraph Projection and its Remediation](https://mlsanity.com/paper/2401.08519/) (2024)
- [Hypergraph: A Unified and Uniform Definition with Application to Chemical Hypergraph and More](https://mlsanity.com/paper/2405.12235/) (2024)
- [Learning to Reduce: Optimal Representations of Structured Data in Prompting Large Language Models](https://mlsanity.com/paper/2402.14195/) (2024)

## Built on by (most cited first, 3 of 3)

- [GraphAgents: Knowledge Graph-Guided Agentic AI for Cross-Domain Materials Design](https://mlsanity.com/paper/2602.07491/) (2026)
- [GRAFT-ATHENA: Self-Improving Agentic Teams for Autonomous Discovery and Evolutionary Numerical Algorithms](https://mlsanity.com/paper/2605.11117/) (2026)
- [TO-Agents: A Multi-Agent AI Framework for Subjective Preference-Guided Topology Optimization](https://mlsanity.com/paper/2605.21622/) (2026)

## Abstract (arXiv)

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.