# Toward Auto-Research: Mining Falsifiable Research Ideas from Paper Knowledge Graphs with Categorical Structure

arXiv: https://arxiv.org/abs/2608.20361 · HTML: https://mlsanity.com/paper/2608.20361/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 42 references that are in the map.
- First posted on arXiv 17 Jun 2026.

## Builds on (most cited first, 29 of 29)

- [Agent Laboratory: Using LLM Agents as Research Assistants](https://mlsanity.com/paper/2501.04227/) (2025)
- [The AI Scientist-v2: Workshop-Level Automated Scientific Discovery via Agentic Tree Search](https://mlsanity.com/paper/2504.08066/) (2025)
- [Can LLMs Generate Novel Research Ideas? A Large-Scale Human Study with 100+ NLP Researchers](https://mlsanity.com/paper/2409.04109/) (2024)
- [ResearchAgent: Iterative Research Idea Generation over Scientific Literature with Large Language Models](https://mlsanity.com/paper/2404.07738/) (2024)
- [SciMON: Scientific Inspiration Machines Optimized for Novelty](https://mlsanity.com/paper/2305.14259/) (2023)
- [AI-Researcher: Autonomous Scientific Innovation](https://mlsanity.com/paper/2505.18705/) (2025)
- [Chain of Ideas: Revolutionizing Research Via Novel Idea Development with LLM Agents](https://mlsanity.com/paper/2410.13185/) (2024)
- [Kosmos: An AI Scientist for Autonomous Discovery](https://mlsanity.com/paper/2511.02824/) (2025)
- [Sheaf Neural Networks](https://mlsanity.com/paper/2012.06333/) (2020)
- [Many Heads Are Better Than One: Improved Scientific Idea Generation by A LLM-Based Multi-Agent System](https://mlsanity.com/paper/2410.09403/) (2024)
- [Sheaf Neural Networks with Connection Laplacians](https://mlsanity.com/paper/2206.08702/) (2022)
- [MLR-Bench: Evaluating AI Agents on Open-Ended Machine Learning Research](https://mlsanity.com/paper/2505.19955/) (2025)
- [Nova: An Iterative Planning and Search Approach to Enhance Novelty and Diversity of LLM Generated Ideas](https://mlsanity.com/paper/2410.14255/) (2024)
- [AI Idea Bench 2025: AI Research Idea Generation Benchmark](https://mlsanity.com/paper/2504.14191/) (2025)
- [Position: Categorical Deep Learning is an Algebraic Theory of All Architectures](https://mlsanity.com/paper/2402.15332/) (2024)
- [Improving Scientific Hypothesis Generation with Knowledge Grounded Large Language Models](https://mlsanity.com/paper/2411.02382/) (2024)
- [IRIS: Interactive Research Ideation System for Accelerating Scientific Discovery](https://mlsanity.com/paper/2504.16728/) (2025)
- [SoundnessBench: Can Your AI Scientist Really Tell Good Research Ideas from Bad Ones?](https://mlsanity.com/paper/2605.30329/) (2026)
- [Knowledge Sheaves: A Sheaf-Theoretic Framework for Knowledge Graph Embedding](https://mlsanity.com/paper/2110.03789/) (2021)
- [In-situ graph reasoning and knowledge expansion using Graph-PReFLexOR](https://mlsanity.com/paper/2501.08120/) (2025)
- [A Survey of AI Scientists](https://mlsanity.com/paper/2510.23045/) (2025)
- [CHIMERA: A Knowledge Base of Scientific Idea Recombinations for Research Analysis and Ideation](https://mlsanity.com/paper/2505.20779/) (2025)
- [Unlocking LLM Creativity in Science through Analogical Reasoning](https://mlsanity.com/paper/2605.11258/) (2026)
- [PARNESS: A Paper Harness for End-to-End Automated Scientific Research with Dynamic Workflows, Full-Text Indexing, and Cross-Run Knowledge Accumulation](https://mlsanity.com/paper/2605.05258/) (2026)
- [Networks of Causal Abstractions: A Sheaf-theoretic Framework](https://mlsanity.com/paper/2509.25236/) (2025)
- [Sheaf-Theoretic Transport and Obstruction for Detecting Scientific Theory Shift in AI Agents](https://mlsanity.com/paper/2605.14033/) (2026)
- [LacMaterial: Large Language Models as Analogical Chemists for Materials Discovery](https://mlsanity.com/paper/2510.22312/) (2025)
- [From Line Knowledge Digraphs to Sheaf Semantics: A Categorical Framework for Knowledge Graphs](https://mlsanity.com/paper/2603.05685/) (2026)
- [Sheaf-Laplacian Obstruction and Projection Hardness for Cross-Modal Compatibility on a Modality-Independent Site](https://mlsanity.com/paper/2604.07632/) (2026)

## Abstract (arXiv)

Automated research-idea generation systems built on large language models (LLMs) share a structural weakness: they reduce ideation to free-text recombination, random paper pairing, or embedding-similarity retrieval. The three approaches fail in the same way: each treats a paper as a flat object, a string or a vector, and so quotients away the typed problem-method-metric-claim arrows a researcher actually uses when reasoning about a cross-domain analogy. We recover the missing structure with the minimal piece of category theory that a typed graph alone does not provide: composition, together with identity arrows, which makes it possible to ask whether a proposed analogy preserves relation chains. Concretely, each paper p is modelled as a small category Cp whose objects are extracted typed research entities and whose morphisms are the relations the paper asserts; a cross-paper bridge from p to q is then a partial functor candidate F: Cp -> Cq that preserves object kinds and covered relation classes. We instantiate the model as a three-layer algorithm: categorical signature clustering, a functor-preservation gate, and a six-axis LLM plausibility judge. Evaluated on a corpus of tens of thousands of full-text-parsed papers under four ablation conditions, the categorical gate filters cross-domain candidates at roughly a 17:1 ratio while the quantitative-falsifier rate of accepted ideas stays above 83% throughout; every rejected candidate is retained with its per-axis rationale, so the gate doubles as a logging layer rather than a silent filter.