# Beyond Equation Search: Conjecture-Guided Discovery with SCOPE and ClosureBench

arXiv: https://arxiv.org/abs/2610.18938 · HTML: https://mlsanity.com/paper/2610.18938/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 50 references that are in the map.
- First posted on arXiv 13 Oct 2026.

## Builds on (most cited first, 30 of 34)

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- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Accelerating scientific discovery with Co-Scientist](https://mlsanity.com/paper/2502.18864/) (2025)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [End-to-end symbolic regression with transformers](https://mlsanity.com/paper/2204.10532/) (2022)
- [LLM-SR: Scientific Equation Discovery via Programming with Large Language Models](https://mlsanity.com/paper/2404.18400/) (2024)
- [Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems](https://mlsanity.com/paper/2307.08423/) (2023)
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- [Kosmos: An AI Scientist for Autonomous Discovery](https://mlsanity.com/paper/2511.02824/) (2025)
- [Symbolic Regression with a Learned Concept Library](https://mlsanity.com/paper/2409.09359/) (2024)
- [Transformer-based Planning for Symbolic Regression](https://mlsanity.com/paper/2303.06833/) (2023)
- [LLM-SRBench: A New Benchmark for Scientific Equation Discovery with Large Language Models](https://mlsanity.com/paper/2504.10415/) (2025)
- [On scientific understanding with artificial intelligence](https://mlsanity.com/paper/2204.01467/) (2022)
- [Symbolic Physics Learner: Discovering governing equations via Monte Carlo tree search](https://mlsanity.com/paper/2205.13134/) (2022)
- [SNIP: Bridging Mathematical Symbolic and Numeric Realms with Unified Pre-training](https://mlsanity.com/paper/2310.02227/) (2023)
- [Any equation is a forest: Symbolic genetic algorithm for discovering open-form partial differential equations (SGA-PDE)](https://mlsanity.com/paper/2106.11927/) (2021)
- [Context-Alignment: Activating and Enhancing LLM Capabilities in Time Series](https://mlsanity.com/paper/2501.03747/) (2025)
- [NewtonBench: Benchmarking Generalizable Scientific Law Discovery in LLM Agents](https://mlsanity.com/paper/2510.07172/) (2025)
- [SR-Scientist: Scientific Equation Discovery With Agentic AI](https://mlsanity.com/paper/2510.11661/) (2025)
- [In-Context Symbolic Regression: Leveraging Large Language Models for Function Discovery](https://mlsanity.com/paper/2404.19094/) (2024)
- [Ai2 Scholar QA: Organized Literature Synthesis with Attribution](https://mlsanity.com/paper/2504.10861/) (2025)
- [Multimodal DeepResearcher: Generating Text-Chart Interleaved Reports From Scratch with Agentic Framework](https://mlsanity.com/paper/2506.02454/) (2025)
- [Discrete Point-wise Attack Is Not Enough: Generalized Manifold Adversarial Attack for Face Recognition](https://mlsanity.com/paper/2301.06083/) (2022)
- [LLM-AutoSciLab: Closed-Loop Scientific Discovery via Active Experimentation with LLMs](https://mlsanity.com/paper/2605.24043/) (2026)
- [ParFam -- (Neural Guided) Symbolic Regression Based on Continuous Global Optimization](https://mlsanity.com/paper/2310.05537/) (2023)
- [Focus on Hiders: Exploring Hidden Threats for Enhancing Adversarial Training](https://mlsanity.com/paper/2312.07067/) (2023)
- [GENSR: Symbolic Regression Based in Equation Generative Space](https://mlsanity.com/paper/2602.20557/) (2026)
- [Retention Time Prediction for Chromatographic Enantioseparation by Quantile Geometry-enhanced Graph Neural Network](https://mlsanity.com/paper/2211.03602/) (2022)

## Abstract (arXiv)

Most symbolic regression methods optimize candidate equations, but improving an equation's fit does not establish whether its underlying scientific conjecture should be retained, revised, or rejected. A conjecture may admit multiple mathematical realizations, and similarly accurate equations may imply different explanations. This motivates a shift from refining individual expressions to developing and testing the conjectures that guide them. We introduce SCOPE, a framework that sustains multiple conjecture-driven research trajectories. Multiple scientist agents independently pursue conjectures through equation modeling, question formulation, and active experimentation, then exchange evidence to revise their conjectures and research directions. Their findings are consolidated into a scientific report linking models, conclusions, and evidence. Existing equation-discovery benchmarks primarily assess recovered expressions, leaving the evidence and scientific conclusions established through the investigation underexamined. We therefore introduce ClosureBench, an interactive benchmark of 60 closure-discovery tasks across five scientific domains. ClosureBench focuses on closure-discovery tasks to give equation discovery a concrete scientific purpose. Each task embeds an unknown algebraic relation in a known PDE system, where agents control experimental conditions in OpenFOAM to acquire new data for equation discovery. Beyond equation accuracy, ClosureBench proposes three metrics to evaluate the discovery process: evidence faithfulness, mechanism insight, and experimental effectiveness. Compared with diverse baselines, SCOPE achieves higher equation accuracy on both ClosureBench and a real-world scientific discovery case, while producing more accurate, reliable, and effective scientific discoveries.