# Lemmanaid: Neuro-Symbolic Lemma Conjecturing

arXiv: https://arxiv.org/abs/2504.04942 · HTML: https://mlsanity.com/paper/2504.04942/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 71 references that are in the map.
- First posted on arXiv 7 Apr 2025.

## Builds on (most cited first, 20 of 20)

- [π0: A Vision-Language-Action Flow Model for General Robot Control](https://mlsanity.com/paper/2410.24164/) (2024)
- [Evaluating Object Hallucination in Large Vision-Language Models](https://mlsanity.com/paper/2305.10355/) (2023)
- [Learning Fine-Grained Bimanual Manipulation with Low-Cost Hardware](https://mlsanity.com/paper/2304.13705/) (2023)
- [GPT-4V(ision) for Robotics: Multimodal Task Planning from Human Demonstration](https://mlsanity.com/paper/2311.12015/) (2023)
- [Efficient Bimanual Manipulation Using Learned Task Schemas](https://mlsanity.com/paper/1909.13874/) (2019)
- [Stabilize to Act: Learning to Coordinate for Bimanual Manipulation](https://mlsanity.com/paper/2309.01087/) (2023)
- [A System for Imitation Learning of Contact-Rich Bimanual Manipulation Policies](https://mlsanity.com/paper/2208.00596/) (2022)
- [Goal-conditioned dual-action imitation learning for dexterous dual-arm robot manipulation](https://mlsanity.com/paper/2203.09749/) (2022)
- [AnyBimanual: Transferring Unimanual Policy for General Bimanual Manipulation](https://mlsanity.com/paper/2412.06779/) (2024)
- [Learning Diverse Bimanual Dexterous Manipulation Skills from Human Demonstrations](https://mlsanity.com/paper/2410.02477/) (2024)
- [DAG-Plan: Generating Directed Acyclic Dependency Graphs for Dual-Arm Cooperative Planning](https://mlsanity.com/paper/2406.09953/) (2024)
- [Bringing motion taxonomies to continuous domains via GPLVM on hyperbolic manifolds](https://mlsanity.com/paper/2210.01672/) (2022)
- [Large Language Models for Orchestrating Bimanual Robots](https://mlsanity.com/paper/2404.02018/) (2024)
- [A Motion Taxonomy for Manipulation Embedding](https://mlsanity.com/paper/2007.06695/) (2020)
- [Learning Bimanual Manipulation via Action Chunking and Inter-Arm Coordination with Transformers](https://mlsanity.com/paper/2503.13916/) (2025)
- [Semantic constraints to represent common sense required in household actions for multi-modal Learning-from-observation robot](https://mlsanity.com/paper/2103.02201/) (2021)
- [Open-Vocabulary Action Localization with Iterative Visual Prompting](https://mlsanity.com/paper/2408.17422/) (2024)
- [A Whole-Body Pose Taxonomy for Loco-Manipulation Tasks](https://mlsanity.com/paper/1503.06839/) (2015)
- [Autonomous Bimanual Functional Regrasping of Novel Object Class Instances](https://mlsanity.com/paper/1910.00343/) (2019)
- [T-DOM: A Taxonomy for Robotic Manipulation of Deformable Objects](https://mlsanity.com/paper/2412.20998/) (2024)

## Built on by (most cited first, 6 of 6)

- [A Survey of Slow Thinking-based Reasoning LLMs using Reinforced Learning and Inference-time Scaling Law](https://mlsanity.com/paper/2505.02665/) (2025)
- [Reliable Proof Generation with LLMs via Analogical Retrieval and Symbolic Verification: A Case Study in Euclidean Geometry](https://mlsanity.com/paper/2505.14479/) (2025)
- [MathlibLemma: Folklore Lemma Generation and Benchmark for Formal Mathematics](https://mlsanity.com/paper/2602.02561/) (2026)
- [MathlibPR: Pull Request Merge-Readiness Benchmark for Formal Mathematical Libraries](https://mlsanity.com/paper/2605.07147/) (2026)
- [MECA: A Mechanism-Centered Agent for Constructing Well-Specified and Valuable Mathematical Conjectures](https://mlsanity.com/paper/2607.27709/) (2026)
- [Agentic Proof and Property-Based Testing via Property-Templates in Data-Intensive Computing](https://mlsanity.com/paper/2607.09072/) (2026)

## Abstract (arXiv)

Mathematicians and computer scientists are increasingly leveraging proof assistants to formalize and check complex proofs, a task that demands substantial expertise. Can we lower the bar by automating the conjecturing of helpful, interesting and novel lemmas? We present the first neuro-symbolic lemma conjecturing tool, LEMMANAID, designed to discover conjectures by drawing analogies between mathematical theories. LEMMANAID uses a fine-tuned LLM to generate lemma templates that describe the shape of a lemma, and symbolic methods to fill in the details. We compare LEMMANAID against the same LLM fine-tuned to generate lemmas directly, as well as a fully symbolic conjecturing method. On test sets from Isabelle's HOL library and Archive of Formal Proofs (AFP), LEMMANAID consistently outperforms both neural and symbolic methods. Using DeepSeek-coder-6.7B as a backend, LEMMANAID discovers 50% (HOL) and 29% (AFP) of the gold standard lemmas, increasing to 55% and 35% when ensembling prompting strategies. In a case study on Octonions, LEMMANAID discovers 79% of the gold standard lemmas, compared to 62% for neural-only and 23% for the state of the art symbolic tool. Furthermore, in a targeted comparison, LEMMANAID discovers more gold standard lemmas than both Claude Opus 4.5 and GPT-5.2. Our results show that LEMMANAID can conjecture a significant number of interesting lemmas across complex formalizations in mathematics and computer science.