Summary of Graph2tac: Online Representation Learning Of Formal Math Concepts, by Lasse Blaauwbroek et al.
Graph2Tac: Online Representation Learning of Formal Math Concepts
by Lasse Blaauwbroek, Miroslav Olšák, Jason Rute, Fidel Ivan Schaposnik Massolo, Jelle Piepenbrock, Vasily Pestun
First submitted to arxiv on: 5 Jan 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Artificial Intelligence (cs.AI)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The paper explores the concept of proximity in proof assistants, where formal mathematical concepts with physical closeness exhibit similar proof structures. By leveraging online learning techniques, the authors develop solving agents that outperform offline learners in proving theorems in unseen settings. The Tactician platform is used to implement two online solvers: a k-nearest neighbor (k-NN) solver that learns from recent proofs and shows a 1.72x improvement over its offline equivalent, and Graph2Tac, a graph neural network that builds hierarchical representations for new definitions, achieving a 1.5x improvement over an offline baseline. The combination of the k-NN and Graph2Tac solvers improves performance by 1.27x and outperforms general-purpose provers, including CoqHammer, Proverbot9001, and a transformer baseline. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper is about using computers to help humans prove mathematical theorems more efficiently. It shows that when computer programs are close together in a special language, they often use similar methods to solve problems. The authors create two new computer programs that can learn from each other and improve their proof-solving abilities over time. One program is better at learning from recent proofs, while the other is better at understanding new definitions. When combined, these programs work even better together than they do separately. This research has important implications for people who use computers to prove mathematical theorems. |
Keywords
* Artificial intelligence * Graph neural network * Nearest neighbor * Online learning * Transformer
