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DTSTART;TZID=America/New_York:20240306T140000
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SUMMARY:LILO: Learning Interpretable Libraries by Compressing and Documenting Code
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Gabe Grand\, MIT CSAIL and Dept. of EE&CS \nTitle: LILO: Learning Interpretable Libraries by Compressing and Documenting Code \nAbstract: While large language models (LLMs) now excel at code generation\, a key aspect of software development is the art of refactoring: consolidating code into libraries of reusable and readable programs. In this paper\, we introduce LILO\, a neurosymbolic framework that iteratively synthesizes\, compresses\, and documents code to build libraries tailored to particular problem domains. LILO combines LLM-guided program synthesis with recent algorithmic advances in automated refactoring from Stitch: a symbolic compression system that efficiently identifies optimal lambda abstractions across large code corpora. To make these abstractions interpretable\, we introduce an auto-documentation (AutoDoc) procedure that infers natural language names and docstrings based on contextual examples of usage. In addition to improving human readability\, we find that AutoDoc boosts performance by helping LILO’s synthesizer to interpret and deploy learned abstractions. We evaluate LILO on three inductive program synthesis benchmarks for string editing\, scene reasoning\, and graphics composition. Compared to existing neural and symbolic methods – including the state-of-the-art library learning algorithm DreamCoder – LILO solves more complex tasks and learns richer libraries that are grounded in linguistic knowledge.
URL:https://cmsa.fas.harvard.edu/event/nt-3624/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-03.06.2024.png
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DTSTART;TZID=America/New_York:20240320T140000
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CREATED:20240130T215041Z
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UID:10001519-1710943200-1710946800@cmsa.fas.harvard.edu
SUMMARY:Solving olympiad geometry without human demonstrations
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Trieu H. Trinh\, Google Deepmind and NYU Dept. of Computer Science \nTitle: Solving olympiad geometry without human demonstrations \nAbstract: Proving mathematical theorems at the olympiad level represents a notable milestone in human-level automated reasoning\, owing to their reputed difficulty among the world’s best talents in pre-university mathematics. Current machine-learning approaches\, however\, are not applicable to most mathematical domains owing to the high cost of translating human proofs into machine-verifiable format. The problem is even worse for geometry because of its unique translation challenges\, resulting in severe scarcity of training data. We propose AlphaGeometry\, a theorem prover for Euclidean plane geometry that sidesteps the need for human demonstrations by synthesizing millions of theorems and proofs across different levels of complexity. AlphaGeometry is a neuro-symbolic system that uses a neural language model\, trained from scratch on our large-scale synthetic data\, to guide a symbolic deduction engine through infinite branching points in challenging problems. On a test set of 30 latest olympiad-level problems\, AlphaGeometry solves 25\, outperforming the previous best method that only solves ten problems and approaching the performance of an average International Mathematical Olympiad (IMO) gold medallist. Notably\, AlphaGeometry produces human-readable proofs\, solves all geometry problems in the IMO 2000 and 2015 under human expert evaluation and discovers a generalized version of a translated IMO theorem in 2004. \n 
URL:https://cmsa.fas.harvard.edu/event/nt-32024/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-03.20.2024.png
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