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DTSTART;TZID=America/New_York:20240207T130000
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DTSTAMP:20240207T220617Z
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SUMMARY:Large language models\, mathematical discovery\, and search in the space of strategies: an anecdote
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Jordan Ellenberg (UW Madison) \nTitle: Large language models\, mathematical discovery\, and search in the space of strategies: an anecdote \nAbstract: I spent a portion of 2023 working with a team at DeepMind on the “cap set problem” – how large can a subset of (Z/3Z)^n be which contains no three terms which sum to zero? (I will explain\, for those not familiar with this problem\, something about the role it plays in combinatorics\, its history\, and why number theorists care about it a lot.) By now\, there are many examples of machine learning mechanisms being used to help generate interesting mathematical knowledge\, and especially interesting examples. This project used a novel protocol; instead of searching directly for large cap sets\, we used LLMs trained on code to search the space of short programs for those which\, when executed\, output large cap sets. One advantage is that a program is much more human-readable than a large collection of vectors over Z/3Z\, bringing us closer to the not-very-well-defined-but-important goal of “interpretable machine learning.” I’ll talk about what succeeded in this project (more than I expected!) what didn’t\, and what role I can imagine this approach to the math-ML interface playing in near-future mathematical practice. \nThe paper: https://www.nature.com/articles/s41586-023-06924-6 \n 
URL:https://cmsa.fas.harvard.edu/event/nt2724/
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-02.07.24.png
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240214T140000
DTEND;TZID=America/New_York:20240214T150000
DTSTAMP:20240130T194619Z
CREATED:20240102T164110Z
LAST-MODIFIED:20240130T194619Z
UID:10000151-1707919200-1707922800@cmsa.fas.harvard.edu
SUMMARY:What Algorithms can Transformers Learn? A Study in Length Generalization
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Preetum Nakkiran\, Apple \nTitle: What Algorithms can Transformers Learn? A Study in Length Generalization \nAbstract: Large language models exhibit many surprising “out-of-distribution” generalization abilities\, yet also struggle to solve certain simple tasks like decimal addition. To clarify the scope of Transformers’ out-of-distribution generalization\, we isolate this behavior in a specific controlled setting: length-generalization on algorithmic tasks. Eg: Can a model trained on 10 digit addition generalize to 50 digit addition? For which tasks do we expect this to work? \nOur key tool is the recently-introduced RASP language (Weiss et al 2021)\, which is a programming language tailor-made for the Transformer’s computational model. We conjecture\, informally\, that: Transformers tend to length-generalize on a task if there exists a short RASP program that solves the task for all input lengths. This simple conjecture remarkably captures most known instances of length generalization on algorithmic tasks\, and can also inform design of effective scratchpads. Finally\, on the theoretical side\, we give a simple separating example between our conjecture and the “min-degree-interpolator” model of learning from Abbe et al. (2023). \nJoint work with Hattie Zhou\, Arwen Bradley\, Etai Littwin\, Noam Razin\, Omid Saremi\, Josh Susskind\, and Samy Bengio. To appear in ICLR 2024. \n 
URL:https://cmsa.fas.harvard.edu/event/nt21424/
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-02.14.2024.png
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240221T140000
DTEND;TZID=America/New_York:20240221T150000
DTSTAMP:20240223T152643Z
CREATED:20240105T034012Z
LAST-MODIFIED:20240223T152643Z
UID:10001113-1708524000-1708527600@cmsa.fas.harvard.edu
SUMMARY:Computers and mathematics in partial differential equations: New developments and challenges
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Javier Gomez Serrano\, Brown University \nTitle: Computers and mathematics in partial differential equations: new developments and challenges \nAbstract: In this talk I will address the interaction between traditional and more modern mathematics and how computers have helped over the last decade providing rigorous (computer-assisted) proofs in the context of partial differential equations. I will also describe new exciting future directions in the field. No background is assumed.
URL:https://cmsa.fas.harvard.edu/event/nt-22124/
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-02.21.2024.png
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