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DTSTART;TZID=America/New_York:20240214T140000
DTEND;TZID=America/New_York:20240214T150000
DTSTAMP:20260717T100824
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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DTSTART;TZID=America/New_York:20240214T160000
DTEND;TZID=America/New_York:20240214T173000
DTSTAMP:20260717T100824
CREATED:20240212T162016Z
LAST-MODIFIED:20240212T211844Z
UID:10002103-1707926400-1707931800@cmsa.fas.harvard.edu
SUMMARY:Quantum Algebra of Chern-Simons Matrix Model and Large N Limit
DESCRIPTION:Quantum Matter in Mathematics and Physics Seminar \nSpeaker: Sen Hu (Shanghai Institute for Mathematics and Interdisciplinary Study) \nTitle: Quantum Algebra of Chern-Simons Matrix Model and Large N Limit \nAbstract: In this talk we discuss the algebra of quantum observables of the Chern-Simons matrix model which was originally proposed by Susskind and Polychronakos to describe electrons in fractional quantum Hall effects. We establish the commutation relations for its generators and study the large N limit of its representation. We show that the large N limit algebra is isomorphic to the uniform in N algebra studied by Costello\, which is conjecturally isomorphic to the deformed double current algebra studied by Guay. Under appropriate scaling limit\, we show that the large N limit algebra degenerates to a Lie algebra which admits a surjective map to the affine Lie algebra of u(p). This leads to a complete proof of the large N emergence of the u(p) current algebra as proposed by Dorey\, Tong and Turner. This also suggests a rigorous derivation of edge excitation of a fractional quantum Hall droplet. This is a joint work with Si Li\, Dongheng Ye and Yehao Zhou (arXiv: 2308.14046).
URL:https://cmsa.fas.harvard.edu/event/qm-21424/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Matter,Seminars
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-02.14.2024.png
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