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DTSTART;TZID=America/New_York:20241007T163000
DTEND;TZID=America/New_York:20241007T173000
DTSTAMP:20260519T202356
CREATED:20240903T194924Z
LAST-MODIFIED:20241003T160128Z
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SUMMARY:Local complexity measures in modern parameterized function classes for supervised learning
DESCRIPTION:Colloquium \nSpeaker: Elisenda Grigsby\, Boston College \nTitle: Local complexity measures in modern parameterized function classes for supervised learning \nAbstract: The parameter space for any fixed architecture of neural networks serves as a proxy during training for the associated class of functions – but how faithful is this representation? For any fixed feedforward ReLU network architecture\, it is well-known that many different parameter settings can determine the same function. It is less well-known that the degree of this redundancy is inhomogeneous across parameter space. I’ll discuss two locally-applicable complexity measures for ReLU network classes and what we know about the relationship between them: (1) the local functional dimension\, and (2) a local version of VC dimension called persistent pseudodimension. The former is easy to compute on finite batches of points\, the latter should give local bounds on the generalization gap. I’ll speculate about how this circle of ideas might help guide our understanding of the double descent phenomenon. All of the work described in this talk is joint with Kathryn Lindsey. Some portions are also joint with Rob Meyerhoff\, David Rolnick\, and Chenxi Wu.
URL:https://cmsa.fas.harvard.edu/event/colloquium-10724/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=application/pdf:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-10.7.2024.docx.pdf
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DTSTART;TZID=America/New_York:20241021T163000
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CREATED:20240903T195022Z
LAST-MODIFIED:20241016T144838Z
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SUMMARY:Higher Vapnik–Chervonenkis theory
DESCRIPTION:Colloquium \nSpeaker: Artem Chernikov\, University of Maryland \nTitle: Higher Vapnik–Chervonenkis theory \nAbstract: Finite VC-dimension\, a combinatorial property of families of sets\, was discovered simultaneously by Vapnik and Chervonenkis in probabilistic learning theory\, and by Shelah in model theory (where it is called NIP). It plays an important role in several areas including machine learning\, combinatorics\, mathematical logic\, functional analysis and topological dynamics. We develop aspects of higher-order VC-theory\, in particular establishing a generalization of the epsilon-net theorem for families of sets (and functions) on n-fold product spaces with bounded VC_n-dimension (i.e. there is a bound on the sizes of n-dimensional boxes that can be shattered). We obtain some applications in combinatorics and in model theory\, including a strong version of Szemerdi’s regularity lemma for hypergraphs omitting a fixed finite n-partite n-hypergraph. Joint work with Henry Towsner.
URL:https://cmsa.fas.harvard.edu/event/colloquium-102124/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-10.21.2024.png
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