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Hierarchical data structures through the lenses of diffusion models

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

https://youtu.be/x7LPDDYZn94 New Technologies in Mathematics Seminar Speaker: Antonio Sclocchi, EPFL Title: Hierarchical data structures through the lenses of diffusion models Abstract: The success of deep learning with high-dimensional data relies on the fact that natural data are highly structured. A key aspect of this structure is hierarchical compositionality, yet quantifying it remains a challenge. In […]

Event Series Mathematical Physics and Algebraic Geometry Seminar

Enumerative geometry and modularity in two-modulus K3-fibered Calabi-Yau threefolds

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

Mathematical Physics and Algebraic Geometry Seminar Speaker: Chuck Doran, Harvard CMSA Title: Enumerative geometry and modularity in two-modulus K3-fibered Calabi-Yau threefolds Abstract: Smooth $M_m$-polarized K3-fibered Calabi-Yau (CY) 3-folds have been classified in terms of the choice of a generalized functional invariant and, in the case $m=1$, a generalized homological invariant. The resulting geometries generally exhibit […]

Holography and Regge Phases at Large U(1) Charge

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

Quantum Field Theory and Physical Mathematics Seminar Speaker: Giulia Fardelli, Boston University Title: Holography and Regge Phases at Large U(1) Charge Abstract: A single Conformal Field Theory (CFT) can have a rich phase diagram with qualitatively different emergent behaviors in a range of different regimes parameterized by the conserved charges of the theory. In this […]

High-dimensional learning of narrow neural networks

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

Member Seminar Speaker: Hugo Cui, CMSA Title: High-dimensional learning of narrow neural networks Abstract: This talk explores the interplay between neural network architectures and data structure through the lens of high-dimensional asymptotics. We focus on a class of narrow neural networks, namely networks possessing a finite number of hidden units, while operating in high dimensions. In the […]

Local complexity measures in modern parameterized function classes for supervised learning

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

Colloquium Speaker: Elisenda Grigsby, Boston College Title: Local complexity measures in modern parameterized function classes for supervised learning Abstract: 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 […]

Continuation of solutions of Einstein’s equations

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

General Relativity Seminar Speaker: Oswaldo Vazquez, Northeastern University Title: Continuation of solutions of Einstein's equations Abstract: Klainerman-Rodnianski improved the continuation criterion for the solutions of Einstein's equations proved by Michael Anderson using Kirchoff-Sobolev type parametrix and geometric Littlewood-Paley theory. Using their technique but a new parametrix we prove a continuation condition in the context of […]

Topics in Deep Learning Theory

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

Topics in Deep Learning Theory Eli Grigsby

Skein traces and curve counting

Science Center Hall E 1 Oxford Street, Cambridge, MA, United States

Geometry and Quantum Theory Seminar Speaker: Sunghyuk Park, Harvard CMSA Title: Skein traces and curve counting Abstract: Skein modules are vector space-valued invariants of 3-manifolds describing the space of line defects modulo skein relations (determined by a choice of a ribbon category). When the 3-manifold is S x I for some surface S, the skein […]