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06/05/2023
Convex Relaxation for Fokker-Planck
We propose an approach to directly estimate the moments or marginals for...
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11/28/2022
Stochastic Steffensen method
Is it possible for a first-order method, i.e., only first derivatives al...
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11/25/2022
LU decomposition and Toeplitz decomposition of a neural network
It is well-known that any matrix A has an LU decomposition. Less well-kn...
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09/29/2022
Generalized matrix nearness problems
We show that the global minimum solution of ‖ A - BXC ‖ can be found in ...
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05/15/2022
What is an equivariant neural network?
We explain equivariant neural networks, a notion underlying breakthrough...
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06/15/2021
Tensors in computations
The notion of a tensor captures three great ideas: equivariance, multili...
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11/01/2020
Distances between probability distributions of different dimensions
Comparing probability distributions is an indispensable and ubiquitous t...
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06/02/2020
Recht-Ré Noncommutative Arithmetic-Geometric Mean Conjecture is False
Stochastic optimization algorithms have become indispensable in modern m...
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04/13/2020
Topology of deep neural networks
We study how the topology of a data set M = M_a ∪ M_b ⊆R^d, representing...
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03/16/2020
Symmetric Grothendieck inequality
We establish an analogue of the Grothendieck inequality where the rectan...
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07/02/2019
Best k-layer neural network approximations
We investigate the geometry of the empirical risk minimization problem f...
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12/18/2018
Semi-Riemannian Manifold Optimization
We introduce in this paper a manifold optimization framework that utiliz...
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05/18/2018
Tropical Geometry of Deep Neural Networks
We establish, for the first time, connections between feedforward neural...
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11/13/2017
Grothendieck constant is norm of Strassen matrix multiplication tensor
We show that two important quantities from two disparate areas of comple...
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10/31/2017
Macroeconomics and FinTech: Uncovering Latent Macroeconomic Effects on Peer-to-Peer Lending
Peer-to-peer (P2P) lending is a fast growing financial technology (FinTe...
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04/05/2016
Cohomology of Cryo-Electron Microscopy
The goal of cryo-electron microscopy (EM) is to reconstruct the 3-dimens...
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11/07/2008