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08/28/2023
Kernel Limit of Recurrent Neural Networks Trained on Ergodic Data Sequences
Mathematical methods are developed to characterize the asymptotics of re...
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02/14/2023
Transport map unadjusted Langevin algorithms
Langevin dynamics are widely used in sampling high-dimensional, non-Gaus...
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09/02/2022
Normalization effects on deep neural networks
We study the effect of normalization on the layers of deep neural networ...
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06/01/2022
Importance sampling for stochastic reaction-diffusion equations in the moderate deviation regime
We develop a provably efficient importance sampling scheme that estimate...
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09/27/2021
Disentangling positive and negative partisanship in affective polarization using a coevolving latent space network with attractors model
We develop a broadly applicable class of coevolving latent space network...
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08/18/2021
Geometry-informed irreversible perturbations for accelerated convergence of Langevin dynamics
We introduce a novel geometry-informed irreversible perturbation that ac...
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05/18/2021
PDE-constrained Models with Neural Network Terms: Optimization and Global Convergence
Recent research has used deep learning to develop partial differential e...
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11/20/2020
Normalization effects on shallow neural networks and related asymptotic expansions
We consider shallow (single hidden layer) neural networks and characteri...
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07/22/2020
Discrete-time inference for slow-fast systems driven by fractional Brownian motion
We study statistical inference for small-noise-perturbed multiscale dyna...
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11/13/2019
Asymptotics of Reinforcement Learning with Neural Networks
We prove that a single-layer neural network trained with the Q-learning ...
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07/09/2019
Scaling Limit of Neural Networks with the Xavier Initialization and Convergence to a Global Minimum
We analyze single-layer neural networks with the Xavier initialization i...
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03/11/2019
Mean Field Analysis of Deep Neural Networks
We analyze multi-layer neural networks in the asymptotic regime of simul...
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12/05/2018
Information geometry for approximate Bayesian computation
The goal of this paper is to explore the basic Approximate Bayesian Comp...
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08/28/2018
Mean Field Analysis of Neural Networks: A Central Limit Theorem
Machine learning has revolutionized fields such as image, text, and spee...
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05/25/2018
Importance sampling for slow-fast diffusions based on moderate deviations
We consider systems of slow-fast diffusions with small noise in the slow...
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10/11/2017
Stochastic Gradient Descent in Continuous Time: A Central Limit Theorem
Stochastic gradient descent in continuous time (SGDCT) provides a comput...
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08/24/2017
DGM: A deep learning algorithm for solving partial differential equations
High-dimensional PDEs have been a longstanding computational challenge. ...
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11/17/2016
