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06/27/2023
Coupling parameter and particle dynamics for adaptive sampling in Neural Galerkin schemes
Training nonlinear parametrizations such as deep neural networks to nume...
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05/30/2023
Efficient Training of Energy-Based Models Using Jarzynski Equality
Energy-based models (EBMs) are generative models inspired by statistical...
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03/15/2023
Stochastic Interpolants: A Unifying Framework for Flows and Diffusions
We introduce a class of generative models based on the stochastic interp...
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10/28/2022
A Functional-Space Mean-Field Theory of Partially-Trained Three-Layer Neural Networks
To understand the training dynamics of neural networks (NNs), prior stud...
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09/30/2022
Building Normalizing Flows with Stochastic Interpolants
A simple generative model based on a continuous-time normalizing flow be...
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06/24/2022
Learning sparse features can lead to overfitting in neural networks
It is widely believed that the success of deep networks lies in their ab...
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06/20/2022
Learning Optimal Flows for Non-Equilibrium Importance Sampling
Many applications in computational sciences and statistical inference re...
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06/09/2022
Probability flow solution of the Fokker-Planck equation
The method of choice for integrating the time-dependent Fokker-Planck eq...
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04/22/2022
On Feature Learning in Neural Networks with Global Convergence Guarantees
We study the optimization of wide neural networks (NNs) via gradient flo...
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03/02/2022
Neural Galerkin Scheme with Active Learning for High-Dimensional Evolution Equations
Machine learning methods have been shown to give accurate predictions in...
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11/29/2021
Estimating earthquake-induced tsunami inundation probabilities without sampling
Given a distribution of earthquake-induced seafloor elevations, we prese...
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07/16/2021
Efficient Bayesian Sampling Using Normalizing Flows to Assist Markov Chain Monte Carlo Methods
Normalizing flows can generate complex target distributions and thus sho...
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07/11/2021
Dual Training of Energy-Based Models with Overparametrized Shallow Neural Networks
Energy-based models (EBMs) are generative models that are usually traine...
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04/15/2021
On Energy-Based Models with Overparametrized Shallow Neural Networks
Energy-based models (EBMs) are a simple yet powerful framework for gener...
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08/21/2020
A Dynamical Central Limit Theorem for Shallow Neural Networks
Recent theoretical work has characterized the dynamics of wide shallow n...
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08/11/2020
Learning with rare data: Using active importance sampling to optimize objectives dominated by rare events
Deep neural networks, when optimized with sufficient data, provide accur...
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07/28/2020
Extreme event probability estimation using PDE-constrained optimization and large deviation theory, with application to tsunamis
We propose and compare methods for the estimation of extreme event proba...
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06/27/2020
Optimization and Generalization of Shallow Neural Networks with Quadratic Activation Functions
We study the dynamics of optimization and the generalization properties ...
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02/05/2019
Global convergence of neuron birth-death dynamics
Neural networks with a large number of parameters admit a mean-field des...
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09/13/2018
Simulated Tempering Method in the Infinite Switch Limit with Adaptive Weight Learning
We investigate the theoretical foundations of the simulated tempering me...
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05/02/2018
Neural networks as Interacting Particle Systems: Asymptotic convexity of the Loss Landscape and Universal Scaling of the Approximation Error
Neural networks, a central tool in machine learning, have demonstrated r...
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12/19/2017