2.3k citations · 2.7k across the 51 of their papers we have counts for
6 papers · 1 filter
Asymptotics of Reinforcement Learning with Neural Networks
Justin Sirignano, Konstantinos Spiliopoulos
We prove that a single-layer neural network trained with the Q-learning algorithm converges in distribution to a random ordinary differential equation as the size of the model and…
Scaling Limit of Neural Networks with the Xavier Initialization and Convergence to a Global Minimum
Justin Sirignano, Konstantinos Spiliopoulos
We analyze single-layer neural networks with the Xavier initialization in the asymptotic regime of large numbers of hidden units and large numbers of stochastic gradient descent tr…
Typical dynamics and fluctuation analysis of slow-fast systems driven by fractional Brownian motion
Solesne Bourguin, Siragan Gailus, Konstantinos Spiliopoulos
This article studies typical dynamics and fluctuations for a slow-fast dynamical system perturbed by a small fractional Brownian noise. Based on an ergodic theorem with explicit ra…
Selection of quasi-stationary states in the stochastically forced Navier-Stokes equation on the torus
Margaret Beck, Eric Cooper, Gabriel Lord +1
The stochastically forced vorticity equation associated with the two dimensional incompressible Navier-Stokes equation on is considered for …
Metastability and exit problems for systems of stochastic reaction-diffusion equations
Michael Salins, Konstantinos Spiliopoulos
In this paper we develop a metastability theory for a class of stochastic reaction-diffusion equations exposed to small multiplicative noise. We consider the case where the unpertu…
Mean Field Analysis of Deep Neural Networks
Justin Sirignano, Konstantinos Spiliopoulos
We analyze multi-layer neural networks in the asymptotic regime of simultaneously (A) large network sizes and (B) large numbers of stochastic gradient descent training iterations.…