7 papers · 1 filter
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…
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.…
Mean Field Analysis of Neural Networks: A Central Limit Theorem
Justin Sirignano, Konstantinos Spiliopoulos
We rigorously prove a central limit theorem for neural network models with a single hidden layer. The central limit theorem is proven in the asymptotic regime of simultaneously (A)…
Importance sampling for slow-fast diffusions based on moderate deviations
Matthew R. Morse, Konstantinos Spiliopoulos
We consider systems of slow--fast diffusions with small noise in the slow component. We construct provably logarithmic asymptotically optimal importance schemes for the estimation…
Mean Field Analysis of Neural Networks: A Law of Large Numbers
Justin Sirignano, Konstantinos Spiliopoulos
Machine learning, and in particular neural network models, have revolutionized fields such as image, text, and speech recognition. Today, many important real-world applications in…