Stochastic gradient descent (SGD) is one of the most popular algorithms in modern machine
learning. The noise encountered in these applications is different from that in many …

This paper develops a new neural network architecture for modeling spatial distributions (ie
distributions on R d) which is more computationally efficient than a traditional fully …

Abstract We prove the Fast Equilibrium Conjecture proposed by Li et al.,(2020), ie,
stochastic gradient descent (SGD) on a scale-invariant loss (eg, using networks with various …

We present a neural network based calibration method that performs the calibration task
within a few milliseconds for the full implied volatility surface. The framework is consistently …

In this book, we study stochastic volatility models and methods of pricing, hedging, and
estimation. Among models, we will study models with heavy tails and long memory or long …

The stochastic gradient descent (SGD) algorithm is the algorithm we use to train neural
networks. However, it remains poorly understood how the SGD navigates the highly …

Stochastic gradient descent is an optimisation method that combines classical gradient
descent with random subsampling within the target functional. In this work, we introduce the …

Stochastic gradient descent (SGD) optimization algorithms are key ingredients in a series of
machine learning applications. In this article we perform a rigorous strong error analysis for …

Stochastic approximation (SA) and stochastic gradient descent (SGD) algorithms are work-
horses for modern machine learning algorithms. Their constant stepsize variants are …

Diffusion approximation provides weak approximation for stochastic gradient descent
algorithms in a finite time horizon. In this paper, we introduce new tools motivated by the …