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Deep neural networks (DNNs) have become integral to a wide range of scientific and practical applications due to their flexibility and strong predictive performance. Despite their accuracy, however, DNNs frequently exhibit poor calibration,…
An antithetical concept, adaptive symmetry, to conservative symmetry in physics is proposed to understand the deep neural networks (DNNs). It characterizes the invariance of variance, where a biotic system explores different pathways of…
Using spectral decomposition techniques and singular perturbation theory, we develop a systematic method to approximate the prices of a variety of options in a fast mean-reverting stochastic volatility setting. Four examples are provided in…
Deep neural networks (DNNs) are quantized for efficient inference on resource-constrained platforms. However, training deep learning models with low-precision weights and activations involves a demanding optimization task, which calls for…
This article studies deep neural network expression rates for optimal stopping problems of discrete-time Markov processes on high-dimensional state spaces. A general framework is established in which the value function and continuation…
Deep learning is a powerful tool whose applications in quantitative finance are growing every day. Yet, artificial neural networks behave as black boxes and this hinders validation and accountability processes. Being able to interpret the…
We propose Impatient Deep Neural Networks (DNNs) which deal with dynamic time budgets during application. They allow for individual budgets given a priori for each test example and for anytime prediction, i.e., a possible interruption at…
In this article, we investigate the existence of a deep neural network (DNN) capable of approximating solutions to partial integro-differential equations while circumventing the curse of dimensionality. Using the Feynman-Kac theorem, we…
Safety concerns on the deep neural networks (DNNs) have been raised when they are applied to critical sectors. In this paper, we define safety risks by requesting the alignment of the network's decision with human perception. To enable a…
Weighted model counting (WMC) has emerged as a prevalent approach for probabilistic inference. In its most general form, WMC is #P-hard. Weighted DNF counting (weighted #DNF) is a special case, where approximations with probabilistic…
In this work, we focus on variational Bayesian inference on the sparse Deep Neural Network (DNN) modeled under a class of spike-and-slab priors. Given a pre-specified sparse DNN structure, the corresponding variational posterior contraction…
This paper considers deep neural networks for learning weakly dependent processes in a general framework that includes, for instance, regression estimation, time series prediction, time series classification. The $\psi$-weak dependence…
Complex design problems are common in the scientific and industrial fields. In practice, objective functions or constraints of these problems often do not have explicit formulas, and can be estimated only at a set of sampling points through…
Advances in deep neural network (DNN) based molecular property prediction have recently led to the development of models of remarkable accuracy and generalization ability, with graph convolution neural networks (GCNNs) reporting…
In the past decade, deep neural networks (DNNs) came to the fore as the leading machine learning algorithms for a variety of tasks. Their raise was founded on market needs and engineering craftsmanship, the latter based more on trial and…
Extracting implied information, like volatility and/or dividend, from observed option prices is a challenging task when dealing with American options, because of the computational costs needed to solve the corresponding mathematical problem…
We study the problem of approximating and estimating classification functions that have their decision boundary in the $RBV^2$ space. Functions of $RBV^2$ type arise naturally as solutions of regularized neural network learning problems and…
This study evaluates deep neural networks for forecasting probability distributions of financial returns. 1D convolutional neural networks (CNN) and Long Short-Term Memory (LSTM) architectures are used to forecast parameters of three…
Deep neural networks (DNNs) have achieved remarkable success in numerous domains, and their application to PDE-related problems has been rapidly advancing. This paper provides an estimate for the generalization error of learning Lipschitz…
Deep neural networks (DNN) has received increasing attention in machine learning applications in the last several years. Recently, a non-asymptotic error bound has been developed to measure the performance of the fully connected DNN…