Related papers: Selection dynamics for deep neural networks
We study a discrete-time portfolio selection problem with partial information and maxi\-mum drawdown constraint. Drift uncertainty in the multidimensional framework is modeled by a prior probability distribution. In this Bayesian framework,…
Large-scale recurrent networks have drawn increasing attention recently because of their capabilities in modeling a large variety of real-world phenomena and physical mechanisms. This paper studies how to identify all authentic connections…
Learning solution operators for differential equations with neural networks has shown great potential in scientific computing, but ensuring their stability under input perturbations remains a critical challenge. This paper presents a robust…
To have a superior generalization, a deep learning neural network often involves a large size of training sample. With increase of hidden layers in order to increase learning ability, neural network has potential degradation in accuracy.…
In this paper, we propose a deep learning framework for solving high-dimensional partial integro-differential equations (PIDEs) based on the temporal difference learning. We introduce a set of Levy processes and construct a corresponding…
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…
The choice of initial learning rate can have a profound effect on the performance of deep networks. We present a class of neural networks with solvable training dynamics, and confirm their predictions empirically in practical deep learning…
This paper presents a novel holistic deep learning framework that simultaneously addresses the challenges of vulnerability to input perturbations, overparametrization, and performance instability from different train-validation splits. The…
I provide an introduction to the application of deep learning and neural networks for solving partial differential equations (PDEs). The approach, known as physics-informed neural networks (PINNs), involves minimizing the residual of the…
We propose a novel distributionally robust $Q$-learning algorithm for the non-tabular case accounting for continuous state spaces where the state transition of the underlying Markov decision process is subject to model uncertainty. The…
We consider the problem of learning optimal solutions of a partially known linear optimization problem and recovering its underlying cost function where a set of past decisions and the feasible set are known. We develop a new framework,…
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…
In deep learning, dense layer connectivity has become a key design principle in deep neural networks (DNNs), enabling efficient information flow and strong performance across a range of applications. In this work, we model densely connected…
Learning is a complex dynamical process shaped by a range of interconnected decisions. Careful design of hyperparameter schedules for artificial neural networks or efficient allocation of cognitive resources by biological learners can…
In this paper, a highly parallel and derivative-free martingale neural network learning method is proposed to solve Hamilton-Jacobi-Bellman (HJB) equations arising from stochastic optimal control problems (SOCPs), as well as general…
Continual learning is inherently a constrained learning problem. The goal is to learn a predictor under a no-forgetting requirement. Although several prior studies formulate it as such, they do not solve the constrained problem explicitly.…
This short, self-contained article seeks to introduce and survey continuous-time deep learning approaches that are based on neural ordinary differential equations (neural ODEs). It primarily targets readers familiar with ordinary and…
One of the fundamental challenges in the deep learning community is to theoretically understand how well a deep neural network generalizes to unseen data. However, current approaches often yield generalization bounds that are either too…
The paper presents an efficient and robust data-driven deep learning (DL) computational framework developed for linear continuum elasticity problems. The methodology is based on the fundamentals of the Physics Informed Neural Networks…
Can neural networks learn to solve partial differential equations (PDEs)? We investigate this question for two (systems of) PDEs, namely, the Poisson equation and the steady Navier--Stokes equations. The contributions of this paper are…