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We show the existence of a deep neural network capable of approximating a wide class of high-dimensional approximations. The construction of the proposed neural network is based on a quasi-optimal polynomial approximation. We show that this…
Training a neural network using backpropagation algorithm requires passing error gradients sequentially through the network. The backward locking prevents us from updating network layers in parallel and fully leveraging the computing…
Deep reinforcement learning (DRL) has recently shown its success in tackling complex combinatorial optimization problems. When these problems are extended to multiobjective ones, it becomes difficult for the existing DRL approaches to…
In recent years, the connections between deep residual networks and first-order Ordinary Differential Equations (ODEs) have been disclosed. In this work, we further bridge the deep neural architecture design with the second-order ODEs and…
The success of deep learning has inspired recent interests in applying neural networks in statistical inference. In this paper, we investigate the use of deep neural networks for nonparametric regression with measurement errors. We propose…
Data point selection (DPS) is becoming a critical topic in deep learning due to the ease of acquiring uncurated training data compared to the difficulty of obtaining curated or processed data. Existing approaches to DPS are predominantly…
Neural networks with binary weights are computation-efficient and hardware-friendly, but their training is challenging because it involves a discrete optimization problem. Surprisingly, ignoring the discrete nature of the problem and using…
When using Neural Networks as trial functions to numerically solve PDEs, a key choice to be made is the loss function to be minimised, which should ideally correspond to a norm of the error. In multiple problems, this error norm coincides…
Deep neural networks are prone to overconfident predictions on outliers. Bayesian neural networks and deep ensembles have both been shown to mitigate this problem to some extent. In this work, we aim to combine the benefits of the two…
In this work, we propose a novel cross Q-learning algorithm, aim at alleviating the well-known overestimation problem in value-based reinforcement learning methods, particularly in the deep Q-networks where the overestimation is exaggerated…
With the prosperity of mobile devices, the distributed learning approach enabling model training with decentralized data has attracted wide research. However, the lack of training capability for edge devices significantly limits the energy…
We present a novel approach for training deep neural networks in a Bayesian way. Classical, i.e. non-Bayesian, deep learning has two major drawbacks both originating from the fact that network parameters are considered to be deterministic.…
We address the challenging problem of deep representation learning--the efficient adaption of a pre-trained deep network to different tasks. Specifically, we propose to explore gradient-based features. These features are gradients of the…
We present in this paper a model for forecasting short-term power loads based on deep residual networks. The proposed model is able to integrate domain knowledge and researchers' understanding of the task by virtue of different neural…
Neural Ordinary Differential Equations (Neural ODEs) represent a significant breakthrough in deep learning, promising to bridge the gap between machine learning and the rich theoretical frameworks developed in various mathematical fields…
This paper develops algorithms for high-dimensional stochastic control problems based on deep learning and dynamic programming. Unlike classical approximate dynamic programming approaches, we first approximate the optimal policy by means of…
Recent research on deep neural networks (DNNs) has primarily focused on improving the model accuracy. Given a proper deep learning framework, it is generally possible to increase the depth or layer width to achieve a higher level of…
Estimation of a regression function from independent and identically distributed random variables is considered. The $L_2$ error with integration with respect to the design measure is used as an error criterion. Over-parametrized deep…
Deep neural networks demonstrate to have a high performance on image classification tasks while being more difficult to train. Due to the complexity and vanishing gradient problem, it normally takes a lot of time and more computational…
The Finite Element Method (FEM) is a well-established procedure for computing approximate solutions to deterministic engineering problems described by partial differential equations. FEM produces discrete approximations of the solution with…