相关论文: Learning Discretized Neural Networks under Ricci F…
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…
We study the performance of stochastically trained deep neural networks (DNNs) whose synaptic weights are implemented using emerging memristive devices that exhibit limited dynamic range, resolution, and variability in their programming…
Surprise Adequacy (SA) has been widely studied as a test adequacy metric that can effectively guide software engineers towards inputs that are more likely to reveal unexpected behaviour of Deep Neural Networks (DNNs). Intuitively, SA is an…
Fitting a function by using linear combinations of a large number $N$ of `simple' components is one of the most fruitful ideas in statistical learning. This idea lies at the core of a variety of methods, from two-layer neural networks to…
The development of a reliable subgrid-scale (SGS) model for large-eddy simulation (LES) is of great importance for many scientific and engineering applications. Recently, deep learning approaches have been tested for this purpose using…
A large fraction of the arithmetic operations required to evaluate deep neural networks (DNNs) consists of matrix multiplications, in both convolution and fully connected layers. We perform end-to-end learning of low-cost approximations of…
Deep neural networks (DNNs) provide high image classification accuracy, but experience significant performance degradation when perturbation from various sources are present in the input. The lack of resilience to input perturbations makes…
We present an efficient deep learning technique for the model reduction of the Navier-Stokes equations for unsteady flow problems. The proposed technique relies on the Convolutional Neural Network (CNN) and the stochastic gradient descent…
Linear layers in neural networks (NNs) trained by gradient descent can be expressed as a key-value memory system which stores all training datapoints and the initial weights, and produces outputs using unnormalised dot attention over the…
Deep neural networks (DNNs) have been used to create models for many complex analysis problems like image recognition and medical diagnosis. DNNs are a popular tool within machine learning due to their ability to model complex patterns and…
This paper establishes statistical properties of deep neural network (DNN) estimators under dependent data. Two general results for nonparametric sieve estimators directly applicable to DNN estimators are given. The first establishes rates…
Deep neural networks (DNNs) are vulnerable to adversarial examples and other data perturbations. Especially in safety critical applications of DNNs, it is therefore crucial to detect misclassified samples. The current state-of-the-art…
We revisit the analogy between feed-forward deep neural networks (DNNs) and discrete dynamical systems derived from neural integral equations and their corresponding partial differential equation (PDE) forms. A comparative analysis between…
There has been a significant recent surge in deep neural network (DNN) techniques. Most of the existing DNN techniques have restricted model formats/assumptions. To overcome their limitations, we propose the nonparametric transformation…
In this paper we consider the limiting case of neural networks (NNs) architectures when the number of neurons in each hidden layer and the number of hidden layers tend to infinity thus forming a continuum, and we derive approximation errors…
This work focuses on designing low complexity hybrid tensor networks by considering trade-offs between the model complexity and practical performance. Firstly, we exploit a low-rank tensor-train deep neural network (TT-DNN) to build an…
The widespread use of neural networks across different scientific domains often involves constraining them to satisfy certain symmetries, conservation laws, or other domain knowledge. Such constraints are often imposed as soft penalties…
We propose a partial differential-integral equation (PDE) framework for deep neural networks (DNNs) and their associated learning problem by taking the continuum limits of both network width and depth. The proposed model captures the…
Solving unsteady partial differential equations (PDEs) using recurrent neural networks (RNNs) typically requires numerical derivatives between each block of the RNN to form the physics informed loss function. However, this introduces the…
Large-scale deep neural networks (DNN) have been successfully used in a number of tasks from image recognition to natural language processing. They are trained using large training sets on large models, making them computationally and…