Related papers: Norm-Based Capacity Control in Neural Networks

The convolutional layers are core building blocks of neural network architectures. In general, a convolutional filter applies to the entire frequency spectrum of the input data. We explore artificially constraining the frequency spectra of…

Convolutional Neural Networks (CNNs) have recently emerged as the dominant model in computer vision. If provided with enough training data, they predict almost any visual quantity. In a discrete setting, such as classification, CNNs are not…

This paper investigates the problem of single-source multicasting over a communication network in the presence of restricted adversaries. When the adversary is constrained to operate only on a prescribed subset of edges, classical cut-set…

We consider the problem of error control in a coded, multicast network, focusing on the scenario where the errors can occur only on a proper subset of the network edges. We model this problem via an adversarial noise, presenting a formal…

Understanding how the test risk scales with model complexity is a central question in machine learning. Classical theory is challenged by the learning curves observed for large over-parametrized deep networks. Capacity measures based on…

For a given stable recurrent neural network (RNN) that is trained to perform a classification task using sequential inputs, we quantify explicit robustness bounds as a function of trainable weight matrices. The sequential inputs can be…

Universal approximation theorems provide a mathematical explanation for the expressive power of neural networks. They assert that, under mild conditions on the activation function, feedforward neural networks are dense in broad function…

This paper discusses the notion of generalization of training samples over long distances in the input space of a feedforward neural network. Such a generalization might occur in various ways, that differ in how great the contribution of…

A key open question in quantum computation is what advantages quantum neural networks (QNNs) may have over classical neural networks (NNs), and in what situations these advantages may transpire. Here we address this question by studying the…

Prior work on neural network verification has focused on specifications that are linear functions of the output of the network, e.g., invariance of the classifier output under adversarial perturbations of the input. In this paper, we extend…

In this paper, we examine an important problem of learning neural networks that certifiably meet certain specifications on input-output behaviors. Our strategy is to find an inner approximation of the set of admissible policy parameters,…

Modern neural networks are highly overparameterized, with capacity to substantially overfit to training data. Nevertheless, these networks often generalize well in practice. It has also been observed that trained networks can often be…

The paper proposes a feed-forward control strategy for mobile robot control that accounts for a non-linear model of the vehicle with interaction between inputs and outputs. It is possible to include specific model uncertainties in the…

The article sets and solves the task to control an error of the artificial neural network with variable signal conductivity. This kind of neural networks was especially developed to construct timetables. Behavior of such a neural network…

Soft-thresholding has been widely used in neural networks. Its basic network structure is a two-layer convolution neural network with soft-thresholding. Due to the network's nature of nonlinearity and nonconvexity, the training process…

Neural network pruning techniques reduce the number of parameters without compromising predicting ability of a network. Many algorithms have been developed for pruning both over-parameterized fully-connected networks (FCNs) and…

Scheduling control problems for a family of unitary networks under heavy traffic with general interarrival and service times, probabilistic routing and an infinite horizon discounted linear holding cost are studied. Diffusion control…

Unknown nonlinear dynamics can limit the performance of model-based feedforward control. The aim of this paper is to develop a feedforward control framework for systems with unknown, typically nonlinear, dynamics. To address the unknown…

The aim of this thesis is to compare the capacity of different models of neural networks. We start by analysing the problem solving capacity of a single perceptron using a simple combinatorial argument. After some observations on the…

Network controllability robustness reflects how well a networked system can maintain its controllability against destructive attacks. Its measure is quantified by a sequence of values that record the remaining controllability of the network…