相关论文: Towards Theoretical Analysis of Transformation Com…

This paper aims to define, quantify, and analyze the feature complexity that is learned by a DNN. We propose a generic definition for the feature complexity. Given the feature of a certain layer in the DNN, our method disentangles feature…

Understanding the computational complexity of training simple neural networks with rectified linear units (ReLUs) has recently been a subject of intensive research. Closing gaps and complementing results from the literature, we present…

We define the local complexity of a neural network with continuous piecewise linear activations as a measure of the density of linear regions over an input data distribution. We show theoretically that ReLU networks that learn…

Studying the invertibility of deep neural networks (DNNs) provides a principled approach to better understand the behavior of these powerful models. Despite being a promising diagnostic tool, a consistent theory on their invertibility is…

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…

We study neural network training (NNT): optimizing a neural network's parameters to minimize the training loss over a given dataset. NNT has been studied extensively under theoretic lenses, mainly on two-layer networks with linear or ReLU…

Each year, deep learning demonstrates new and improved empirical results with deeper and wider neural networks. Meanwhile, with existing theoretical frameworks, it is difficult to analyze networks deeper than two layers without resorting to…

In this paper, we interpret Deep Neural Networks with Complex Network Theory. Complex Network Theory (CNT) represents Deep Neural Networks (DNNs) as directed weighted graphs to study them as dynamical systems. We efficiently adapt CNT…

Based on its great successes in inference and denosing tasks, Dictionary Learning (DL) and its related sparse optimization formulations have garnered a lot of research interest. While most solutions have focused on single layer…

We consider the computational complexity of training depth-2 neural networks composed of rectified linear units (ReLUs). We show that, even for the case of a single ReLU, finding a set of weights that minimizes the squared error (even…

This paper presents a method to explain how the information of each input variable is gradually discarded during the forward propagation in a deep neural network (DNN), which provides new perspectives to explain DNNs. We define two types of…

Despite the tremendous successes of deep neural networks (DNNs) in various applications, many fundamental aspects of deep learning remain incompletely understood, including DNN trainability. In a trainability study, one aims to discern what…

The vulnerability to slight input perturbations is a worrying yet intriguing property of deep neural networks (DNNs). Despite many previous works studying the reason behind such adversarial behavior, the relationship between the…

Adversarial training is a widely-applied approach to training deep neural networks to be robust against adversarial perturbation. However, although adversarial training has achieved empirical success in practice, it still remains unclear…

In this paper, we evaluate the quality of knowledge representations encoded in deep neural networks (DNNs) for 3D point cloud processing. We propose a method to disentangle the overall model vulnerability into the sensitivity to the…

On account of its many successes in inference tasks and denoising applications, Dictionary Learning (DL) and its related sparse optimization problems have garnered a lot of research interest. While most solutions have focused on single…

Deep neural networks (DNNs), particularly those using Rectified Linear Unit (ReLU) activation functions, have achieved remarkable success across diverse machine learning tasks, including image recognition, audio processing, and language…

Representation learning, i.e. the generation of representations useful for downstream applications, is a task of fundamental importance that underlies much of the success of deep neural networks (DNNs). Recently, robustness to adversarial…

Adversarial examples, or nearly indistinguishable inputs created by an attacker, significantly reduce machine learning accuracy. Theoretical evidence has shown that the high intrinsic dimensionality of datasets facilitates an adversary's…

We derive upper bounds on the complexity of ReLU neural networks approximating the solution of a linear system given the matrix and the right-hand side. We focus on matrices which are symmetric positive definite and sparse, as they appear…