Related papers: Convergence of Deep Neural Networks with General A…
We establish in this work approximation results of deep neural networks for smooth functions measured in Sobolev norms, motivated by recent development of numerical solvers for partial differential equations using deep neural networks. {Our…
Convex relaxations are a key component of training and certifying provably safe neural networks. However, despite substantial progress, a wide and poorly understood accuracy gap to standard networks remains, raising the question of whether…
In the present study, we investigate a universality of neural networks, which concerns a density of the set of two-layer neural networks in a function spaces. There are many works that handle the convergence over compact sets. In the…
Despite the unresolved 'dying ReLU problem', the classical ReLU activation function (AF) has been extensively applied in Deep Neural Networks (DNN), in particular Convolutional Neural Networks (CNN), for image classification. The common…
Rectified Linear Units (ReLU) are the default choice for activation functions in deep neural networks. While they demonstrate excellent empirical performance, ReLU activations can fall victim to the dead neuron problem. In these cases, the…
In the desire to quantify the success of neural networks in deep learning and other applications, there is a great interest in understanding which functions are efficiently approximated by the outputs of neural networks. By now, there…
Understanding theoretical properties of deep and locally connected nonlinear network, such as deep convolutional neural network (DCNN), is still a hard problem despite its empirical success. In this paper, we propose a novel theoretical…
We study the approximation of two-layer compositions $f(x) = g(\phi(x))$ via deep networks with ReLU activation, where $\phi$ is a geometrically intuitive, dimensionality reducing feature map. We focus on two intuitive and practically…
We study the complexity of functions computable by deep feedforward neural networks with piecewise linear activations in terms of the symmetries and the number of linear regions that they have. Deep networks are able to sequentially map…
We propose the Hyperbolic Tangent Exponential Linear Unit (TeLU), a neural network hidden activation function defined as TeLU(x)=xtanh(exp(x)). TeLU's design is grounded in the core principles of key activation functions, achieving strong…
Deep learning has been widely used in many fields, but the model training process usually consumes massive computational resources and time. Therefore, designing an efficient neural network training method with a provable convergence…
We discuss approximation of functions using deep neural nets. Given a function $f$ on a $d$-dimensional manifold $\Gamma \subset \mathbb{R}^m$, we construct a sparsely-connected depth-4 neural network and bound its error in approximating…
Recent findings suggest that consecutive layers of neural networks with the ReLU activation function \emph{fold} the input space during the learning process. While many works hint at this phenomenon, an approach to quantify the folding was…
Modern neural networks have been successful in many regression-based tasks such as face recognition, facial landmark detection, and image generation. In this work, we investigate an intuitive but understudied characteristic of modern neural…
Neuron death is a complex phenomenon with implications for model trainability: the deeper the network, the lower the probability of finding a valid initialization. In this work, we derive both upper and lower bounds on the probability that…
Researchers have proposed various activation functions. These activation functions help the deep network to learn non-linear behavior with a significant effect on training dynamics and task performance. The performance of these activations…
In many numerical simulations stochastic gradient descent (SGD) type optimization methods perform very effectively in the training of deep neural networks (DNNs) but till this day it remains an open problem of research to provide a…
Deep ReLU neural networks admit nontrivial functional symmetries: vastly different architectures and parameters (weights and biases) can realize the same function. We address the complete identification problem -- given a function f,…
Depth prediction plays a key role in understanding a 3D scene. Several techniques have been developed throughout the years, among which Convolutional Neural Network has recently achieved state-of-the-art performance on estimating depth from…
Deep Reinforcement Learning (RL) powered by neural net approximation of the Q function has had enormous empirical success. While the theory of RL has traditionally focused on linear function approximation (or eluder dimension) approaches,…