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Convolutional neural networks have been successful in solving many socially important and economically significant problems. This ability to learn complex high-dimensional functions hierarchically can be attributed to the use of nonlinear…

An emerging design principle in deep learning is that each layer of a deep artificial neural network should be able to easily express the identity transformation. This idea not only motivated various normalization techniques, such as…

Pruning of deep neural networks has been an effective technique for reducing model size while preserving most of the performance of dense networks, crucial for deploying models on memory and power-constrained devices. While recent sparse…

This note provides a family of classification problems, indexed by a positive integer $k$, where all shallow networks with fewer than exponentially (in $k$) many nodes exhibit error at least $1/6$, whereas a deep network with 2 nodes in…

One fundamental problem in deep learning is understanding the outstanding performance of deep Neural Networks (NNs) in practice. One explanation for the superiority of NNs is that they can realize a large class of complicated functions,…

Deep spiking neural networks (SNNs) offer the promise of low-power artificial intelligence. However, training deep SNNs from scratch or converting deep artificial neural networks to SNNs without loss of performance has been a challenge.…

We develop exact representations of training two-layer neural networks with rectified linear units (ReLUs) in terms of a single convex program with number of variables polynomial in the number of training samples and the number of hidden…

Activation functions play a pivotal role in the function learning using neural networks. The non-linearity in the learned function is achieved by repeated use of the activation function. Over the years, numerous activation functions have…

We present a novel algorithm for training deep neural networks in supervised (classification and regression) and unsupervised (reinforcement learning) scenarios. This algorithm combines the standard stochastic gradient descent and the…

The ability of neural networks to provide `best in class' approximation across a wide range of applications is well-documented. Nevertheless, the powerful expressivity of neural networks comes to naught if one is unable to effectively train…

The Rectified Power Unit (RePU) activation function, a differentiable generalization of the Rectified Linear Unit (ReLU), has shown promise in constructing neural networks due to its smoothness properties. However, deep RePU networks often…

We analyze the convergence of (stochastic) gradient descent algorithm for learning a convolutional filter with Rectified Linear Unit (ReLU) activation function. Our analysis does not rely on any specific form of the input distribution and…

Activation function has a significant impact on the dynamics, convergence, and performance of deep neural networks. The search for a consistent and high-performing activation function has always been a pursuit during deep learning model…

We give the first dimension-efficient algorithms for learning Rectified Linear Units (ReLUs), which are functions of the form $\mathbf{x} \mapsto \max(0, \mathbf{w} \cdot \mathbf{x})$ with $\mathbf{w} \in \mathbb{S}^{n-1}$. Our algorithm…

ReLU, a commonly used activation function in deep neural networks, is prone to the issue of "Dying ReLU". Several enhanced versions, such as ELU, SeLU, and Swish, have been introduced and are considered to be less commonly utilized.…

Activation functions are essential for deep learning methods to learn and perform complex tasks such as image classification. Rectified Linear Unit (ReLU) has been widely used and become the default activation function across the deep…

As the emerging field of machine learning, deep learning shows excellent ability in solving complex learning problems. However, the size of the networks becomes increasingly large scale due to the demands of the practical applications,…

Neural networks trained to minimize the logistic (a.k.a. cross-entropy) loss with gradient-based methods are observed to perform well in many supervised classification tasks. Towards understanding this phenomenon, we analyze the training…

We consider the problem of learning an unknown ReLU network with respect to Gaussian inputs and obtain the first nontrivial results for networks of depth more than two. We give an algorithm whose running time is a fixed polynomial in the…

The paper briefy reviews several recent results on hierarchical architectures for learning from examples, that may formally explain the conditions under which Deep Convolutional Neural Networks perform much better in function approximation…