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This paper explores the expressive power of deep neural networks for a diverse range of activation functions. An activation function set $\mathscr{A}$ is defined to encompass the majority of commonly used activation functions, such as…

There has been a growing interest in expressivity of deep neural networks. However, most of the existing work about this topic focuses only on the specific activation function such as ReLU or sigmoid. In this paper, we investigate the…

Previous works proved that the combination of the linear neuron network with nonlinear activation functions (e.g. ReLu) can achieve nonlinear function approximation. However, simply widening or deepening the network structure will introduce…

Title: Comparison between layer-to-layer network training and conventional network training using Deep Convolutional Neural Networks Abstract: Convolutional neural networks (CNNs) are widely used in various applications due to their…

Nonlinear activation functions are widely recognized for enhancing the expressivity of neural networks, which is the primary reason for their widespread implementation. In this work, we focus on ReLU activation and reveal a novel and…

Amongst others, the adoption of Rectified Linear Units (ReLUs) is regarded as one of the ingredients of the success of deep learning. ReLU activation has been shown to mitigate the vanishing gradient issue, to encourage sparsity in the…

The reason behind CNNs capability to learn high-dimensional complex features from the images is the non-linearity introduced by the activation function. Several advanced activation functions have been discovered to improve the training…

Recent research has found that the activation function (AF) selected for adding non-linearity into the output can have a big impact on how effectively deep learning networks perform. Developing activation functions that can adapt…

The first provably efficient algorithm for learning graph neural networks (GNNs) with one hidden layer for node information convolution is provided in this paper. Two types of GNNs are investigated, depending on whether labels are attached…

We propose a simple extension to the ReLU-family of activation functions that allows them to shift the mean activation across a layer towards zero. Combined with proper weight initialization, this alleviates the need for normalization…

Convolutional neural networks have achieved great success in various vision tasks; however, they incur heavy resource costs. By using deeper and wider networks, network accuracy can be improved rapidly. However, in an environment with…

Artificial neural networks typically have a fixed, non-linear activation function at each neuron. We have designed a novel form of piecewise linear activation function that is learned independently for each neuron using gradient descent.…

Deep neural networks (DNNs) are widely studied in various applications. A DNN consists of layers of neurons that compute affine combinations, apply nonlinear operations, and produce corresponding activations. The rectified linear unit…

The success of deep neural networks is in part due to the use of normalization layers. Normalization layers like Batch Normalization, Layer Normalization and Weight Normalization are ubiquitous in practice, as they improve generalization…

We point out that (continuous or discontinuous) piecewise linear functions on a convex polytope mesh can be represented by two-hidden-layer ReLU neural networks in a weak sense. In addition, the numbers of neurons of the two hidden layers…

For most state-of-the-art architectures, Rectified Linear Unit (ReLU) becomes a standard component accompanied with each layer. Although ReLU can ease the network training to an extent, the character of blocking negative values may suppress…

In this paper, we study 1-bit convolutional neural networks (CNNs), of which both the weights and activations are binary. While efficient, the lacking of representational capability and the training difficulty impede 1-bit CNNs from…

Activation functions have come up as one of the essential components of neural networks. The choice of adequate activation function can impact the accuracy of these methods. In this study, we experiment for finding an optimal activation…

We study training of Convolutional Neural Networks (CNNs) with ReLU activations and introduce exact convex optimization formulations with a polynomial complexity with respect to the number of data samples, the number of neurons, and data…

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…