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Rectified linear units, or ReLUs, have become the preferred activation function for artificial neural networks. In this paper we consider two basic learning problems assuming that the underlying data follow a generative model based on a…

Convolutional Neural Networks (CNNs) have been widely applied. But as the CNNs grow, the number of arithmetic operations and memory footprint also increase. Furthermore, typical non-linear activation functions do not allow associativity of…

We study the numerical and Boolean expressiveness of MPLang, a declarative language that captures the computation of graph neural networks (GNNs) through linear message passing and activation functions. We begin with A-MPLang, the fragment…

Activation in deep neural networks is fundamental to achieving non-linear mappings. Traditional studies mainly focus on finding fixed activations for a particular set of learning tasks or model architectures. The research on flexible…

Rectified Linear Units (ReLU) seem to have displaced traditional 'smooth' nonlinearities as activation-function-du-jour in many - but not all - deep neural network (DNN) applications. However, nobody seems to know why. In this article, we…

This paper proposes a novel nonlinear activation mechanism typically for convolutional neural network (CNN), named as reborn mechanism. In sharp contrast to ReLU which cuts off the negative phase value, the reborn mechanism enjoys the…

We propose ReDense as a simple and low complexity way to improve the performance of trained neural networks. We use a combination of random weights and rectified linear unit (ReLU) activation function to add a ReLU dense (ReDense) layer to…

Deep networks are gradually penetrating almost every domain in our lives due to their amazing success. However, with substantive performance accuracy improvements comes the price of \emph{irreproducibility}. Two identical models, trained on…

Deep learning models are effective for sequential data modeling, yet commonly used activation functions such as ReLU, LeakyReLU, and PReLU often exhibit gradient instability when applied to noisy, non-stationary financial time series. This…

This work provides a thorough study on how reward scaling can affect performance of deep reinforcement learning agents. In particular, we would like to answer the question that how does reward scaling affect non-saturating ReLU networks in…

As a widely used non-linear activation, Rectified Linear Unit (ReLU) separates noise and signal in a feature map by learning a threshold or bias. However, we argue that the classification of noise and signal not only depends on the…

Element-wise activation functions play a critical role in deep neural networks via affecting the expressivity power and the learning dynamics. Learning-based activation functions have recently gained increasing attention and success. We…

Nonlinear activation functions are pivotal to the success of deep neural nets, and choosing the appropriate activation function can significantly affect their performance. Most networks use fixed activation functions (e.g., ReLU, GELU,…

We propose the Gaussian Error Linear Unit (GELU), a high-performing neural network activation function. The GELU activation function is $x\Phi(x)$, where $\Phi(x)$ the standard Gaussian cumulative distribution function. The GELU…

Most deep neural networks use simple, fixed activation functions, such as sigmoids or rectified linear units, regardless of domain or network structure. We introduce differential equation units (DEUs), an improvement to modern neural…

Deep neural networks, particularly those employing Rectified Linear Units (ReLU), are often perceived as complex, high-dimensional, non-linear systems. This complexity poses a significant challenge to understanding their internal learning…

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 prove new upper and lower bounds on the VC-dimension of deep neural networks with the ReLU activation function. These bounds are tight for almost the entire range of parameters. Letting $W$ be the number of weights and $L$ be the number…

Neural networks are a powerful class of functions that can be trained with simple gradient descent to achieve state-of-the-art performance on a variety of applications. Despite their practical success, there is a paucity of results that…

Privacy-Preserving Machine Learning algorithms must balance classification accuracy with data privacy. This can be done using a combination of cryptographic and machine learning tools such as Convolutional Neural Networks (CNN). CNNs…