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The dominant paradigm in modern neural networks relies on simple, monotonically-increasing activation functions like ReLU. While effective, this paradigm necessitates large, massively-parameterized models to approximate complex functions.…

Motivated by the growing theoretical understanding of neural networks that employ the Rectified Linear Unit (ReLU) as their activation function, we revisit the use of ReLU activation functions for learning implicit neural representations…

This paper explores the topological signatures of ReLU neural network activation patterns. We consider feedforward neural networks with ReLU activation functions and analyze the polytope decomposition of the feature space induced by the…

Recently, neural networks have been widely applied in the power system area. They can be used for better predicting input information and modeling system performance with increased accuracy. In some applications such as battery degradation…

We show how neural models can be used to realize piece-wise constant functions such as decision trees. The proposed architecture, which we call locally constant networks, builds on ReLU networks that are piece-wise linear and hence their…

This paper analyses both nonlinear activation functions and spatial max-pooling for Deep Convolutional Neural Networks (DCNNs) by means of the algebraic basis of mathematical morphology. Additionally, a general family of activation…

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…

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…

Activation functions (AFs) play a pivotal role in the performance of neural networks. The Rectified Linear Unit (ReLU) is currently the most commonly used AF. Several replacements to ReLU have been suggested but improvements have proven…

Activation functions are fundamental to deep neural networks, governing gradient flow, optimization stability, and representational capacity. Within historic deep architectures, while ReLU has been the dominant choice for the activation…

When optimizing a nonlinear objective, one can employ a neural network as a surrogate for the nonlinear function. However, the resulting optimization model can be time-consuming to solve globally with exact methods. As a result, local…

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…

Deep learning researchers have a keen interest in proposing two new novel activation functions which can boost network performance. A good choice of activation function can have significant consequences in improving network performance. A…

This paper studies the approximation property of ReLU neural networks (NNs) to piecewise constant functions with unknown interfaces in bounded regions in $\mathbb{R}^d$. Under the assumption that the discontinuity interface $\Gamma$ may be…

In this paper, we introduce a novel type of Rectified Linear Unit (ReLU), called a Dual Rectified Linear Unit (DReLU). A DReLU, which comes with an unbounded positive and negative image, can be used as a drop-in replacement for a tanh…

The most widely used activation functions in current deep feed-forward neural networks are rectified linear units (ReLU), and many alternatives have been successfully applied, as well. However, none of the alternatives have managed to…

We contribute to a better understanding of the class of functions that can be represented by a neural network with ReLU activations and a given architecture. Using techniques from mixed-integer optimization, polyhedral theory, and tropical…

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…

Rectified linear activation units are important components for state-of-the-art deep convolutional networks. In this paper, we propose a novel S-shaped rectified linear activation unit (SReLU) to learn both convex and non-convex functions,…

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…