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ReLU (rectified linear units) neural network has received significant attention since its emergence. In this paper, a univariate ReLU (UReLU) neural network is proposed to both modelling the nonlinear dynamic system and revealing insights…

Rectified linear unit (ReLU) is a widely used activation function for deep convolutional neural networks. However, because of the zero-hard rectification, ReLU networks miss the benefits from negative values. In this paper, we propose a…

The application of the deep learning model in classification plays an important role in the accurate detection of the target objects. However, the accuracy is affected by the activation function in the hidden and output layer. In this…

Activation functions have been shown to affect the performance of deep neural networks significantly. While the Rectified Linear Unit (ReLU) remains the dominant choice in practice, the optimal activation function for deep neural networks…

Deep Convolutional Neural Networks are able to identify complex patterns and perform tasks with super-human capabilities. However, besides the exceptional results, they are not completely understood and it is still impractical to…

We introduce stochastic activations. This novel strategy randomly selects between several non-linear functions in the feed-forward layer of a large language model. In particular, we choose between SILU or RELU depending on a Bernoulli draw.…

Activation functions are non-linearities in neural networks that allow them to learn complex mapping between inputs and outputs. Typical choices for activation functions are ReLU, Tanh, Sigmoid etc., where the choice generally depends on…

Activation functions influence behavior and performance of DNNs. Nonlinear activation functions, like Rectified Linear Units (ReLU), Exponential Linear Units (ELU) and Scaled Exponential Linear Units (SELU), outperform the linear…

Deep neural networks (DNNs) have garnered significant attention in various fields of science and technology in recent years. Activation functions define how neurons in DNNs process incoming signals for them. They are essential for learning…

It is commonly recognized that the expressiveness of deep neural networks is contingent upon a range of factors, encompassing their depth, width, and other relevant considerations. Currently, the practical performance of the majority of…

We consider neural networks with rational activation functions. The choice of the nonlinear activation function in deep learning architectures is crucial and heavily impacts the performance of a neural network. We establish optimal bounds…

Despite their prevalence in neural networks we still lack a thorough theoretical characterization of ReLU layers. This paper aims to further our understanding of ReLU layers by studying how the activation function ReLU interacts with the…

Consider the multivariate nonparametric regression model. It is shown that estimators based on sparsely connected deep neural networks with ReLU activation function and properly chosen network architecture achieve the minimax rates of…

We analyze a simple one-hidden-layer neural network with ReLU activation functions and fixed biases, with one-dimensional input and output. We study both continuous and discrete versions of the model, and we rigorously prove the convergence…

Activation function is a key component in deep learning that performs non-linear mappings between the inputs and outputs. Rectified Linear Unit (ReLU) has been the most popular activation function across the deep learning community.…

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…

Activation functions play a critical role in deep neural networks by shaping gradient flow, optimization stability, and generalization. While ReLU remains widely used due to its simplicity, it suffers from gradient sparsity and dead-neuron…

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,…

Activation functions are the linchpins of deep learning, profoundly influencing both the representational capacity and training dynamics of neural networks. They shape not only the nature of representations but also optimize convergence…

The activation function is at the heart of a deep neural networks nonlinearity; the choice of the function has great impact on the success of training. Currently, many practitioners prefer the Rectified Linear Unit (ReLU) due to its…