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It has recently been shown that neural networks but also other classifiers are vulnerable to so called adversarial attacks e.g. in object recognition an almost non-perceivable change of the image changes the decision of the classifier.…

The Rectified Linear Unit (ReLU) is a foundational activation function in artficial neural networks. Recent literature frequently misattributes its origin to the 2018 (initial) version of this paper, which exclusively investigated ReLU at…

We propose \textbf{ULU}, a novel non-monotonic, piecewise activation function defined as $\{f(x;\alpha_1),x<0; f(x;\alpha_2),x>=0 \}$, where $f(x;\alpha)=0.5x(tanh(\alpha x)+1),\alpha >0$. ULU treats positive and negative inputs…

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…

We provide a theoretical explanation of the role of the number of nodes at each layer in deep neural networks. We prove that the largest variation of a deep neural network with ReLU activation function arises when the layer with the fewest…

The choice of activation function in deep networks has a significant effect on the training dynamics and task performance. At present, the most effective and widely-used activation function is ReLU. However, because of the non-zero mean,…

Activation functions play a crucial role in neural networks because they are the nonlinearities which have been attributed to the success story of deep learning. One of the currently most popular activation functions is ReLU, but several…

Rectifier neuron units (ReLUs) have been widely used in deep convolutional networks. An ReLU converts negative values to zeros, and does not change positive values, which leads to a high sparsity of neurons. In this work, we first examine…

The primary neural networks decision-making units are activation functions. Moreover, they evaluate the output of networks neural node; thus, they are essential for the performance of the whole network. Hence, it is critical to choose the…

Sparse computation offers a compelling solution for the inference of Large Language Models (LLMs) in low-resource scenarios by dynamically skipping the computation of inactive neurons. While traditional approaches focus on ReLU-based LLMs,…

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,…

It is difficult to describe in mathematical terms what a neural network trained on data represents. On the other hand, there is a growing mathematical understanding of what neural networks are in principle capable of representing.…

The impressive expressive power of deep neural networks (DNNs) underlies their widespread applicability. However, while the theoretical capacity of deep architectures is high, the practical expressive power achieved through successful…

Dynamic adaptation in single-neuron response plays a fundamental role in neural coding in biological neural networks. Yet, most neural activation functions used in artificial networks are fixed and mostly considered as an inconsequential…

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…

Despite recent algorithmic advances, we still lack principled ways to leverage the well-documented rescaling symmetries in ReLU neural network parameters. While two properly rescaled weights implement the same function, the training…

Rectified linear unit (ReLU) activations can also be thought of as 'gates', which, either pass or stop their pre-activation input when they are 'on' (when the pre-activation input is positive) or 'off' (when the pre-activation input is…

In this paper, we consider robust nonparametric regression using deep neural networks with ReLU activation function. While several existing theoretically justified methods are geared towards robustness against identical heavy-tailed noise…

Formal certification of Neural Networks (NNs) is crucial for ensuring their safety, fairness, and robustness. Unfortunately, on the one hand, sound and complete certification algorithms of ReLU-based NNs do not scale to large-scale NNs. On…

Outsourcing deep neural networks (DNNs) inference tasks to an untrusted cloud raises data privacy and integrity concerns. While there are many techniques to ensure privacy and integrity for polynomial-based computations, DNNs involve…