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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…

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…

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…

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.…

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…

The performance of artificial neural networks (ANNs) is influenced by weight initialization, the nature of activation functions, and their architecture. There is a wide range of activation functions that are traditionally used to train a…

Deep neural networks often suffer from poor performance or even training failure due to the ill-conditioned problem, the vanishing/exploding gradient problem, and the saddle point problem. In this paper, a novel method by acting the…

Selecting the most suitable activation function is a critical factor in the effectiveness of deep learning models, as it influences their learning capacity, stability, and computational efficiency. In recent years, the Gaussian Error Linear…

Activation functions are essential to introduce nonlinearity into neural networks, with the Rectified Linear Unit (ReLU) often favored for its simplicity and effectiveness. Motivated by the structural similarity between a shallow…

Recent Progress has shown that exploitation of hidden layer neurons in convolution neural networks incorporating with a carefully designed activation function can yield better classification results in the field of computer vision. The…

Quantized or low-bit neural networks are attractive due to their inference efficiency. However, training deep neural networks with quantized activations involves minimizing a discontinuous and piecewise constant loss function. Such a loss…

Linear Regression and neural networks are widely used to model data. Neural networks distinguish themselves from linear regression with their use of activation functions that enable modeling nonlinear functions. The standard argument for…

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…

The success of artificial neural networks (ANNs) hinges greatly on the judicious selection of an activation function, introducing non-linearity into network and enabling them to model sophisticated relationships in data. However, the search…

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…

The ability of neural networks to provide `best in class' approximation across a wide range of applications is well-documented. Nevertheless, the powerful expressivity of neural networks comes to naught if one is unable to effectively train…

The paper briefy reviews several recent results on hierarchical architectures for learning from examples, that may formally explain the conditions under which Deep Convolutional Neural Networks perform much better in function approximation…

We introduce the "exponential linear unit" (ELU) which speeds up learning in deep neural networks and leads to higher classification accuracies. Like rectified linear units (ReLUs), leaky ReLUs (LReLUs) and parametrized ReLUs (PReLUs), ELUs…

Recent theoretical work has demonstrated that deep neural networks have superior performance over shallow networks, but their training is more difficult, e.g., they suffer from the vanishing gradient problem. This problem can be typically…

We investigate to what extent it is possible to solve linear inverse problems with $ReLu$ networks. Due to the scaling invariance arising from the linearity, an optimal reconstruction function $f$ for such a problem is positive homogeneous,…