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Spintronic technology is emerging as a direction for the hardware implementation of neurons and synapses of neuromorphic architectures. In particular, a single spintronic device can be used to implement the nonlinear activation function of…

Understanding implicit bias of gradient descent for generalization capability of ReLU networks has been an important research topic in machine learning research. Unfortunately, even for a single ReLU neuron trained with the square loss, it…

Recently there has been much interest in understanding why deep neural networks are preferred to shallow networks. We show that, for a large class of piecewise smooth functions, the number of neurons needed by a shallow network to…

Modeling sophisticated activation functions within deep learning architectures has evolved into a distinct research direction. Functions such as GELU, SELU, and SiLU offer smooth gradients and improved convergence properties, making them…

Neural networks are universal function approximators which are known to generalize well despite being dramatically overparameterized. We study this phenomenon from the point of view of the spectral bias of neural networks. Our contributions…

The success of deep networks has been attributed in part to their expressivity: per parameter, deep networks can approximate a richer class of functions than shallow networks. In ReLU networks, the number of activation patterns is one…

Activation functions are essential for deep learning methods to learn and perform complex tasks such as image classification. Rectified Linear Unit (ReLU) has been widely used and become the default activation function across the deep…

Gated Linear Units (arXiv:1612.08083) consist of the component-wise product of two linear projections, one of which is first passed through a sigmoid function. Variations on GLU are possible, using different nonlinear (or even linear)…

Activation functions play a pivotal role in determining the training dynamics and neural network performance. The widely adopted activation function ReLU despite being simple and effective has few disadvantages including the Dying ReLU…

Deep learning is computationally intensive, with significant efforts focused on reducing arithmetic complexity, particularly regarding energy consumption dominated by data movement. While existing literature emphasizes inference, training…

Many neural network architectures rely on the choice of the activation function for each hidden layer. Given the activation function, the neural network is trained over the bias and the weight parameters. The bias catches the center of the…

Non-linear activation functions, e.g., Sigmoid, ReLU, and Tanh, have achieved great success in neural networks (NNs). Due to the complex non-linear characteristic of samples, the objective of those activation functions is to project samples…

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…

In spite of finite dimension ReLU neural networks being a consistent factor behind recent deep learning successes, a theory of feature learning in these models remains elusive. Currently, insightful theories still rely on assumptions…

Researchers have proposed that deep learning, which is providing important progress in a wide range of high complexity tasks, might inspire new insights into learning in the brain. However, the methods used for deep learning by artificial…

Implicit deep learning has received increasing attention recently due to the fact that it generalizes the recursive prediction rules of many commonly used neural network architectures. Its prediction rule is provided implicitly based on the…

ReLU neural-networks have been in the focus of many recent theoretical works, trying to explain their empirical success. Nonetheless, there is still a gap between current theoretical results and empirical observations, even in the case of…

We develop a variational framework to understand the properties of functions learned by fitting deep neural networks with rectified linear unit activations to data. We propose a new function space, which is reminiscent of classical bounded…

We propose the Moderate Adaptive Linear Unit (MoLU), a novel activation function for deep neural networks, defined analytically as: f(x)=x \times (1+tanh(x))/2. MoLU combines mathematical elegance with empirical effectiveness, exhibiting…

Deep learning has exhibited remarkable results across diverse areas. To understand its success, substantial research has been directed towards its theoretical foundations. Nevertheless, the majority of these studies examine how well deep…