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Optical neural networks promise ultrafast, low-energy information processing by performing computation directly with photons. Current implementations, however, are largely restricted to steady-state operation and rely on high-latency…

While it is well-known that neural networks enjoy excellent approximation capabilities, it remains a big challenge to compute such approximations from point samples. Based on tools from Information-based complexity, recent work by Grohs and…

We study the necessary and sufficient complexity of ReLU neural networks---in terms of depth and number of weights---which is required for approximating classifier functions in $L^2$. As a model class, we consider the set $\mathcal{E}^\beta…

The activation functions are fundamental to neural networks as they introduce non-linearity into data relationships, thereby enabling deep networks to approximate complex data relations. Existing efforts to enhance neural network…

In this article we identify a general class of high-dimensional continuous functions that can be approximated by deep neural networks (DNNs) with the rectified linear unit (ReLU) activation without the curse of dimensionality. In other…

Large number of ReLU and MAC operations of Deep neural networks make them ill-suited for latency and compute-efficient private inference. In this paper, we present a model optimization method that allows a model to learn to be shallow. In…

With the advancement of deep learning, reducing computational complexity and memory consumption has become a critical challenge, and ternary neural networks (NNs) that restrict parameters to $\{-1, 0, +1\}$ have attracted attention as a…

We show that hybrid zonotopes offer an equivalent representation of feed-forward fully connected neural networks with ReLU activation functions. Our approach demonstrates that the complexity of binary variables is equal to the total number…

We formalize and interpret the geometric structure of $d$-dimensional fully connected ReLU layers in neural networks. The parameters of a ReLU layer induce a natural partition of the input domain, such that the ReLU layer can be…

Recently, convolutional neural networks (CNNs) have been used as a powerful tool to solve many problems of machine learning and computer vision. In this paper, we aim to provide insight on the property of convolutional neural networks, as…

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…

Rectified Linear Units (ReLU) are the default choice for activation functions in deep neural networks. While they demonstrate excellent empirical performance, ReLU activations can fall victim to the dead neuron problem. In these cases, the…

Current research suggests that the key factors in designing neural network architectures involve choosing number of filters for every convolution layer, number of hidden neurons for every fully connected layer, dropout and pruning. The…

We study the computation complexity of deep ReLU (Rectified Linear Unit) neural networks for the approximation of functions from the H\"older-Zygmund space of mixed smoothness defined on the $d$-dimensional unit cube when the dimension $d$…

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…

We can compare the expressiveness of neural networks that use rectified linear units (ReLUs) by the number of linear regions, which reflect the number of pieces of the piecewise linear functions modeled by such networks. However,…

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…

Activation functions in neural networks are typically selected from a set of empirically validated, commonly used static functions such as ReLU, tanh, or sigmoid. However, by optimizing the shapes of a network's activation functions, we can…

The rapid scaling of deep neural networks comes at the cost of unsustainable power consumption. While optical neural networks offer an alternative, their capabilities remain constrained by the lack of efficient optical nonlinearities. To…

Appropriate weight initialization settings, along with the ReLU activation function, have become cornerstones of modern deep learning, enabling the training and deployment of highly effective and efficient neural network models across…