Related papers: ReCA: A Parametric ReLU Composite Activation Funct…

In this effort, we derive a formula for the integral representation of a shallow neural network with the Rectified Power Unit activation function. Mainly, our first result deals with the univariate case of representation capability of RePU…

Neural networks with the Rectified Linear Unit (ReLU) nonlinearity are described by a vector of parameters $\theta$, and realized as a piecewise linear continuous function $R_{\theta}: x \in \mathbb R^{d} \mapsto R_{\theta}(x) \in \mathbb…

Activation functions play a decisive role in determining the capacity of Deep Neural Networks as they enable neural networks to capture inherent nonlinearities present in data fed to them. The prior research on activation functions…

Non-linear activation functions are crucial in Convolutional Neural Networks. However, until now they have not been well described in the frequency domain. In this work, we study the spectral behavior of ReLU, a popular activation function.…

Understanding the computational complexity of training simple neural networks with rectified linear units (ReLUs) has recently been a subject of intensive research. Closing gaps and complementing results from the literature, we present…

Despite their widespread success, deep neural networks remain critically vulnerable to adversarial attacks, posing significant risks in safety-sensitive applications. This paper investigates activation functions as a crucial yet…

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…

The choice of activation function plays a critical role in neural networks, yet most architectures still rely on fixed, uniform activation functions across all neurons. We introduce SmartMixed, a two-phase training strategy that allows…

In this work, we propose to train a deep neural network by distributed optimization over a graph. Two nonlinear functions are considered: the rectified linear unit (ReLU) and a linear unit with both lower and upper cutoffs (DCutLU). The…

Deep neural networks are known to be vulnerable to adversarially perturbed inputs. A commonly used defense is adversarial training, whose performance is influenced by model capacity. While previous works have studied the impact of varying…

The effectiveness of deep neural architectures has been widely supported in terms of both experimental and foundational principles. There is also clear evidence that the activation function (e.g. the rectifier and the LSTM units) plays a…

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,…

A simple approach is proposed to obtain complexity controls for neural networks with general activation functions. The approach is motivated by approximating the general activation functions with one-dimensional ReLU networks, which reduces…

Deep neural networks paved the way for significant improvements in image visual categorization during the last years. However, even though the tasks are highly varying, differing in complexity and difficulty, existing solutions mostly build…

This work provides a thorough study on how reward scaling can affect performance of deep reinforcement learning agents. In particular, we would like to answer the question that how does reward scaling affect non-saturating ReLU networks in…

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…

Overwhelming theoretical and empirical evidence shows that mildly overparametrized neural networks -- those with more connections than the size of the training data -- are often able to memorize the training data with $100\%$ accuracy. This…

In this paper, we construct neural networks with ReLU, sine and $2^x$ as activation functions. For general continuous $f$ defined on $[0,1]^d$ with continuity modulus $\omega_f(\cdot)$, we construct ReLU-sine-$2^x$ networks that enjoy an…

We present a simple, effective, and general activation function we term ACON which learns to activate the neurons or not. Interestingly, we find Swish, the recent popular NAS-searched activation, can be interpreted as a smooth approximation…

Many industrial and real life problems exhibit highly nonlinear periodic behaviors and the conventional methods may fall short of finding their analytical or closed form solutions. Such problems demand some cutting edge computational tools…