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In this paper we investigate the performance of different types of rectified activation functions in convolutional neural network: standard rectified linear unit (ReLU), leaky rectified linear unit (Leaky ReLU), parametric rectified linear…

The scope of research in the domain of activation functions remains limited and centered around improving the ease of optimization or generalization quality of neural networks (NNs). However, to develop a deeper understanding of deep…

Neural networks are a powerful class of functions that can be trained with simple gradient descent to achieve state-of-the-art performance on a variety of applications. Despite their practical success, there is a paucity of results that…

Artificial Neural Networks (ANNs) are prevalent machine learning models that are applied across various real-world classification tasks. However, training ANNs is time-consuming and the resulting models take a lot of memory to deploy. In…

Convolutional Neural Network's (CNN's) performance disparity on clean and corrupted datasets has recently come under scrutiny. In this work, we analyse common corruptions in the frequency domain, i.e., High Frequency corruptions (HFc, e.g.,…

Activation functions introduce non-linearity into Neural Networks, enabling them to learn complex patterns. Different activation functions vary in speed and accuracy, ranging from faster but less accurate options like ReLU to slower but…

Activation functions play a critical role in deep neural networks by shaping gradient flow, optimization stability, and generalization. While ReLU remains widely used due to its simplicity, it suffers from gradient sparsity and dead-neuron…

The weight initialization and the activation function of deep neural networks have a crucial impact on the performance of the training procedure. An inappropriate selection can lead to the loss of information of the input during forward…

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…

A pivotal aspect in the design of neural networks lies in selecting activation functions, crucial for introducing nonlinear structures that capture intricate input-output patterns. While the effectiveness of adaptive or trainable activation…

We introduce SPLASH units, a class of learnable activation functions shown to simultaneously improve the accuracy of deep neural networks while also improving their robustness to adversarial attacks. SPLASH units have both a simple…

Activation function is crucial to the recent successes of deep neural networks. In this paper, we first propose a new activation function, Multiple Parametric Exponential Linear Units (MPELU), aiming to generalize and unify the rectified…

An activation function has crucial role in a deep neural network. A simple rectified linear unit (ReLU) are widely used for the activation function. In this paper, a weighted sigmoid gate unit (WiG) is proposed as the activation function.…

Modern Neural Radiance Fields (NeRFs) learn a mapping from position to volumetric density leveraging proposal network samplers. In contrast to the coarse-to-fine sampling approach with two NeRFs, this offers significant potential for…

Even in recent neural network architectures such as Transformers and Extended LSTM (xLSTM), and traditional ones like Convolutional Neural Networks, Activation Functions are an integral part of nearly all neural networks. They enable more…

Recent seminal work at the intersection of deep neural networks practice and random matrix theory has linked the convergence speed and robustness of these networks with the combination of random weight initialization and nonlinear…

Real-world analog systems intrinsically suffer from noise that can impede model convergence and accuracy on a variety of deep learning models. We demonstrate that differentiable activations like GELU and SiLU enable robust propagation of…

Artificial neural networks usually consist of successive linear multiply-accumulate operations and nonlinear activation functions. However, most optical neural networks only achieve the linear operation in the optical domain, while the…

Gradient descent (GD) type optimization schemes are the standard methods to train artificial neural networks (ANNs) with rectified linear unit (ReLU) activation. Such schemes can be considered as discretizations of gradient flows (GFs)…

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…