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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…
In recent years, functional neural networks have been proposed and studied in order to approximate nonlinear continuous functionals defined on $L^p([-1, 1]^s)$ for integers $s\ge1$ and $1\le p<\infty$. However, their theoretical properties…
In this report we demonstrate that with same parameters and computational budgets, models with wider features before ReLU activation have significantly better performance for single image super-resolution (SISR). The resulted SR residual…
Deep learning training training algorithms are a huge success in recent years in many fields including speech, text,image video etc. Deeper and deeper layers are proposed with huge success with resnet structures having around 152 layers.…
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…
Deep networks are gradually penetrating almost every domain in our lives due to their amazing success. However, with substantive performance accuracy improvements comes the price of \emph{irreproducibility}. Two identical models, trained on…
With the continuous growth of neural network scales, low-precision quantization is widely used in edge accelerators. Classic multi-threshold activation hardware requires 2^n thresholds for n-bit outputs, causing a rapid increase in hardware…
It is well-known that deep neural networks are vulnerable to adversarial attacks. Recent studies show that well-designed classification parts can lead to better robustness. However, there is still much space for improvement along this line.…
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…
We present a unified representation of the most popular neural network activation functions. Adopting Mittag-Leffler functions of fractional calculus, we propose a flexible and compact functional form that is able to interpolate between…
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…
Recently, much attention has been devoted to finding highly efficient and powerful activation functions for CNN layers. Because activation functions inject different nonlinearities between layers that affect performance, varying them is one…
Rectified Linear Units (ReLU) have become the main model for the neural units in current deep learning systems. This choice has been originally suggested as a way to compensate for the so called vanishing gradient problem which can undercut…
In this paper, we revise two commonly used saturated functions, the logistic sigmoid and the hyperbolic tangent (tanh). We point out that, besides the well-known non-zero centered property, slope of the activation function near the origin…
Stable and efficient training of ReLU networks with large depth is highly sensitive to weight initialization. Improper initialization can cause permanent neuron inactivation dying ReLU and exacerbate gradient instability as network depth…
Effective activation functions introduce non-linear transformations, providing neural networks with stronger fitting capa-bilities, which help them better adapt to real data distributions. Huawei Noah's Lab believes that dynamic activation…
We study layered neural networks of rectified linear units (ReLU) in a modelling framework for stochastic training processes. The comparison with sigmoidal activation functions is in the center of interest. We compute typical learning…
The most widely used activation functions in current deep feed-forward neural networks are rectified linear units (ReLU), and many alternatives have been successfully applied, as well. However, none of the alternatives have managed to…
Product unit neural networks (PUNNs) are powerful representational models with a strong theoretical basis, but have proven to be difficult to train with gradient-based optimizers. We present windowed product unit neural networks (WPUNNs), a…
In our previous work [Ma and Chan (2023)], we presented a feedforward unitary equivariant neural network. We proposed three distinct activation functions tailored for this network: a softsign function with a small residue, an identity…