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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…
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…
Activation functions are non-linearities in neural networks that allow them to learn complex mapping between inputs and outputs. Typical choices for activation functions are ReLU, Tanh, Sigmoid etc., where the choice generally depends on…
The primary neural networks decision-making units are activation functions. Moreover, they evaluate the output of networks neural node; thus, they are essential for the performance of the whole network. Hence, it is critical to choose the…
To enhance the nonlinearity of neural networks and increase their mapping abilities between the inputs and response variables, activation functions play a crucial role to model more complex relationships and patterns in the data. In this…
The choice of activation functions in deep networks has a significant effect on the training dynamics and task performance. Currently, the most successful and widely-used activation function is the Rectified Linear Unit (ReLU). Although…
Recent studies have shown that the choice of activation function can significantly affect the performance of deep learning networks. However, the benefits of novel activation functions have been inconsistent and task dependent, and…
Activation functions have come up as one of the essential components of neural networks. The choice of adequate activation function can impact the accuracy of these methods. In this study, we experiment for finding an optimal activation…
Activation functions are essential to deep learning networks. Popular and versatile activation functions are mostly monotonic functions, some non-monotonic activation functions are being explored and show promising performance. But by…
Activation functions play a key role in providing remarkable performance in deep neural networks, and the rectified linear unit (ReLU) is one of the most widely used activation functions. Various new activation functions and improvements on…
Recent research has found that the activation function (AF) selected for adding non-linearity into the output can have a big impact on how effectively deep learning networks perform. Developing activation functions that can adapt…
Neural networks have shown tremendous growth in recent years to solve numerous problems. Various types of neural networks have been introduced to deal with different types of problems. However, the main goal of any neural network is to…
The nonlinearity of activation functions used in deep learning models are crucial for the success of predictive models. There are several commonly used simple nonlinear functions, including Rectified Linear Unit (ReLU) and Leaky-ReLU…
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…
We consider neural networks with rational activation functions. The choice of the nonlinear activation function in deep learning architectures is crucial and heavily impacts the performance of a neural network. We establish optimal bounds…
We study neural networks with trainable low-degree rational activation functions and show that they are more expressive and parameter-efficient than modern piecewise-linear and smooth activations such as ELU, LeakyReLU, LogSigmoid, PReLU,…
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 neural networks, non-linearity is introduced by activation functions. One commonly used activation function is Rectified Linear Unit (ReLU). ReLU has been a popular choice as an activation but has flaws. State-of-the-art functions like…
This paper provides an analysis of state-of-the-art activation functions with respect to supervised classification of deep neural network. These activation functions comprise of Rectified Linear Units (ReLU), Exponential Linear Unit (ELU),…
The choice of activation function can have a large effect on the performance of a neural network. While there have been some attempts to hand-engineer novel activation functions, the Rectified Linear Unit (ReLU) remains the most…