Exponential Linear Squashing Activation

The Exponential Linear Squashing Activation Function, or ELiSH, is a type of activation function commonly used in neural networks. It is similar to the Swish function, which combines ELU and Sigmoid functions, but has unique properties that make it useful for various machine learning tasks.

What is an Activation Function?

Before we dive into ELiSH, let's first review what an activation function is and why it's important for neural networks. In a neural network, each neuron has an activation function, which decides whether or not the neuron should be activated. The activation function takes in a weighted sum of the inputs and produces an output, which is then passed to the next layer of neurons.

Activation functions play a crucial role in neural networks. They allow the network to learn and make predictions by adding non-linearity to the input data. Without an activation function, neural networks would simply be performing linear operations, which would severely limit their ability to model complex data.

ELiSH: An Overview

ELiSH is a relatively new activation function that was introduced in 2020. It was proposed as an alternative to the popular ReLU activation function, which suffers from the "dying ReLU" problem. The dying ReLU problem occurs when a large portion of the neurons in a network become inactive, which slows down the learning process and reduces model accuracy.

ELiSH uses a combination of the Exponential Linear Unit (ELU) and Sigmoid functions. The ELU function is similar to ReLU, but it is differentiable at zero and produces negative outputs for negative inputs. The Sigmoid function is a standard activation function that produces outputs between 0 and 1.

The ELiSH function can be written as:

$$f\left(x\right) = \frac{x}{1+e^{-x}} \text{ if } x \geq 0 $$ $$f\left(x\right) = \frac{e^{x} - 1}{1+e^{-x}} \text{ if } x < 0 $$

The first part of the ELiSH function is the same as the Sigmoid function, while the second part is the ELU function. The two functions are combined in a way that allows them to improve information flow while also solving the problem of vanishing gradients.

Properties of ELiSH

ELiSH has several properties that make it a promising activation function for use in neural networks. Here are a few:

1. Non-monotonicity

ELiSH is non-monotonic, which means that it has regions where the output increases and regions where it decreases. This property allows the function to produce more complex decision boundaries, which can improve the accuracy of the model.

2. Smoothness

ELiSH is a smooth activation function, which means that it is differentiable everywhere. This property is important because it allows the gradient to be computed at every point, which makes backpropagation more stable and efficient.

3. Saturation avoidance

ELiSH has a built-in mechanism for avoiding saturation. Saturation occurs when the input to the activation function is too large, causing the output to approach 0 or 1. This can cause the gradient to vanish, which makes it difficult for the network to learn. ELiSH avoids saturation by having a linear region for large positive inputs, which allows the gradient to continue to flow.

Applications of ELiSH

ELiSH has already been used in a variety of machine learning applications, including image recognition, natural language processing, and speech recognition. One study found that ELiSH outperformed other commonly used activation functions, including ReLU, Leaky ReLU, and Swish, on several benchmark datasets.

The Exponential Linear Squashing Activation Function, or ELiSH, is a promising alternative to traditional activation functions like ReLU. It combines the properties of the ELU and Sigmoid functions to create a non-monotonic, smooth, and saturation-avoiding activation function that is well-suited for use in neural networks. As machine learning continues to advance, it will be interesting to see how ELiSH and other activation functions continue to evolve and improve.

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