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University of Michigan - Ann Arbor

In a neural network, numeric data points, called inputs, are fed into the neurons in the input layer. Each neuron has a weight, and multiplying the input number with the weight gives the output of the neuron, which is transferred to the next layer.
The activation function is a mathematical “gate” in between the input feeding the current neuron and its output going to the next layer. It can be as simple as a step function that turns the neuron output on and off, depending on a rule or threshold. Or it can be a transformation that maps the input signals into output signals that are needed for the neural network to function.
Activation functions are mathematical equations that determine the output of a neural network. The function is attached to each neuron in the network, and determines whether it should be activated (“fired”) or not, based on whether each neuron’s input is relevant for the model’s prediction. Activation functions also help normalize the output of each neuron to a range between 1 and 0 or between -1 and 1. When used in a multilayer neural network, activation functions can be different for different layers. 

Activation Functions in Neural Networks

There are 12 types of activation functions:

- Binary Step
- Linear
- Sigmoid
- Tanh
- ReLU
- Leaky ReLU
- Parameterised ReLU
- Exponential Linear Unit
- Swish
- Softmax

https://www.analyticsvidhya.com/blog/2020/01/fundamentals-deep-learning-activation-functions-when-to-use-them/

Types of Activation Functions

In a neural network, numeric data points, called inputs, are fed into the neurons in the input layer. Each neuron has a weight, and multiplying the input number with the weight gives the output of the neuron, which is transferred to the next layer.

The activation function is a mathematical “gate” in between the input feeding the current neuron and its output going to the next layer. It can be as simple as a step function that turns the neuron output on and off, depending on a rule or threshold. Or it can be a transformation that maps the input signals into output signals that are needed for the neural network to function.

Role of the Activation Functions in Neural Networks

How to Select an Activation Function

A neural network with multiple hidden layers is designed so that for every neuron, its output is simply the direct weighted sum of its inputs. No further mathematical transformation is applied to this sum before it is passed to the next layer. What is the most significant consequence of this design on the network's overall capability?

An engineer is training a deep neural network and observes that the raw output values from many neurons (the weighted sum of their inputs) are becoming extremely large, leading to an unstable training process where the model fails to learn effectively. To solve this, a specific type of mathematical function is typically applied to the raw output of each neuron before it is passed to the next layer.

Diagnosing Neural Network Instability

A data scientist is building a neural network with several hidden layers to classify images. They consider two approaches for the hidden layers. In Approach A, the output of each neuron is the direct weighted sum of its inputs. In Approach B, a non-linear mathematical function is applied to the weighted sum before passing the result to the next layer. Which approach is fundamentally more capable of learning the complex patterns in the images, and why? Explain the critical limitation of the less capable approach.

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