Which of the following are activation functions?

University of Michigan - Ann Arbor

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

A binary step function is a threshold-based activation function. If the input value is above or below a certain threshold, the neuron is activated and sends exactly the same signal to the next layer.

Binary Step Function

A linear activation function takes the form: $$y = cx$$. It takes the inputs, multiplied by the weights for each neuron, and creates an output signal proportional to the input. In one sense, a linear function is better than a step function because it allows multiple outputs, not just yes and no.

Linear Activation Function

Modern neural network models use non-linear activation functions. They allow the model to create complex mappings between the network’s inputs and outputs, which are essential for learning and modeling complex data, such as images, video, audio, and data sets which are non-linear or have high dimensionality.

There are 8 common non-linear activation functions:
 - Sigmoid / Logistic
 - TanH / Hyperbolic Tangent
 - ELU (Exponential Linear Unit)
 - ReLU (Rectified Linear Unit)
 - Leaky ReLU
 - Parametric ReLU
 - Softmax
 - Swish

Non-Linear Activation Functions

Activation functions are a critical part of the design of a neural network- A hidden layer in a neural network is a layer that receives input from another layer (such as another hidden layer or an input layer) and provides output to another layer (such as another hidden layer or an output layer).

There are perhaps three activation functions you may want to consider for use in hidden layers; they are:

- Rectified Linear Activation (ReLU)
The rectified linear activation function calculated as max(0.0, x)
It is common because it is both simple to implement and effective at overcoming the limitations of other previously popular activation functions, such as Sigmoid and Tanh.


- Logistic (Sigmoid)
The sigmoid activation function is also called the logistic function, and calculated as 1.0 / (1.0 + e^-x)
It is used in the logistic regression classification algorithm.

- Hyperbolic Tangent (Tanh)
The function takes any real value as input and outputs values in the range -1 to 1. The larger the input (more positive), the closer the output value will be to 1.0, whereas the smaller the input (more negative), the closer the output will be to -1.0.
IT is calculated as (e^x – e^-x) / (e^x + e^-x)

It is common practive to choose activation function based on the type of model you work on.
Multilayer Perceptron (MLP): ReLU activation function.
Convolutional Neural Network (CNN): ReLU activation function.
Recurrent Neural Network: Tanh and/or Sigmoid activation function.



How to Choose an Activation Function for Deep Learning

Comparing the advantages and disadvantages of Sigmoid, Hyperbolic Tangent (Tanh), and Rectified Linear Unit (ReLU) activation functions in neural networks:

**Sigmoid**
- **Pros:** Useful for binary classification tasks, typically in the output layer, as it maps values to a range between 0 and 1.
- **Cons:** Not zero-centered, which can make optimization harder, and is susceptible to the vanishing gradient problem.

**Hyperbolic Tangent (Tanh)**
- **Pros:** Zero-centered, mapping values between -1 and 1, which helps model negative, neutral, and positive inputs and makes backpropagation more stable.
- **Cons:** Computationally more expensive than ReLU and still suffers from vanishing gradients for very large or small inputs.

**Rectified Linear Unit (ReLU)**
- **Pros:** Extremely simple and computationally efficient, which accelerates model convergence and makes it the default choice for hidden layers.
- **Cons:** Suffers from the dying ReLU problem, where the derivative becomes 0 when the input $$z < 0$$, preventing backpropagation for those neurons.

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