Contents

- 1 Which activation function is differentiable?
- 2 Is neural network differentiable?
- 3 Why do we need derivative of activation function?
- 4 Which activation function is continuous and differentiable?
- 5 What can a neural network do without an activation function?
- 6 Do you need an activation function to be differentiable?
- 7 Why do we use non linear activation functions?
- 8 Why do activation functions have to be monotonic?

## Which activation function is differentiable?

The main reason why we use sigmoid function is because it exists between (0 to 1). Therefore, it is especially used for models where we have to predict the probability as an output. Since probability of anything exists only between the range of 0 and 1, sigmoid is the right choice. The function is differentiable.

## Is neural network differentiable?

Since neural networks are themselves differentiable, you can use the resulting network as a differentiable loss function (don’t forget to freeze the network weights). This approach has been used among other things for differentiable rendering.

## Why do we need derivative of activation function?

In order to determine where that steepest slope is, you need the derivative of the activation function. Basically, you want to sort out how much each unit in your network contributes to an error, and adjust in the direction that contributes the most.

## Which activation function is continuous and differentiable?

As you can see, the range of values is between -1 to 1. Apart from that, all other properties of tanh function are the same as that of the sigmoid function. Similar to sigmoid, the tanh function is continuous and differentiable at all points.

## What can a neural network do without an activation function?

A neural network without an activation function is just a linear regression model. Generally, neural networks use non-linear activation functions, which can help the network learn complex data, compute and learn almost any function representing a question, and provide accurate predictions.

## Do you need an activation function to be differentiable?

No, it is not necessary that an activation function is differentiable. In fact, one of the most popular activation functions, the rectifier, is non-differentiable at zero!

## Why do we use non linear activation functions?

Non-linear functions address the problems of a linear activation function: They allow back-propagation because they have a derivative function which is related to the inputs. They allow “stacking” of multiple layers of neurons to create a deep neural network.

## Why do activation functions have to be monotonic?

Using http://mathonline.wikidot.com/lebesgue-s-theorem-for-the-differentiability-of-monotone-fun, assuming our activation function to be monotone, we can say that on the real line, our function will be differentiable. So, the gradient of the activation function will not be a erratic function.