<p>Nonlinear relations between input and output can be achieved by using a nonlinear activation function on the value of each neuron, before it's passed on to the neurons in the next layer.</p>

CC BY-SA 4.0
2018-08-19T20:27:04.710Z
2018-08-19T20:27:04.710Z
Mr. Eivind
<p>As I know, a single layer neural network can only do linear operations, but multilayered ones can.</p>

<p>Also, I recently learned that finite matrices/tensors, which are used in many neural networks, can <em>only represent linear</em> operations.</p>

<p>However, multi-layered neural networks can represent non-linear (even much more complex than being just a nonlinear) operations.</p>

<p>What makes it happen? The activation layer?</p>

CC BY-SA 4.0
2018-08-19T19:45:26.750Z
The very quick answer is; yes, nonlinear **activation functions** in between linear transformations (matrix multiplications) allow for the "total" to represent non-linear functions.
Dennis Soemers
<neural-networks><machine-learning><math><activation-functions><function-approximation>
What makes multi-layer neural networks able to perform nonlinear operations?
Hyeonseo Yang
# What makes multi-layer neural networks able to perform nonlinear operations?

(Asked by: username_0 on 2018-08-19)

As I know, a single layer neural network can only do linear operations, but multilayered ones can.

Also, I recently learned that finite matrices/tensors, which are used in many neural networks, can *only represent linear* operations.

However, multi-layered neural networks can represent non-linear (even much more complex than being just a nonlinear) operations.

What makes it happen? The activation layer?

**Tags:** neural-networks, machine-learning, math, activation-functions, function-approximation

> **Comments:**
> **username_1**: The very quick answer is; yes, nonlinear **activation functions** in between linear transformations (matrix multiplications) allow for the "total" to represent non-linear functions.  

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## 1 answers

### Answer by username_2 on 2018-08-19. Score: 5 | Accepted answer

Nonlinear relations between input and output can be achieved by using a nonlinear activation function on the value of each neuron, before it's passed on to the neurons in the next layer.


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