<blockquote>
  <p>In Single Perceptron / Multi-layer Perceptron(MLP), we only have linear separability because they are composed of input and output layers(some hidden layers in MLP)</p>
</blockquote>

<p>This is <strong>wrong</strong>. </p>

<p>A multi-layer perceptron (i.e. a feed-forward neural network) with non-linear activation functions can perform non-linear classification and regression. In fact, an MLP with one hidden layer with an arbitrary number of hidden nodes, each of them with a sigmoid (which is a non-linear function), can approximate any continuous function (up to an approximation error).</p>

<p>On the other hand, perceptrons can't do that. They perform only linear classification/regression.</p>

<blockquote>
  <p>I thought the MLP was a non-linear classifier.</p>
</blockquote>

<p>You're right, unless the MLP only uses linear activation functions. In that case, it won't be able to perform non-linear classification/regression.</p>

<p>(P.S.: I suggest you always question the truth and correctness of what you read on the web, especially, on sites like Medium, as you actually did!)</p>

CC BY-SA 4.0
2020-04-23T10:45:16.527Z
Is it true to say that, in a MLP the neurons in the hidden layer can use only nonlinear activation functions while the neurons in the output layer can use or a linear or a non linear activation function ?
AleWolf
CC BY-SA 4.0
2020-04-23T11:18:19.077Z
@AleWolf They can use linear or non-linear activation functions everywhere, in principle.
nbro
CC BY-SA 4.0
2020-04-23T11:49:30.013Z
But, if they use linear activation function everywhere then that particular MLP would be linear, right ?
AleWolf
CC BY-SA 4.0
2020-04-23T11:56:19.333Z
@AleWolf It would be linear in the sense that it would represent a straight-line.
nbro
CC BY-SA 4.0
2020-04-22T18:55:13.377Z
2020-04-22T19:01:12.027Z
2020-04-22T19:01:12.027Z
nbro
<p>In this <a href="https://towardsdatascience.com/radial-basis-functions-neural-networks-all-we-need-to-know-9a88cc053448" rel="nofollow noreferrer">page</a> it's told:</p>

<blockquote>
  <p>In Single Perceptron / Multi-layer Perceptron(MLP), we only have linear separability because they are composed of input and output layers(some hidden layers in MLP)</p>
</blockquote>

<p>What does it mean? I thought the MLP was a non-linear classifier. Could you explain it to me?</p>

<deep-learning><multilayer-perceptrons><perceptron>
Why can't MLPs perform non-linear regression and classification?
AleWolf
# Why can't MLPs perform non-linear regression and classification?

(Asked by: username_0 on 2020-04-22)

In this [page](https://towardsdatascience.com/radial-basis-functions-neural-networks-all-we-need-to-know-9a88cc053448) it's told:

> In Single Perceptron / Multi-layer Perceptron(MLP), we only have linear separability because they are composed of input and output layers(some hidden layers in MLP)

What does it mean? I thought the MLP was a non-linear classifier. Could you explain it to me?

**Tags:** deep-learning, multilayer-perceptrons, perceptron


---

## 1 answers

### Answer by username_1 on 2020-04-22. Score: 2 | Accepted answer

> In Single Perceptron / Multi-layer Perceptron(MLP), we only have linear separability because they are composed of input and output layers(some hidden layers in MLP)

This is **wrong**.

A multi-layer perceptron (i.e. a feed-forward neural network) with non-linear activation functions can perform non-linear classification and regression. In fact, an MLP with one hidden layer with an arbitrary number of hidden nodes, each of them with a sigmoid (which is a non-linear function), can approximate any continuous function (up to an approximation error).

On the other hand, perceptrons can't do that. They perform only linear classification/regression.

> I thought the MLP was a non-linear classifier.

You're right, unless the MLP only uses linear activation functions. In that case, it won't be able to perform non-linear classification/regression.

(P.S.: I suggest you always question the truth and correctness of what you read on the web, especially, on sites like Medium, as you actually did!)

> **Comments:**
> **username_0**: Is it true to say that, in a MLP the neurons in the hidden layer can use only nonlinear activation functions while the neurons in the output layer can use or a linear or a non linear activation function ?  
> **username_1**: @username_0 They can use linear or non-linear activation functions everywhere, in principle.  
> **username_0**: But, if they use linear activation function everywhere then that particular MLP would be linear, right ?  
> **username_1**: @username_0 It would be linear in the sense that it would represent a straight-line.  

---

