Answers.Body: <p>The perceptron uses the <em>Heaviside step</em> (or <em>sign</em>) function as the <a href="https://en.wikipedia.org/wiki/Activation_function" rel="nofollow noreferrer">activation function</a> (so you are not free to use any activation function), while a GLM is a generalization of linear regression, where the <em>link function</em> can be, for example, the <em>logit</em> (which leads to the <em>logistic regression</em>), <em>identity</em> function (which leads to <em>linear regression</em>), and so on. The sign function has the role in the perceptron as the <em>sigmoid</em> in logistic regression.</p>
  <p>So, GLM models have a <em>probabilistic</em> interpretation (i.e. you assume that the response variable follows some distribution), while perceptrons do not, even though, for example, the perceptron and logistic regression can both be used for classification.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2021-08-07T15:18:01.420Z
Answers.LastActivityDate: 2021-08-07T17:32:19.070Z
Answers.LastEditDate: 2021-08-07T17:32:19.070Z
Answers.UserDisplayName: nbro
Body: <p>In a comment to <a href="https://ai.stackexchange.com/q/30037/18652">this question</a> user nbro comments:</p>
  <blockquote>
  <p>As a side note, &quot;perceptrons&quot; and &quot;neural networks&quot; may not be the same thing. People usually use the term perceptron to refer to a very simple neural network that has no hidden layer. Maybe you meant the term &quot;multi-layer perceptron&quot; (MLP).</p>
  </blockquote>
  <p>As I understand it, a simple neural network with no hidden layer would simply be a linear model with a non-linearity put on top of it. That sounds exactly like a generalized linear model (GLM), with the non-linearity being the GLM's link function.</p>
  <p>Is there a notable difference between (non-multi-layer) perceptrons and GLMs? Or is it simply another case of two equivalent methods having different names from different researchers?</p>
  
Tags: <perceptron>
Title: What's the difference between a "perceptron" and a GLM?
UserDisplayName: R.M.
ThreadText: # What's the difference between a "perceptron" and a GLM?
  
  (Asked by: username_0 on 2021-08-07)
  
  In a comment to [this question](https://ai.stackexchange.com/q/30037/18652) user nbro comments:
  
  > As a side note, "perceptrons" and "neural networks" may not be the same thing. People usually use the term perceptron to refer to a very simple neural network that has no hidden layer. Maybe you meant the term "multi-layer perceptron" (MLP).
  
  As I understand it, a simple neural network with no hidden layer would simply be a linear model with a non-linearity put on top of it. That sounds exactly like a generalized linear model (GLM), with the non-linearity being the GLM's link function.
  
  Is there a notable difference between (non-multi-layer) perceptrons and GLMs? Or is it simply another case of two equivalent methods having different names from different researchers?
  
  **Tags:** perceptron
  
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  ## 1 answers
  
  ### Answer by username_1 on 2021-08-07. Score: 3 | Accepted answer
  
  The perceptron uses the *Heaviside step* (or *sign*) function as the [activation function](https://en.wikipedia.org/wiki/Activation_function) (so you are not free to use any activation function), while a GLM is a generalization of linear regression, where the *link function* can be, for example, the *logit* (which leads to the *logistic regression*), *identity* function (which leads to *linear regression*), and so on. The sign function has the role in the perceptron as the *sigmoid* in logistic regression.
  
  So, GLM models have a *probabilistic* interpretation (i.e. you assume that the response variable follows some distribution), while perceptrons do not, even though, for example, the perceptron and logistic regression can both be used for classification.
  
  
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