Answers.Body: <p>Both uses of the word <em>bias</em> are appropriate, and they are consistent.</p>
  <p>In a threshold perceptron, the output <span class="math-container">$a$</span> (from activation) is given by</p>
  <p><span class="math-container">$a=$</span></p>
  <p><span class="math-container">$1$</span> if <strong><span class="math-container">$wx$</span></strong><span class="math-container">$+b &gt; 0$</span></p>
  <p><span class="math-container">$0$</span> otherwise,</p>
  <p>so the output indicates whether <strong><span class="math-container">$wx$</span></strong> is larger than <span class="math-container">$-b$</span> or not.</p>
  <p>Recall the linear equation before the threshold, where <strong><span class="math-container">$w$</span></strong> is a vector of weights <span class="math-container">$w_i$</span> for the inputs <span class="math-container">$x_i$</span>. If you have only one input, <span class="math-container">$x_1$</span>, this single weight <span class="math-container">$w=w_1$</span> corresponds to the slope of the straight line <span class="math-container">$y=w_1 x_1+b$</span>.</p>
  <p>If your goal is prediction by linear regression, instead of comparison, you may use a linear neuron, with the identity function as an activation function instead of the threshold.
  Here the output is simply the linear combination of the inputs</p>
  <p><span class="math-container">$a=$</span><strong><span class="math-container">$wx$</span></strong><span class="math-container">$+b$</span></p>
  <p>In this case the function of the bias is shifting the prediction obtained from multiplying the inputs by the weights only, as you mention.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2022-09-01T14:14:20.540Z
Answers.Text: So, the bias is called the threshold because wx has to be greater than -b, because otherwise a = 0, e.g. the threshold is not met? 
  
  Wouldn't we then have to call -b the threshold and not b itself?
Answers.UserDisplayName: DerOeko
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Answers.Text: Mmm, I would not link threshold and bias. The bias is b and the threshold is 0, or the hyperplane wx+b=0.
Answers.UserDisplayName: Jaume Oliver Lafont
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Answers.CreationDate: 2022-08-31T10:41:19.500Z
Answers.LastActivityDate: 2022-08-31T10:41:19.500Z
Answers.UserDisplayName: Jaume Oliver Lafont
Body: <p>I just have a quick question, maybe I am too nit picky here.</p>
  <p>We recently had an introductory lecture to AI in university and the professor talked about McCulloch-Pitts neurons, e.g. activation as soon as the sum of inputs is reaching a certain threshold amount. My problem is that the professor said that the threshold amount is also called &quot;bias&quot;, is that correct?</p>
  <p>I thought biases are analogous to the y intercept of a linear equation and added on every equation made with the neural network, in order to balance out systematic error in predictions.</p>
  <p>To be specific, my question is, whether the threshold met in a McCulloch-Pitts neuron is actually called bias or not.</p>
  <p>Any hints appreciated! :)</p>
  <p>Best regards,
  Sam!</p>
  
Tags: <terminology><ai-basics><bias>
Title: Confusion about bias in McCulloch-Pitts neurons
UserDisplayName: DerOeko
ThreadText: # Confusion about bias in McCulloch-Pitts neurons
  
  (Asked by: username_0 on 2022-08-31)
  
  I just have a quick question, maybe I am too nit picky here.
  
  We recently had an introductory lecture to AI in university and the professor talked about McCulloch-Pitts neurons, e.g. activation as soon as the sum of inputs is reaching a certain threshold amount. My problem is that the professor said that the threshold amount is also called "bias", is that correct?
  
  I thought biases are analogous to the y intercept of a linear equation and added on every equation made with the neural network, in order to balance out systematic error in predictions.
  
  To be specific, my question is, whether the threshold met in a McCulloch-Pitts neuron is actually called bias or not.
  
  Any hints appreciated! :)
  
  Best regards,
  Sam!
  
  **Tags:** terminology, ai-basics, bias
  
  
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  ## 1 answers
  
  ### Answer by username_1 on 2022-08-31. Score: 1 | Accepted answer
  
  Both uses of the word *bias* are appropriate, and they are consistent.
  
  In a threshold perceptron, the output $a$ (from activation) is given by
  
  $a=$
  
  $1$ if **$wx$**$+b > 0$
  
  $0$ otherwise,
  
  so the output indicates whether **$wx$** is larger than $-b$ or not.
  
  Recall the linear equation before the threshold, where **$w$** is a vector of weights $w\_i$ for the inputs $x\_i$. If you have only one input, $x\_1$, this single weight $w=w\_1$ corresponds to the slope of the straight line $y=w\_1 x\_1+b$.
  
  If your goal is prediction by linear regression, instead of comparison, you may use a linear neuron, with the identity function as an activation function instead of the threshold.
  Here the output is simply the linear combination of the inputs
  
  $a=$**$wx$**$+b$
  
  In this case the function of the bias is shifting the prediction obtained from multiplying the inputs by the weights only, as you mention.
  
  > **Comments:**
  > **username_0**: So, the bias is called the threshold because wx has to be greater than -b, because otherwise a = 0, e.g. the threshold is not met?   Wouldn't we then have to call -b the threshold and not b itself?  
  > **username_1**: Mmm, I would not link threshold and bias. The bias is b and the threshold is 0, or the hyperplane wx+b=0.  
  
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