Answers.Body: <p>I assume you're talking about a <a href="https://en.wikipedia.org/wiki/Perceptron" rel="nofollow noreferrer">perceptron</a> threshold function. One definition of it with an explicit threshold is
  <span class="math-container">$$f(\textbf{x})= 
  \begin{cases}
  1&amp; \text{if } \textbf{w}\cdot\textbf{x} &gt; t\\
  0&amp; \text{otherwise}
  \end{cases}.$$</span></p>
  
  <p>Another form with a bias is
  <span class="math-container">$$f(\textbf{x})= 
  \begin{cases}
  1&amp; \text{if } \textbf{w}\cdot\textbf{x} + b &gt; 0\\
  0&amp; \text{otherwise}
  \end{cases}.$$</span></p>
  
  <p>But these forms are of course equivalent if you set <span class="math-container">$b=-t$</span>.</p>
  
  <p>There's nothing stopping you from using a perceptron definition with both a bias and a threshold:
  <span class="math-container">$$f(\textbf{x})= 
  \begin{cases}
  1&amp; \text{if } \textbf{w}\cdot\textbf{x} +b &gt; t\\
  0&amp; \text{otherwise}
  \end{cases}.$$</span></p>
  
  <p>But this is also equivalent to the other two forms. We can rewrite this as
  <span class="math-container">$$f(\textbf{x})= 
  \begin{cases}
  1&amp; \text{if } \textbf{w}\cdot\textbf{x} &gt; t'\\
  0&amp; \text{otherwise}
  \end{cases}$$</span>
  where <span class="math-container">$t'=t-b$</span> is the new threshold. Or, we could rewrite it as 
  <span class="math-container">$$f(\textbf{x})= 
  \begin{cases}
  1&amp; \text{if } \textbf{w}\cdot\textbf{x} + a&gt; 0\\
  0&amp; \text{otherwise}
  \end{cases}$$</span>
  where <span class="math-container">$a=b-t$</span> is the new bias.</p>
  
  <p>You never see definitions of this function with both a threshold and a bias because it has simpler forms.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2019-04-06T07:03:27.060Z
Answers.LastActivityDate: 2019-04-06T07:03:27.060Z
Answers.UserDisplayName: Philip Raeisghasem
Body: <p>I have not seen a neuron that uses both a bias and a threshold. Why is this? </p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-04-06T04:41:00.897Z
Comments.Text: I'm unsure about what this question is asking. Could you clarify and provide some context?
Comments.UserDisplayName: Philip Raeisghasem
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-04-06T06:26:44.700Z
Comments.Text: i have seen that if we set bias in activation function then we don't have to set threshold value, one of them will be  use in activation function.  is this necessary in every case or there is any specific reason for that?
Comments.UserDisplayName: hina munir
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-04-06T07:23:28.253Z
Comments.Text: I did my best interpreting and answering your question. Please let me know if I understood you correctly.
Comments.UserDisplayName: Philip Raeisghasem
Tags: <neural-networks><neurons><perceptron>
Title: Can a neuron have both a bias and a threshold?
UserDisplayName: hina munir
ThreadText: # Can a neuron have both a bias and a threshold?
  
  (Asked by: username_0 on 2019-04-06)
  
  I have not seen a neuron that uses both a bias and a threshold. Why is this?
  
  **Tags:** neural-networks, neurons, perceptron
  > **Comments:**
  > **username_1**: I'm unsure about what this question is asking. Could you clarify and provide some context?  
  > **username_0**: i have seen that if we set bias in activation function then we don't have to set threshold value, one of them will be  use in activation function.  is this necessary in every case or there is any specific reason for that?  
  > **username_1**: I did my best interpreting and answering your question. Please let me know if I understood you correctly.  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_1 on 2019-04-06. Score: 4
  
  I assume you're talking about a [perceptron](https://en.wikipedia.org/wiki/Perceptron) threshold function. One definition of it with an explicit threshold is
  $$f(\textbf{x})=
  \begin{cases}
  1& \text{if } \textbf{w}\cdot\textbf{x} > t\\
  0& \text{otherwise}
  \end{cases}.$$
  
  Another form with a bias is
  $$f(\textbf{x})=
  \begin{cases}
  1& \text{if } \textbf{w}\cdot\textbf{x} + b > 0\\
  0& \text{otherwise}
  \end{cases}.$$
  
  But these forms are of course equivalent if you set $b=-t$.
  
  There's nothing stopping you from using a perceptron definition with both a bias and a threshold:
  $$f(\textbf{x})=
  \begin{cases}
  1& \text{if } \textbf{w}\cdot\textbf{x} +b > t\\
  0& \text{otherwise}
  \end{cases}.$$
  
  But this is also equivalent to the other two forms. We can rewrite this as
  $$f(\textbf{x})=
  \begin{cases}
  1& \text{if } \textbf{w}\cdot\textbf{x} > t'\\
  0& \text{otherwise}
  \end{cases}$$
  where $t'=t-b$ is the new threshold. Or, we could rewrite it as
  $$f(\textbf{x})=
  \begin{cases}
  1& \text{if } \textbf{w}\cdot\textbf{x} + a> 0\\
  0& \text{otherwise}
  \end{cases}$$
  where $a=b-t$ is the new bias.
  
  You never see definitions of this function with both a threshold and a bias because it has simpler forms.
  
  
  ---
  
  