Answers.Body: <p>In reallity any continous function on a compact can be approximated by a neural network having one hidden layer with a finite number of neurones (This is the <a href="https://en.wikipedia.org/wiki/Universal_approximation_theorem" rel="nofollow noreferrer">Universal Approximation Theorem</a>). Thus you only need one hidden layer to approximate the multiplication on a compact, note that you need to apply a non linear activation on the hidden layer to do this. </p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-01-03T19:44:00.613Z
Answers.Text: All functions are bounded on a compact
Answers.UserDisplayName: hola
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-01-03T18:55:06.510Z
Answers.LastActivityDate: 2020-01-04T20:15:47.240Z
Answers.LastEditDate: 2020-01-04T20:15:47.240Z
Answers.UserDisplayName: hola
Body: <p>A single neuron with <strong>2 weights and identity activation</strong> can learn addition/subtraction as the 2 weights will converge to <strong>1 and 1</strong> (addition), or <strong>1 and -1</strong> (subtraction).</p>
  
  <p>However, for <strong>multiplication</strong> and <strong>division</strong>, it's not that easy. Can a single neuron learn multiplication or division? If not, how many layers of DNN can learn these?</p>
  
Tags: <neural-networks><machine-learning><deep-learning><feedforward-neural-networks>
Title: How to make DNN learn multiplication/division?
UserDisplayName: Dan D.
ThreadText: # How to make DNN learn multiplication/division?
  
  (Asked by: username_0 on 2019-12-26)
  
  A single neuron with **2 weights and identity activation** can learn addition/subtraction as the 2 weights will converge to **1 and 1** (addition), or **1 and -1** (subtraction).
  
  However, for **multiplication** and **division**, it's not that easy. Can a single neuron learn multiplication or division? If not, how many layers of DNN can learn these?
  
  **Tags:** neural-networks, machine-learning, deep-learning, feedforward-neural-networks
  
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  ## 1 answers
  
  ### Answer by username_1 on 2020-01-03. Score: 3 | Accepted answer
  
  In reallity any continous function on a compact can be approximated by a neural network having one hidden layer with a finite number of neurones (This is the [Universal Approximation Theorem](https://en.wikipedia.org/wiki/Universal_approximation_theorem)). Thus you only need one hidden layer to approximate the multiplication on a compact, note that you need to apply a non linear activation on the hidden layer to do this.
  
  > **Comments:**
  > **username_1**: All functions are bounded on a compact  
  
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