Answers.Body: <p>This is not be a full answer to your question, but a good start I believe.
  Take a look at TDA (Topological Data Analysis) and how is topology used in nlp.</p>
  
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Answers.CreationDate: 2024-05-09T17:47:46.047Z
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Answers.UserDisplayName: Mostafa Eid
Answers.Body: <p><strong>YES</strong></p>
  <p><a href="https://en.wikipedia.org/wiki/Universal_approximation_theorem#Arbitrary_width" rel="nofollow noreferrer">Cybenko's 1989 universal approximation theorem</a>, loosely speaking, says that any &quot;decent&quot; function can be approximated as close as desired, using a neural network. This is part of why neural networks are so popular in many AI applications, because there is a theoretical argument for why they can fit complex relationships.</p>
  <p>One of the technical conditions about what constitutes a &quot;decent&quot; function relates to the topology, chiefly set compactness.</p>
  
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Answers.CreationDate: 2024-06-10T10:57:26.633Z
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Answers.UserDisplayName: Dave
Body: <p>Basic knowledge of topology
  How it relates to ai
  Does ai need to understand or integrate topology
  Can ai provide useful answers to hard topological problems</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-05-09T18:10:32.307Z
Comments.Text: Does this answer your question? [In what ways is the term "topology" applied to Artificial Intelligence?](https://ai.stackexchange.com/questions/7488/in-what-ways-is-the-term-topology-applied-to-artificial-intelligence)
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Comments.Text: This seems to ask two questions: 1) How does topology come in in the theoretical mathematics underlying artificial intelligence? 2) Can AI help us solve open problems in topology like the Hodge conjecture? I don't see these as the same.
Comments.UserDisplayName: Dave
Tags: <topology>
Title: Does topology have a place in ai
UserDisplayName: Raphael Pallais
ThreadText: # Does topology have a place in ai
  
  (Asked by: username_0 on 2024-05-09)
  
  Basic knowledge of topology
  How it relates to ai
  Does ai need to understand or integrate topology
  Can ai provide useful answers to hard topological problems
  
  **Tags:** topology
  
  > **Comments:**
  > **username_1**: Does this answer your question? [In what ways is the term "topology" applied to Artificial Intelligence?](https://ai.stackexchange.com/questions/7488/in-what-ways-is-the-term-topology-applied-to-artificial-intelligence)  
  > **username_2**: This seems to ask two questions: 1) How does topology come in in the theoretical mathematics underlying artificial intelligence? 2) Can AI help us solve open problems in topology like the Hodge conjecture? I don't see these as the same.  
  
  ---
  
  ## 2 answers
  
  ### Answer by username_3 on 2024-05-09. Score: 1
  
  This is not be a full answer to your question, but a good start I believe.
  Take a look at TDA (Topological Data Analysis) and how is topology used in nlp.
  
  
  ---
  
  ### Answer by username_2 on 2024-06-10. Score: 0
  
  **YES**
  
  [Cybenko's 1989 universal approximation theorem](https://en.wikipedia.org/wiki/Universal_approximation_theorem#Arbitrary_width), loosely speaking, says that any "decent" function can be approximated as close as desired, using a neural network. This is part of why neural networks are so popular in many AI applications, because there is a theoretical argument for why they can fit complex relationships.
  
  One of the technical conditions about what constitutes a "decent" function relates to the topology, chiefly set compactness.
  
  
  ---
  
  