<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>

CC BY-SA 4.0
2024-05-09T17:47:46.047Z
2024-05-09T17:47:46.047Z
Mostafa Eid
<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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2024-06-10T10:57:26.633Z
2024-06-10T10:57:26.633Z
Dave
<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>

CC BY-SA 4.0
2024-05-09T18:10:32.307Z
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)
nbro
CC BY-SA 4.0
2024-06-10T10:55:46.290Z
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.
Dave
<topology>
Does topology have a place in ai
Raphael Pallais
# 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.  

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## 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.


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### 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.


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