Answers.Body: <p>There is at least a TaylorSwiftNet (<a href="https://arxiv.org/abs/2110.14392" rel="nofollow noreferrer">Arxiv</a>). They model a (finite) Taylor series to predict the evolution of the hidden state, and a decoder to predict the observed state in a future time step.</p>
  <blockquote>
  <p>In this work, we therefore propose to approximate the motion in a
  video by a continuous function using the Taylor series. To this end,
  we introduce TayloSwiftNet, a novel convolutional neural network that
  learns to estimate the higher order terms of the Taylor series for a
  given input video. TayloSwiftNet can swiftly predict any desired
  future frame in just one forward pass and change the temporal
  resolution on-the-fly. The experimental results on various datasets
  demonstrate the superiority of our model.</p>
  </blockquote>
  <p><a href="https://i.sstatic.net/b77Gg.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/b77Gg.png" alt="enter image description here" /></a></p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2022-05-11T12:37:03.867Z
Answers.LastActivityDate: 2022-05-13T09:04:51.337Z
Answers.LastEditDate: 2022-05-13T09:04:51.337Z
Answers.UserDisplayName: NikoNyrh
Body: <p>In mathematics, <a href="https://tutorial.math.lamar.edu/classes/calcii/PowerSeries.aspx" rel="nofollow noreferrer">power series</a> is given by</p>
  <p><span class="math-container">$$f(x) = \sum\limits_{n=0}^{\infty} c_n (x-a)^n$$</span></p>
  <p>where <span class="math-container">$c_n , a \in \mathbb{R}$</span></p>
  <p>Although most of the courses in academics cover <em>moment generating functions</em> in probability theory for AI, which is power series by itself, I didn't encounter yet an application or analysis that contains power series in either textbooks or research papers.</p>
  <p>So, I want to know whether the power series has any usability in any branch of AI.</p>
  
Tags: <math><applications><academia>
Title: Usability of power series in AI analysis
UserDisplayName: hanugm
ThreadText: # Usability of power series in AI analysis
  
  (Asked by: username_0 on 2022-05-11)
  
  In mathematics, [power series](https://tutorial.math.lamar.edu/classes/calcii/PowerSeries.aspx) is given by
  
  $$f(x) = \sum\limits\_{n=0}^{\infty} c\_n (x-a)^n$$
  
  where $c\_n , a \in \mathbb{R}$
  
  Although most of the courses in academics cover *moment generating functions* in probability theory for AI, which is power series by itself, I didn't encounter yet an application or analysis that contains power series in either textbooks or research papers.
  
  So, I want to know whether the power series has any usability in any branch of AI.
  
  **Tags:** math, applications, academia
  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_1 on 2022-05-11. Score: 1
  
  There is at least a TaylorSwiftNet ([Arxiv](https://arxiv.org/abs/2110.14392)). They model a (finite) Taylor series to predict the evolution of the hidden state, and a decoder to predict the observed state in a future time step.
  
  > In this work, we therefore propose to approximate the motion in a
  > video by a continuous function using the Taylor series. To this end,
  > we introduce TayloSwiftNet, a novel convolutional neural network that
  > learns to estimate the higher order terms of the Taylor series for a
  > given input video. TayloSwiftNet can swiftly predict any desired
  > future frame in just one forward pass and change the temporal
  > resolution on-the-fly. The experimental results on various datasets
  > demonstrate the superiority of our model.
  
  [![enter image description here](https://i.sstatic.net/b77Gg.png)](https://i.sstatic.net/b77Gg.png)
  
  
  ---
  
  