<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>

CC BY-SA 4.0
2022-05-11T12:37:03.867Z
2022-05-13T09:04:51.337Z
2022-05-13T09:04:51.337Z
NikoNyrh
<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>

<math><applications><academia>
Usability of power series in AI analysis
hanugm
# 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


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## 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)


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