# Usability of power series in AI analysis

In mathematics, power series 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.

There is at least a TaylorSwiftNet (Arxiv). 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.