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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.
