Learning from complex, multidimensional data has become central to computational mathematics, and among the most successful high-dimensional function approximators are deep neural networks (DNNs).

Abstract: In this paper we analyzed definitions of the metric tensor, Christopher's symbols, Riemann and Ricci tensors, scalar curvature of space for different spaces. The component of the metric ...

前回はNumPyを使ってテンソルに触れてみました。今回はPyTorchのTensorを取り扱います。 すでに学んだNumPyのテンソルの知識は、どのように役立つでしょうか。 画像データなどはNumPy形式のデータとして扱われることが多くPyTorchのTensorもNumPyのデータを ...

Data collected at very frequent intervals is usually extremely sparse and has no structure that is exploitable by modern tensor decomposition algorithms. Thus, the utility of such tensors is low, in ...

We now introduce the core ideas of tensor networks, highlighting their connections with probabilistic graphical models (PGM) to align the terminology between them. For our purposes, a tensor is ...

A custom-built chip for machine learning from Google. Introduced in 2016 and found only in Google datacenters, the Tensor Processing Unit (TPU) is optimized for matrix multiplications, which are ...