Good approximations are an essential part of today’s numerical methods and are therefore highly desirable, especially when dealing with high-dimensional datasets. One tool for approximating such data are tensor networks. Already introduced in the early 90s for simulating quantum spin chains, tensor networks have proven to be applicable to classical data as well and offer a well-established framework for doing arithmetic with compressed data.

In this talk, we will introduce linear tensor networks, also called tensor trains in literature, and show their applications when dealing with classical data or simulations. Starting with the basics on how the data is approximated, we will continue with the arithmetic of compressed data described by tensor networks. We especially emphasize how tensor network libraries compare to other libraries like NumPy or Torch and describe their benefits and drawbacks.

Topics of the talk:

Introduction to linear tensor networks
Quantics representation
Arithmetic of compressed data
Tensor networks as extension of normal tensors
Functions as tensor networks
Examples: Data compression, neural networks, simulations

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