Compressing multivariate functions with tree tensor networks
Year: 2026
Type: article
Abstract: Tensor networks are a compressed format for multi-dimensional data. One dimensional tensor networks—often referred to as tensor trains (TT) or matrix product states (MPS)—are increasingly being used as a numerical Ansatz for continuum functions by ``quantizing’’ the inputs into discrete binary digits. Here we demonstrate the power of more general tree tensor networks (TTNs) for this purpose. We provide direct constructions of a number of elementary functions as generic tree tensor networks and interpolative constructions for more complicated functions via a generalization of the tensor cross interpolation algorithm. For a range of multi-dimensional functions we show how more structured tree tensor networks offer a significantly more efficient Ansatz than the commonly used tensor train. Finally, we demonstrate how the methods introduced in this work can be used to realize a TTN-based solver for multi-dimensional, non-linear Fredholm equations.
Source: SciPost Physics
Institutions: Flatiron Institute, PsiQuantum (United States)
Language: English
Subfield: Computational Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Funder: Flatiron Health
OpenAlex ID: W4403884692