Compressing multivariate functions with tree tensor networks
The work demonstrates using general tree tensor networks (TTNs) to numerically represent complex multivariate functions by quantizing inputs into binary digits. It shows how to construct elementary functions exactly and use interpolation algorithms like Tensor Cross Interpolation to learn general functions. Results indicate that structured TTNs, such as the Comb Tree Tensor Network (CTTN), outperform tensor train methods for high-dimensional problems.