Active learning with quantics tensor networks

Kurzfassung

Tensor networks are a computational technique originating in condensed matter physics, however in recent years they have been increasingly applied to machine learning, in particular in the context of more efficient classical models and model compression, as well as a natural language for quantum machine learning. Here we present a novel active learning algorithm for constructing models of black-box functions from very few samples, which is based on a DMRG-like local optimization of tensor networks, but utilizing the tensor cross-interpolation which bypasses the need for defining an energy. We underscore the potential of this method for scientific computing, particularly in the context of fast differentiation/integration and Fourier transforms. We illustrate these features using examples of simple mathematical functions.