Learning with Quantum-Inspired Tensor Networks

          @misc{ pirsa_PIRSA:16080007,
            doi = {10.48660/16080007},
            url = {https://pirsa.org/16080007},
            author = {Stoudenmire, Miles},
            keywords = {Condensed Matter},
            language = {en},
            title = {Learning with Quantum-Inspired Tensor Networks},
            publisher = {Perimeter Institute},
            year = {2016},
            month = {aug},
            note = {PIRSA:16080007 see, \url{https://pirsa.org}}
          }
          

Abstract

We propose a family of models with an exponential number of parameters, but which are approximated by a tensor network. Tensor networks are used to represent quantum wavefunctions, and powerful methods for optimizing them can be extended to machine learning applications as well. We use a matrix product state to classify images, and find that a surprisingly small bond dimension yields state-of-the-art results. Tensor networks offer many advantages for machine learning, such as better scaling for existing machine learning approaches and the ability to adapt hyperparameters during training. We will also propose a generative interpretation of the trained models.