The goal of this paper is to demonstrate a method for tensorizing neural networks based upon an efficient way of approximating scale invariant quantum states, the Multi-scale Entanglement Renormalization Ansatz (MERA). We employ MERA as a replacement for linear layers in a neural network and test this implementation on the CIFAR-10 dataset. The proposed method outperforms factorization using tensor trains, providing greater compression for the same level of accuracy and greater accuracy for the same level of compression. We demonstrate MERA-layers with 3900 times fewer parameters and a reduction in accuracy of less than 1% compared to the equivalent fully connected layers.

We replace the fully connected layers of a neural network with the multi-scale entanglement renormalization ansatz, a type of quantum operation which describes long range correlations.  In the paper the authors suggest to use MERA tensorization technique for compressing neural networks. A new parameterization of linear maps for neural network use, using a hierarchical factorization of the linear map that reduces the number of parameters while still allowing for relatively complex interactions to be modelled. Studies compressing feed forward layers using low rank tensor decompositions and explore a tree like decomposition