Efficient Finite Initialization with Partial Norms for Tensorized Neural Networks and Tensor Networks Algorithms

Fuente: arXiv
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Autores principales: Ali, Alejandro Mata, Delgado, Iñigo Perez, Roura, Marina Ristol, de Leceta, Aitor Moreno Fdez.
Formato: Preprint
Publicado: 2023
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author Ali, Alejandro Mata
Delgado, Iñigo Perez
Roura, Marina Ristol
de Leceta, Aitor Moreno Fdez.
author_facet Ali, Alejandro Mata
Delgado, Iñigo Perez
Roura, Marina Ristol
de Leceta, Aitor Moreno Fdez.
contents We present two algorithms to initialize layers of tensorized neural networks and general tensor network algorithms using partial computations of their Frobenius norms and positive lineal entrywise sums, depending on the type of tensor network involved. The core of this method is the use of the norm of subnetworks of the tensor network in an iterative way, so that we normalize by the finite values of the norms that led to the divergence or zero norm. In addition, the method benefits from the reuse of intermediate calculations. We have also applied it to the Matrix Product State/Tensor Train (MPS/TT) and Matrix Product Operator/Tensor Train Matrix (MPO/TT-M) layers and have seen its scaling versus the number of nodes, bond dimension, and physical dimension. All code is publicly available.
format Preprint
id arxiv_https___arxiv_org_abs_2309_06577
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Efficient Finite Initialization with Partial Norms for Tensorized Neural Networks and Tensor Networks Algorithms
Ali, Alejandro Mata
Delgado, Iñigo Perez
Roura, Marina Ristol
de Leceta, Aitor Moreno Fdez.
Machine Learning
Quantum Physics
68Q12, 15A69, 68T07
We present two algorithms to initialize layers of tensorized neural networks and general tensor network algorithms using partial computations of their Frobenius norms and positive lineal entrywise sums, depending on the type of tensor network involved. The core of this method is the use of the norm of subnetworks of the tensor network in an iterative way, so that we normalize by the finite values of the norms that led to the divergence or zero norm. In addition, the method benefits from the reuse of intermediate calculations. We have also applied it to the Matrix Product State/Tensor Train (MPS/TT) and Matrix Product Operator/Tensor Train Matrix (MPO/TT-M) layers and have seen its scaling versus the number of nodes, bond dimension, and physical dimension. All code is publicly available.
title Efficient Finite Initialization with Partial Norms for Tensorized Neural Networks and Tensor Networks Algorithms
topic Machine Learning
Quantum Physics
68Q12, 15A69, 68T07
url https://arxiv.org/abs/2309.06577