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Quantum Machine Learning

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

arXiv

Authors: Alejandro Mata Ali, Iñigo Perez Delgado, Marina Ristol Roura, Aitor Moreno Fdez. de Leceta

Year

2023

Paper ID

54990

Status

Preprint

Abstract Read

~2 min

Abstract Words

130

Citations

N/A

Abstract

We present two algorithms to initialize layers of tensorized neural networks and general tensor network algorithms using partial computations of their Frobenius norms and lineal entrywise norms, 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.

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This paper contributes to the Quantum Machine Learning research area in the Quantum Articles archive.
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We present two algorithms to initialize layers of tensorized neural networks and general tensor network algorithms using partial computations of their Frobenius norms and...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2309.06577 [2] arXiv https://arxiv.org/abs/2309.06577 [3] Publisher https://arxiv.org/abs/2309.06577

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