Modeling sequences with quantum states: a look under the hood
| Autor: | Tai-Danae Bradley, John Terilla, E. Miles Stoudenmire |
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| Rok vydání: | 2020 |
| Předmět: |
FOS: Computer and information sciences
Quantum Physics Computer Science - Machine Learning Computer science Density matrix renormalization group FOS: Physical sciences Machine Learning (stat.ML) Function (mathematics) Machine Learning (cs.LG) Human-Computer Interaction Statistics - Machine Learning Artificial Intelligence Quantum state Probability distribution Fraction (mathematics) Statistical physics Tensor Marginal distribution Quantum Physics (quant-ph) Software Network model |
| Zdroj: | Machine Learning: Science and Technology. 1:035008 |
| ISSN: | 2632-2153 |
| DOI: | 10.1088/2632-2153/ab8731 |
| Popis: | Classical probability distributions on sets of sequences can be modeled using quantum states. Here, we do so with a quantum state that is pure and entangled. Because it is entangled, the reduced densities that describe subsystems also carry information about the complementary subsystem. This is in contrast to the classical marginal distributions on a subsystem in which information about the complementary system has been integrated out and lost. A training algorithm based on the density matrix renormalization group (DMRG) procedure uses the extra information contained in the reduced densities and organizes it into a tensor network model. An understanding of the extra information contained in the reduced densities allow us to examine the mechanics of this DMRG algorithm and study the generalization error of the resulting model. As an illustration, we work with the even-parity dataset and produce an estimate for the generalization error as a function of the fraction of the dataset used in training. Comment: 27 pages |
| Databáze: | OpenAIRE |
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