Modeling Sequences with Quantum States: A Look Under the Hood

Abstract

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.

27 pages

References in corpus (10)

• The density-matrix renormalization group in the age of matrix product states
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Equivalence of restricted Boltzmann machines and tensor network states
• Tree Tensor Networks for Generative Modeling
• Machine Learning by Unitary Tensor Network of Hierarchical Tree Structure
• Learning Relevant Features of Data with Multi-scale Tensor Networks
• Supervised Learning with Quantum-Inspired Tensor Networks
• Matrix Product Operators for Sequence to Sequence Learning
• Probabilistic Modeling with Matrix Product States
• Shortcut Matrix Product States and its applications

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