Modeling Sequences with Quantum States: A Look Under the Hood
This work addresses the challenge of improving sequence modeling for machine learning researchers by leveraging quantum mechanics to potentially enhance information retention, though it appears incremental as it builds on existing DMRG methods.
The paper tackles the problem of modeling sequences using quantum states, specifically by employing a pure entangled quantum state to retain information about complementary subsystems, unlike classical marginal distributions. They developed a training algorithm based on the density matrix renormalization group (DMRG) to organize this extra information into a tensor network model, and as an illustration, estimated the generalization error as a function of the training dataset fraction for the even-parity dataset.
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.