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# SchrödingerRNN: Generative modeling of raw audio as a continuously observed quantum state

*Proceedings of the First Mathematical and Scientific Machine Learning Conference*, PMLR 107:74-106, 2020.

#### Abstract

We introduce SchrödingeRNN, a quantum-inspired generative model for raw audio. Audio data is wave-like and is sampled from a continuous signal. Although generative modeling of raw audio has made great strides lately, relational inductive biases relevant to these two characteristics are mostly absent from models explored to date. Quantum Mechanics is a natural source of probabilistic models of wave behavior. Our model takes the form of a stochastic Schrödinger equation describing the continuous time measurement of a quantum system, and is equivalent to the

*continuous Matrix Product State*(cMPS) representation of wavefunctions in one dimensional many-body systems. This constitutes a deep autoregressive architecture in which the system’s state is a latent representation of the past observations. We test our model on synthetic data sets of stationary and non-stationary signals. This is the first time cMPS are used in machine learning.