Schr"odingeRNN: Generative Modeling of Raw Audio as a Continuously Observed Quantum State

We introduce Schr"odingeRNN, a quantum inspired generative model for raw audio. Audio data is wave-like and is sampled from a continuous signal. Although generative modelling 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 behaviour. Our model takes the form of a stochastic Schr"odinger 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 systems 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.