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

Beñat Mencia Uranga, Austen Lamacraft
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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v107-mencia-uranga20a, title = {SchrödingerRNN: {G}enerative modeling of raw audio as a continuously observed quantum state}, author = {Mencia Uranga, Be\~nat and Lamacraft, Austen}, booktitle = {Proceedings of the First Mathematical and Scientific Machine Learning Conference}, pages = {74--106}, year = {2020}, editor = {Lu, Jianfeng and Ward, Rachel}, volume = {107}, series = {Proceedings of Machine Learning Research}, month = {20--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v107/mencia-uranga20a/mencia-uranga20a.pdf}, url = {https://proceedings.mlr.press/v107/mencia-uranga20a.html}, 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.} }
Endnote
%0 Conference Paper %T SchrödingerRNN: Generative modeling of raw audio as a continuously observed quantum state %A Beñat Mencia Uranga %A Austen Lamacraft %B Proceedings of the First Mathematical and Scientific Machine Learning Conference %C Proceedings of Machine Learning Research %D 2020 %E Jianfeng Lu %E Rachel Ward %F pmlr-v107-mencia-uranga20a %I PMLR %P 74--106 %U https://proceedings.mlr.press/v107/mencia-uranga20a.html %V 107 %X 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.
APA
Mencia Uranga, B. & Lamacraft, A.. (2020). SchrödingerRNN: Generative modeling of raw audio as a continuously observed quantum state. Proceedings of the First Mathematical and Scientific Machine Learning Conference, in Proceedings of Machine Learning Research 107:74-106 Available from https://proceedings.mlr.press/v107/mencia-uranga20a.html.

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