Quantum latent distributions from boson samplers are shown in theory to expand the output distribution class of invertible Lipschitz generators, and in GAN benchmarks on QM9 to beat Gaussian, Bernoulli, and distinguishable-photon baselines, though the gain is hyperparameter-sensitive.
Generalization Properties of Optimal Transport GANs with Latent Distribution Learning
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abstract
The Generative Adversarial Networks (GAN) framework is a well-established paradigm for probability matching and realistic sample generation. While recent attention has been devoted to studying the theoretical properties of such models, a full theoretical understanding of the main building blocks is still missing. Focusing on generative models with Optimal Transport metrics as discriminators, in this work we study how the interplay between the latent distribution and the complexity of the pushforward map (generator) affects performance, from both statistical and modelling perspectives. Motivated by our analysis, we advocate learning the latent distribution as well as the pushforward map within the GAN paradigm. We prove that this can lead to significant advantages in terms of sample complexity.
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Quantum latent distributions in deep generative models
Quantum latent distributions from boson samplers are shown in theory to expand the output distribution class of invertible Lipschitz generators, and in GAN benchmarks on QM9 to beat Gaussian, Bernoulli, and distinguishable-photon baselines, though the gain is hyperparameter-sensitive.