Generative networks as inverse problems with Scattering transforms
This work addresses the lack of mathematical understanding in generative models for researchers, but it appears incremental as it builds on existing concepts without a major breakthrough.
The paper tackled the problem of understanding the mathematics behind generative models like GANs and VAEs by proposing a method to compute deep convolutional network generators through inverting a fixed embedding operator, specifically using a wavelet Scattering transform, which eliminates the need for discriminators or encoders and shows similar properties in numerical experiments.
Generative Adversarial Nets (GANs) and Variational Auto-Encoders (VAEs) provide impressive image generations from Gaussian white noise, but the underlying mathematics are not well understood. We compute deep convolutional network generators by inverting a fixed embedding operator. Therefore, they do not require to be optimized with a discriminator or an encoder. The embedding is Lipschitz continuous to deformations so that generators transform linear interpolations between input white noise vectors into deformations between output images. This embedding is computed with a wavelet Scattering transform. Numerical experiments demonstrate that the resulting Scattering generators have similar properties as GANs or VAEs, without learning a discriminative network or an encoder.