Conditional Generation Using Polynomial Expansions

Grigorios Chrysos, Markos Georgopoulos, Yannis Panagakis

Keywords: polynomial expansions, polynomial neural networks, GAN, VAE, unseen combinations, conditional data generation

Abstract: Generative modeling has evolved to a notable field of machine learning. Deep polynomial neural networks (PNNs) have demonstrated impressive results in unsupervised image generation, where the task is to map an input vector (i.e., noise) to a synthesized image. However, the success of PNNs has not been replicated in conditional generation tasks, such as super-resolution. Existing PNNs focus on single-variable polynomial expansions which do not fare well to two-variable inputs, i.e., the noise variable and the conditional variable. In this work, we introduce a general framework, called CoPE, that enables a polynomial expansion of two input variables and captures their auto- and cross-correlations. We exhibit how CoPE can be trivially augmented to accept an arbitrary number of input variables. CoPE is evaluated in five tasks (class-conditional generation, inverse problems, edges-to-image translation, image-to-image translation, attribute-guided generation) involving eight datasets. The thorough evaluation suggests that CoPE can be useful for tackling diverse conditional generation tasks. The source code of CoPE is available at https://github.com/grigorisg9gr/polynomial_nets_for_conditional_generation.

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TL;DR: We condition the generator of a genertive model using a polynomial expansion

Code: https://github.com/grigorisg9gr/polynomial_nets_for_conditional_generation