Generative models are important tools to capture and investigate the properties of complex empirical data. Recent developments such as Generative Adversarial Networks (GANs) and Variational Auto-Encoders (VAEs) use two very similar, but \textit{reverse}, deep convolutional architectures, one to generate and one to extract information from data. Does learning the parameters of both architectures obey the same rules? We exploit the causality principle of independence of mechanisms to quantify how the weights of successive layers adapt to each other. Using the recently introduced Spectral Independence Criterion, we quantify the dependencies between the kernels of successive convolutional layers and show that those are more independent for the generative process than for information extraction, in line with results from the field of causal inference. In addition, our experiments on generation of human faces suggest that more independence between successive layers of generators results in improved performance of these architectures.

We use causal inference to characterise the architecture of generative models This paper examines the nature of convolutional filters in the encoder and a decoder of a VAE, and a generator and a discriminator of a GAN. This work exploits the causality principle to quantify how the weights of successive layers adapt to each other.