  This paper addresses the problem of finding interpretable directions in the
latent space of pre-trained Generative Adversarial Networks (GANs) to
facilitate controllable image synthesis. Such interpretable directions
correspond to transformations that can affect both the style and geometry of
the synthetic images. However, existing approaches that utilise linear
techniques to find these transformations often fail to provide an intuitive way
to separate these two sources of variation. To address this, we propose to a)
perform a multilinear decomposition of the tensor of intermediate
representations, and b) use a tensor-based regression to map directions found
using this decomposition to the latent space. Our scheme allows for both linear
edits corresponding to the individual modes of the tensor, and non-linear ones
that model the multiplicative interactions between them. We show experimentally
that we can utilise the former to better separate style- from geometry-based
transformations, and the latter to generate an extended set of possible
transformations in comparison to prior works. We demonstrate our approach's
efficacy both quantitatively and qualitatively compared to the current
state-of-the-art.
