  A popular series of style transfer methods apply a style to a content image
by controlling mean and covariance of values in early layers of a feature
stack. This is insufficient for transferring styles that have strong structure
across spatial scales like, e.g., textures where dots lie on long curves. This
paper demonstrates that controlling inter-layer correlations yields visible
improvements in style transfer methods. We achieve this control by computing
cross-layer, rather than within-layer, gram matrices. We find that (a)
cross-layer gram matrices are sufficient to control within-layer statistics.
Inter-layer correlations improves style transfer and texture synthesis. The
paper shows numerous examples on "hard" real style transfer problems (e.g. long
scale and hierarchical patterns); (b) a fast approximate style transfer method
can control cross-layer gram matrices; (c) we demonstrate that multiplicative,
rather than additive style and content loss, results in very good style
transfer. Multiplicative loss produces a visible emphasis on boundaries, and
means that one hyper-parameter can be eliminated.
