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.
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