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The visual world is vast and varied, but its variations divide intostructured and unstructured factors. We compose free-form filters andstructured Gaussian filters, optimized end-to-end, to factorize deeprepresentations and learn both local features and their degree of locality. Oursemi-structured composition is strictly more expressive than free-formfiltering, and changes in its structured parameters would require changes infree-form architecture. In effect this optimizes over receptive field size andshape, tuning locality to the data and task. Dynamic inference, in which theGaussian structure varies with the input, adapts receptive field size tocompensate for local scale variation. Optimizing receptive field size improvessemantic segmentation accuracy on Cityscapes by 1-2 points for strong dilatedand skip architectures and by up to 10 points for suboptimal designs. Adaptingreceptive fields by dynamic Gaussian structure further improves results,equaling the accuracy of free-form deformation while improving efficiency.

Blurring the Line Between Structure and Learning to Optimize and Adapt Receptive Fields