Convolutions for DL

I'd like to use this excellent package for the filters commonly used in deep learning. I tried a naive implementation here, but performance isn't great and I'm wondering if we need support in this package to improve that.

To give a rough outline of the semantics, we have a D×C×N image array where: D are the data dimension(s) (e.g. width and height), C is the channel dimension (e.g. colour) and N is a batch dimension (so we can convolve N independent images at once). This is convolved with a K×C×F filter (K being the filter dimension(s) and F being the number of filters / output channels) to produce a D′×F×N output array. Each slice along F is treated as a separate "filter" that spans the channel dimension, and the filter outputs are concatenated.

Hope that's clear and I'm happy to give more references if it's useful. Does this looks like something that's easy and appropriate for this package to support, or would it require an entirely new implementation?

Start by reviewing the naive implementation in the linked NNlib.jl pull request and compare its proposed D×C×N and K×C×F semantics with ImageFiltering.jl's existing convolution capabilities. Determine the appropriate API and performance requirements before implementation; done would mean supported deep-learning-style convolutions with the stated output shape and acceptable performance.