How would I represent this approach using convolution neural networks? • /r/MachineLearning

You don't necessarily need to write it as a neural network. At least in Tensorflow and Theano you can just write your computations as described and then let the library compute the gradients and update the values of your parameters (in this case 3x3x512). You would have to set a 3x3 constant filter filled with 1/9 so it computes the mean. Then apply it to the input to produce a map where every position is the mean around a 3x3 area. Then find a way to compute your 9-bit value for each position (maybe generating 9 copies of your map) or produce your number somehow and then select your weights (from the 512), for instance, put all your weights in a 9x512 matrix and multiply by a 512-dimensional vector with a one in the position you want.