On page 27 of the DeepMind AlphaGo paper appears the following sentence:
The first hidden layer zero pads the input into a $23 \times 23$ image, then convolves $k$ filters of kernel size $5 \times 5$ with stride $1$ with the input image and applies a rectifier nonlinearity.
What does "convolves $k$ filters" mean here?
Does it mean the following:
The first hidden layer is a convolutional layer with $k$ groups of $(19 \times 19)$ neurons, where there is a kernel of $(5 \times 5 \times numChannels + 1)$ parameters (input weights plus a bias term) used by all the neurons of each group. $numChannels$ is 48 (the number of feature planes in the input image stack).
All $(19 \times 19 \times k)$ neurons' outputs are available to the second hidden layer (which happens to be another convolutional layer, but could in principle be fully connected).