What are the inputs to the NN? The whole grid, or just nearby cells? What happens if two NNs overlap on the same grid? (Gonna go read the paper).

The input to the NN is just the 3x3 neighborhood around a cell. We can overlap two NNs on the same grid (through interpolation). Checkout https://meshnca.github.io to see the effect. When the brush is in graft mode, it basically allows you to paint some regions that will follow a different NN rule.