I see three ways which neural networks for chess may take in future...
1. With more processing power available, the network size will raise, and we will have really big nets on one side of the extreme, which drop the search algorithm part and perform only a depth 1 search for evaluation.
2. With neural network accelerators with less latency, we will see engines with multiple, smaller neural networks, which perform deeper AlphaBeta searches on the other side.
3. Something in beetween 1. and 2.