It would be interesting to see if there were some way to extract a couple of new heuristics from AlphaZero that could be implemented fast enough to incorporate in Stockfish's evaluator though. I suppose this is the age old problem of black-box models: _why_ does it think this?
I think that it is almost always possible to extract optimized models from nn and implement them faster. I wonder if this can be generalized. Nn to optimized fix algo for Max speed?
I dunno, seems like Google would just do this instead of keep around the pesky neural net at runtime. There's an _awful_ lot of computation going on inside, and it's necessarily hugely interconnected. I'd be impressed if someone had already done it, but it seems a great avenue of research if not. I suppose it goes hand in hand with models for which you can actually _explain_ their results, which certainly is an active area of research.
There are well-known techniques that work pretty well to shrink neural nets a lot while keeping almost all of their performance. See Geoffrey Hinton's model distillation papers.
The first AlphaGo paper had a system that used tons of computation, and was followed up by one that used much less and worked even better. Not speaking for Google, but I think it's a bit of a race to publish great results first. I wouldn't be surprised to see something better than this that uses 1000 times less resources published in a year or two, just like what happened with Go. First prove it's possible, than figure out how to make it much more efficient.
A really good example of model distillation also comes from DM: their new realtime WaveNet used in Google Assistant. The first WaveNet was ungodly slow due to redundant computation; but even after that, it still was not realtime simply because the CNN is too deep and slow. But you need the CNN to be deep & big in order to train good audio generation. Model distillation to the rescue: take a wide fast small CNN and train it to imitate the slow deep WaveNet. Result: WaveNet quality realtime voice generation which can be deployed to the masses.