While browsing the online, I found an interesting idea "chain pooling" presented here: https://github.com/jmgilmer/GoCNN
The idea is to have some early layers that perform a max-pool across solidly-connected stones. I could also imagine it being useful to perform a sum. So the input would be a 19x19 layer, and the output would be a 19x19 layer where the output at a given position, if that position is occupied by a stone, is equal to the maximum (or the sum of) all the values in the input layer across all stones that are solidly connected to that group. One might imagine going further and allowing the neural net some early convolutional layers that determine the connectivity strength for this pooling between groups, so that it could choose to pool across definite single-point eyes or bamboo joints, etc. It's possible that one would not want to force all layers through this operation, so possibly only some feature planes would be fed through this operation, or perhaps all of them but the identity transformation would also be an output of the layer to feed into the next. Speculatively, in the best case one might imagine this has a chance to improve the ability of the neural net to evaluate large semeai or to judge the status of large dragons, by letting it propagate liberty count information (including virtual liberties due to approach moves) and information about eyes across the board more rapidly than a series of local convolutions could do so. In fact, it seems that convolutional layers followed by an early pooling of this sort would make it unnecessary to provide liberties as an input feature because it would become easy for the neural net to compute it on its own, although one would still probably want to provide it to save the network the effort of having to learn it. Of course, this idea could also easily turn out worthless. One thing I'm very not sure about is how GPU-friendly this kind of operation could be made to be, since I don't understand GPUs. Any thoughts?
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