Perhaps you would like to clarify how you are intending to use the word “local”?
My usage here is as follows: a “local pattern” is something whose presence or absence you can evaluate by looking at a small region of the board. (The smaller, the more local; locality comes in degrees. Presence or absence of a pattern might do, too.) So e.g. an empty triangle is an extremely local pattern; you can tell whether it is present by looking at a very small region of the board. A ponnuki is slightly less local, a table-shape slightly less local again, but these are all very local. A double-wing formation is substantially less local: to determine that one is present you need to look at (at least) a corner region and about half of one adjacent side. A ladder in one corner together with a ladder-breaker in the opposite corner is substantially less local again: to see that that’s present you need to look all the way across the board.
(I should maybe reiterate that the networks aren’t really computing simple binary “is there an empty triangle here?” values, at least not in later layers. But what they’re doing in their earlier layers is at least a little bit like asking whether a given pattern is present at each board location.)
This seems to me to be the standard sense, but I might well be missing something. I had a quick look through some books but didn’t spot any uses of the word “local” :-).
(One can talk about things other than patterns being local. E.g., you might say that a move is locally good, meaning something like “there is some, hopefully obvious, portion of the board within which this move is good for most plausible configurations of the rest of the board, but it’s possible that in the actual global position it’s not a good move”. Or sometimes you might say the same thing meaning just “this is the best move among moves in this part of the board”. Or you might say that a group is locally alive, meaning something similar: for the group to be dead there would need to be unusual things elsewhere on the board that somehow interact with it. All these things seem entirely compatible with what I’m saying about “local patterns”.)
The KataGo network is not pure CNN. It does something called “global pooling”, where at various points in the network the mean and max values across all board locations of some of the channels are computed and used to bias the values of the other channels in the next layer. So it learns to use those channels to compute things that are of global interest. I’m not sure how much is known about exactly what things they are, but I expect them to be things like which player is winning by how much, whether there are kos on the board or likely to be on the board soon, who has more ko threats, etc.
(In case you aren’t familiar with the relevant terminology, a “channel” is one of the things computed on each layer for each location on the board.)
Perhaps you would like to clarify how you are intending to use the word “local”?
My usage here is as follows: a “local pattern” is something whose presence or absence you can evaluate by looking at a small region of the board. (The smaller, the more local; locality comes in degrees. Presence or absence of a pattern might do, too.) So e.g. an empty triangle is an extremely local pattern; you can tell whether it is present by looking at a very small region of the board. A ponnuki is slightly less local, a table-shape slightly less local again, but these are all very local. A double-wing formation is substantially less local: to determine that one is present you need to look at (at least) a corner region and about half of one adjacent side. A ladder in one corner together with a ladder-breaker in the opposite corner is substantially less local again: to see that that’s present you need to look all the way across the board.
(I should maybe reiterate that the networks aren’t really computing simple binary “is there an empty triangle here?” values, at least not in later layers. But what they’re doing in their earlier layers is at least a little bit like asking whether a given pattern is present at each board location.)
This seems to me to be the standard sense, but I might well be missing something. I had a quick look through some books but didn’t spot any uses of the word “local” :-).
(One can talk about things other than patterns being local. E.g., you might say that a move is locally good, meaning something like “there is some, hopefully obvious, portion of the board within which this move is good for most plausible configurations of the rest of the board, but it’s possible that in the actual global position it’s not a good move”. Or sometimes you might say the same thing meaning just “this is the best move among moves in this part of the board”. Or you might say that a group is locally alive, meaning something similar: for the group to be dead there would need to be unusual things elsewhere on the board that somehow interact with it. All these things seem entirely compatible with what I’m saying about “local patterns”.)
The KataGo network is not pure CNN. It does something called “global pooling”, where at various points in the network the mean and max values across all board locations of some of the channels are computed and used to bias the values of the other channels in the next layer. So it learns to use those channels to compute things that are of global interest. I’m not sure how much is known about exactly what things they are, but I expect them to be things like which player is winning by how much, whether there are kos on the board or likely to be on the board soon, who has more ko threats, etc.
(In case you aren’t familiar with the relevant terminology, a “channel” is one of the things computed on each layer for each location on the board.)
That is a lot to consider. I’ll try to take my time to parse it apart a bit more before I try to respond.