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 Post subject: Using AI to study general board positions
Post #1 Posted: Sat Nov 19, 2022 5:29 pm 
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One of the down sides of AIs is that they only gives an opinion on a specific board position. My understanding is that this is because the input to the AI engine are two matrices (a black matrix and a white matrix) where the white and black stones are marked as a 1 at their respective positions. I am curious what would happen if a fractional value were to be input into these matrices?

The general problem I'm interested in is trying to get AI analysis of a corner position without great regard for the rest of the board. 15-20 years ago we would have used GoGOD and Kombilo to search on a corner pattern. Suppose we place a group of black stones in an adjacent corner with weights of 0.6 or something, to indicate some kind of black position there without being specific about what it is. Would the AI networks provide sensible output in that case?


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Post #2 Posted: Sat Nov 19, 2022 8:14 pm 
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Interesting idea pwaldron! I linked this on the Computer Go Community discord. You may know that most the bots also have additional history inputs where they give the board state for the previous N moves. But katago trained sometimes with similar idea to yours -- the board state was not given so the net has to deal with sometimes the history is not there (I don't know if the history is given as all 1s, all 0s, all 0.5 or what).

Anyways for the near-term you have to use workarounds. Katago author posted some research on corner stuff where he would usually put some minimal stones in the other corners, like maybe just 4-4 stone or maybe 4-4 stone with some approach or similar.

Also some katago GUIs support a feature where it locks katago into only playing in a specific part of the board which could help.

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Post #3 Posted: Mon Nov 21, 2022 6:16 am 
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yoyoma wrote:

Also some katago GUIs support a feature where it locks katago into only playing in a specific part of the board which could help.


I'd imagine that this would be somewhat straightforward. If you can limit AI analysis to a 9x9 board or a 13x13 board, it'd seem possible to generalize: limit the set of valid moves to an arbitrary boundary.

I'd imagine that the trained policy network may produce suboptimal moves for arbitrary "board boundaries" since it was trained on a 19x19 board, but maybe it'd still produce a decent analysis...

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Post #4 Posted: Mon Nov 21, 2022 8:57 am 
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yoyoma wrote:
I linked this on the Computer Go Community discord.


Would mind sharing a link to that discord server?

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Post #5 Posted: Wed Nov 23, 2022 6:13 am 
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pwaldron wrote:
The general problem I'm interested in is trying to get AI analysis of a corner position without great regard for the rest of the board.


Kirby wrote:
yoyoma wrote:
I'd imagine that this would be somewhat straightforward. If you can limit AI analysis to a 9x9 board or a 13x13 board, it'd seem possible to generalize: limit the set of valid moves to an arbitrary boundary.


Yes, but that doesn't solve the stated problem, as the AI still "knows" what the rest of the board looks like. You've stopped it offering tenukis, but it will still evaluate moves in the chosen region by how well they work in the global position.

Consider a joseki choice problem: in the top right, you might prefer move "A" if black has thickness in the lower right, or move "B" if black is weak in the lower right. The AI will always be biased in one direction or another, while a human can give a judgement along the lines of "move A is the shape move for this position, but B would be a special-purpose move" or vice versa. How do you get the AI to give this "all else being equal" kind of opinion?

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Post #6 Posted: Wed Nov 23, 2022 9:21 am 
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What is the underlying truth?

The whole board position always matters.

Only looking in a database for the moves in a restricted area without considering the whole board position was only half the task in the past. You had to check the games to get the complete picture.

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Post #7 Posted: Wed Nov 23, 2022 12:04 pm 
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Gomoto wrote:
Only looking in a database for the moves in a restricted area without considering the whole board position was only half the task in the past. You had to check the games to get the complete picture.


Let's take a very hypothetical position to illustrate what motivated the question. Suppose we have the corner position below. It's a complicated position, with multiple variations.
Click Here To Show Diagram Code
[go]$$
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . . . X . |
$$ . . . . . X X O . |
$$ . . . . X O O . . |
$$ . . . . . X O . . |
$$ . . . . . X O . . |
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ ---------------------[/go]


As you say, context is everything, but surely we ought to be able to draw conclusions on generalities as well--we've been playing go for a long time doing just that. So what variation might be expected when Black has some influence radiating from the bottom left? Here are three positions in that general category.

Click Here To Show Diagram Code
[go]$$
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . X . |
$$ | . O . . . . . . . . . . . . . X X O . |
$$ | . . . X . . . . . . . . . . X O O . . |
$$ | . . O X . . . . . . . . . . . X O . . |
$$ | . . O X . . . . . . . . . . . X O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------[/go]


Click Here To Show Diagram Code
[go]$$
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . O X . . . . . . . . . . . . . . X . |
$$ | . O X . . . . . . . . . . . . X X O . |
$$ | . O X . . . . . . . . . . . X O O . . |
$$ | . . O X . . . . . . . . . . . X O . . |
$$ | . . O X . . . . . . . . . . . X O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------[/go]


Click Here To Show Diagram Code
[go]$$
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . X . |
$$ | . . . . . . . . . . . . . . . X X O . |
$$ | . . . . . . . . . . . . . . X O O . . |
$$ | . . X . . X . . . . . . . . . X O . . |
$$ | . . . . . . . . . . . . . . . X O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------[/go]


The positions are different, but they have some similarities. When I posted the original question, the idea was whether I could distribute some group of black stones with fractional weight into the area to indicate that black, in essence, has friends in an adjacent area without fixing the position too much.

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Post #8 Posted: Wed Nov 23, 2022 1:19 pm 
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My point is, probably disappointingly, that every single stone on the board is important :-)

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Post #9 Posted: Thu Nov 24, 2022 2:58 am 
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Click Here To Show Diagram Code
[go]$$
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . . . X . |
$$ . . . . b X X O . |
$$ . . . c X O O . . |
$$ . . . . a X O . . |
$$ . . . . . X O . . |
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ ---------------------[/go]

When I put this corner into katago, the general choice is between White a and White b. Along the way, it seems that whether the ladder after White b Black c works or not is at least as important as the lower left corner position. This seems to imply that "vague" information on the other parts of the board will not yield meaningful analysis.

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Post #10 Posted: Thu Nov 24, 2022 6:39 am 
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ez4u wrote:
When I put this corner into katago, the general choice is between White a and White b. Along the way, it seems that whether the ladder after White b Black c works or not is at least as important as the lower left corner position. This seems to imply that "vague" information on the other parts of the board will not yield meaningful analysis.


We could just as easily ask about inserting vague information into the opposite corner to influence ladder questions. Fundamentally my question was whether providing stones with fractional weights as inputs to the neural net would provide a practical way of providing vague information that would influence the results.

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Post #11 Posted: Thu Nov 24, 2022 6:44 am 
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Gomoto wrote:
My point is, probably disappointingly, that every single stone on the board is important :-)


We know this can't be the universal situation. We have dozens of joseki books that look at corner sequences, and we know that, to a first approximation, the direct 3-3 invasion is a reasonable move in the opening regardless of what the adjacent corners are.

Whether that level of vagueness can be conveyed to an AI is a different question, and that was the one I was interested in.

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Post #12 Posted: Thu Nov 24, 2022 7:18 am 
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Quote:
The general problem I'm interested in is trying to get AI analysis of a corner position without great regard for the rest of the board.


I think this question is bedevilled by the confusing word 'analysis'.

From previous discussions of positions put through the AI meat grinders, most people seem to want to know the evaluations for various game moves based on the point score for the AI's best move. But as you are happy to disregard the rest of the board to some degree, I infer that is not really what you are looking for.

I further infer that you want to see various lines locally, and to get some sense of which ones may generally be the best. I would say that corresponds to the usual sense of 'analysis' in chess, which of course is a highly tactical game. If this is your area of interest, I'd further infer that you are hoping to want to use AI simply to get more tactical insights.

If all that is correct (probably not, in light of the thread title 'general' board positions), you may wish to be aware that Japanese magazines take this latter approach quite often, and Go Weekly even has a regular column devoted to it. They never talk about point scores or percentages (hooray!) but do talk about various unexpected tactical lines in corner positions that have been found recently (I assume AI input is to be taken as read). There is then a brief evaluation in terms either of what a particular line achieves (e.g. sabaki or thickness) or whether a line is playable or the like. There is rarely any mention of a wider board position, and no indication of how an AI search, if any, has been carried out, but I'm guessing that they just run a position through a bot and see what unexpected moves turn up, and the humans take it from there.

I think the column has been running for close to two years now, but maybe just looking at two or three may be enough to show you how to do it all for yourself, plus the sort of rewards this approach might give.

Incidentally, I may have just missed it as I don't pay much attention to that column, but I've been vaguely surprised that there has not yet been any use of tewari in discussing these positions in Go Weekly. People of my generation will recall the wonder of discovering tewari in Takagawa's Vital Points, a wonder that has stayed with me.

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Post #13 Posted: Thu Nov 24, 2022 8:01 am 
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Your summary largely hits what I'm after, John, including the vagaries of the word 'analysis'.

My general interest was trying to get back up to speed after a hiatus away from go. There's new josekis since the last time I played seriously and I'm trying to figure what plays are viable in different contexts. It got me thinking about how to use an AI to get that kind of information.

My phrasing about 'general board positions' was the idea that a line of play (joseki?) certainly depends on the full board position, but likely not the exact position. Positions with similar general properties--outside influence for one colour in an adjacent corner or (un)favourable ladders--will likely have similar continuations. Maybe that's not entirely true, but I suspect it's reasonable. If every single stone mattered critically in a position then we wouldn't have joseki that survive from game to game.

But how to get the AI to deal with that? If I firmly plant down a stone on the board and start the AI then it's going to do its AI thing and give me a specific line of play for a specific position. The idea was that maybe a single stone weight (=1.0) could be distributed around 5 neighbouring points with a fractional weight. Might a neural network interpret that as some kind of vague statement about the type of position it was dealing with?

The initial question was largely to the AI programming experts who would understand what input to a neural network actually represented.

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Post #14 Posted: Fri Nov 25, 2022 4:19 pm 
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pwaldron wrote:
My phrasing about 'general board positions' was the idea that a line of play (joseki?) certainly depends on the full board position, but likely not the exact position. Positions with similar general properties--outside influence for one colour in an adjacent corner or (un)favourable ladders--will likely have similar continuations. Maybe that's not entirely true, but I suspect it's reasonable. If every single stone mattered critically in a position then we wouldn't have joseki that survive from game to game.

But how to get the AI to deal with that?

I'm with you on this, and I believe it should be possible, but it would take a fair bit of work. Then again, I'm a dabbler in neural nets, not by any means an expert.

To put it crudely, a network contains a bunch of layers, the earlier layers capture local information about shape (e.g. recognising when a stone is in atari, or learning that empty triangles are likely to be bad), and the later layers are about building up that local knowledge into full-board judgement. A human is able to look at the whole board and choose what we think is the best move; a human can also choose to be a bit vague about the whole-board position and talk about the best local move, or the best move for a class of whole-board positions (e.g. "when black has thickness in the lower left" without specifying the exact shape). I believe it should be possible for an AI to "filter" the network in a similar way and pull out different sorts of judgements. The network contains more knowledge about go than is in any one human brain, so the answers you're looking for must be in there somewhere! But I'm not aware that anyone has tried.

I have a feeling that your suggestion of assigning fractional values to stones will cause weird side effects. But it's worth trying it anyway to see exactly what does go wrong. If I somehow end up with a spare 20 hours when I feel like hacking away at some code, I might give it a go. But I don't foresee that happening soon, sorry. Hopefully one of the real experts is up for such an experiment.

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Post #15 Posted: Tue Nov 29, 2022 1:13 pm 
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Further to my post above mentioning one new approach to writing about josekis in Go Weekly Japan, here is an example from the latest issue. This is number 99 in the series, time for a Cadbury's Flake.

The format is to give a problem and ask the reader to do something - nothing outlandish but perhaps not the sort of thing you expect to see in a joseki book. In this case, the task is to "find the only move that defends coolly."

There is always a bit of unrelated waffle which usually is outlandish. In this case it's a look at the pros and cons of hometown tax, a Japanese version of getting tax relief for giving money to charity. If you designate some money to another municipality other than the one you live (typically your furusato or home village - furusato is a very evocative word to the Japanese). You get to choose what the money is spent on, and you may get local goodies in return. It gets weirder - skin care comes into it. I'll take a chance and say this sort of thing is not what western go players are looking for.

There is also a hint. You may not want this either, but you are going to get it: White 1 is a mainstream technique for starting a fight against the Black shimari. It is now necessary to answer White 11 coolly (i.e. it is Black to play, and you need to play out the moves to White 11 while applying your moisturiser). The answer involves an unusual way of defending.

Problem



Answer 1



Diagram 1 - A modern joseki
Defending with Black 1 is the principal joseki line. In compensation for allowing White to strike at the head of two stones with 2, Black gobbles up four stones with 3 then 5, and so it is not a bad exchange for him.

Comment from me: I don't recall seeing this shape, so I'm assuming that 'joseki' is being used in the loose sense of corner opening, which is not uncommon in Japanese. But another possibility is that is seen a lot in online play and so is a joseki in the traditional sense. But apart from that, I find it hard to accept that White can truly be satisfied with this. He has played a stone less, but he is giving up a lot and is left with a thin gruel of a shape. He does have sente, though. The best inference I can make is that striking at the head of two stones in this sort of context is something worth doing according to AI, and I sense in any case that AI values sente even more than human pros do.


Answer 2



Diagram 2 - Reinforcing in sente
If Black defends 1, the probe of White is a burdensome move. When Black plays 3, White defends prophylactically in sente at 4. There remains something unsatisfactory for Black in this sequence.


Answer 3



Diagram 3 - Shortage of liberties
As to why [see Diag. 2], if Black resists with 1 instead of the Black 3 in the previous Diagram, that will make it hard for him to retaliate against White 2. For example, after the hane at Black 3, White devastates the lower side with 4 etc. If now Black hanes at 'A', White 'B' and so on crush Black.

Comment from me: Traditionally we'd expect bland comments at the level of "Black gets the corner and White gets thickness." But in this column, as here, we are getting ultra-fine shadings of evaluation, presumably based on AI evaluation (which is, however, not cited), and the typical dénouement, again as here, is that there is a nasty tactical sequence lurking in the position, which (I'm guessing) has only come to light when looking at AI. The only thing I have seen similar to this from pre-AI days is a book by Go Seigen called something like "After the Joseki" but I'm too lazy to look it up. It's certainly not the "How to Think about Joseki" by him, which is well worth a read (but it's for dan players, he says). In the book I'm thinking about, he shows common-or-garden josekis we all think we know but then he proceeds to show what might be hidden there when adjacent things happen in a real game. He doesn't just pull rabbits out of a hat, but giraffes, rhinoceroses and wardrobes. Some of the sequences make you physically gasp, and of course this is part of the reason why so many people think the AI style was already invented by Go. My view of the Go Weekly series is that they do likewise conjure up a lot of rabbits, as here, but nothing bigger and often something smaller. But the thinking behind the new approach (or 'the Go approach' may be more accurate) is there to be inferred in just the same way. These small weekly capsules can keep your go healthy and vibrant.

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Post #16 Posted: Wed Nov 30, 2022 12:38 pm 
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I've seen a similar shape with :w10: at S5 more often, then N5 O4 L6 tenuki or N5 O4 N7 Q7.

As for evaluation, this is an irresistable example.

answer1:
B has 2 stones more locally, taking gote after having 2 more stones originally. B expects 14*2=28 more stones.

counting N5 to T1 is 7*5 = 35. Plus P6 to T6 is 35+5=40 stones.

W has 4 stones only. However, with one move, the influence helps surround side territory, especially after M3. M3 is also supported by the option of N4 sente, which is more important than it looks, otherwise, the boundary is too thin to make territory with one move. After that, W will have an extra 3 lines of "head" as well as perhaps a 2*2 block of K5 to L4 extra compared to a normal 3rd line more. And B has little more than the line of N already counted. The main question is whether W's potential is territory or not and how much W can get from the attack. On an even board, we often count each extra line of head as 3 stones worth, which decreases to zero if the opponent is alive nearby (since the value is counterbalanced by the opponent's potential stones). In this case, we have in part already counted this in the 2x2 block, and not fully counted W's weak points either. However, the extra centre stone should surely help by "curling" around to counterattack if B comes near. This won't matter if B is alive enough nearby. But if B is weak, it may bring a kill half a move closer. Or push them away, so that W expects B to prepare with 1/2 move before, so perhaps we count 1-1/sqrt(2)=0.293 of W's potential rather than 1/2. At the same time, the local temperature is higher if there are weak points, so for example, B at K3 threatens both M2 and L4, so we give a larger portion to B before halving and so on.

It looks as though an integral could help here, but the corridor principle seems quite general. Assume in your opponent's area that you have influence corresponding to the value of your first move. This is strict if it is sente, and less if gote.

For now, B can at the least get M2 in semi sente, so lets estimate W as gaining control of K6 to M1 with a bit more, but subtracting 3 stones around M2.

What about B's influence? Note this is reduced by W's centre stones which are relatively light even if B is strong on both sides, because W's stones are relatively worthless if undermined. This means that by the time the temperature is low enough that capturing them is big, connecting them is likely also big.

It seems L3 is best locally, after which W M4 is likely (eventually) sente for N3. Then, B gets as extra perhaps only half of the M1 to M4 line at best and then perhaps with K2, 7 stones on the outside solid with potential for at least 3 more.

Then averaging between these, and cancelling the "at least", it seems we should count around K6, K5, L5, M5, M4 for W locally with half more on 7 others. This is 8.5 stones. Adding N6, O6 (not M6 due to weak point), it is around 11 stones.

Probably should be less because W isn't yet alive, and even locally, B has moves like M4.

This sort of analysis points out to me how much I underestimate strength on the 2nd line. It makes moyos much less interesting for either side, reducing temperature greatly.

On the other side, W can peep Q7 eventually say with O8 or R9 support. I am unsure how to count it as W has reasonable potential with both O8 and R9. And if W R9, then B cutting around P8 isn't really high temperature, so it seems plausible for W to get both. It seems that counting the usual 2 extra stones for B's 5 line wall is usual here. subtracting 1 from height due to Q7. However, if so, then it seems we should expect W gets O8 in sente or so, which is perhaps also a line of 2 extra from W's 5 stone centre wall. Presumably B's side wall counts for more, but I don't know how to judge W's shape. Perhaps count 4 extra stones for B from this?

This comes to 40+4-11=36 stones more for B.

This is 8 stones over expected, which is quite surprising. I can only conclude that the difference is made up for by W's centre potential, and that quite a bit can be gained by threatening to make territory on the sides, even after B spends a move. Basically I counted a height up to 6 on the lower side and a width of 5 from horizontally. However, there is also potential curving around in the J7 direction.

If this justification for the discrepancy is correct, my komi calculation is also missing something serious here. In that case, komi is expected to be exponential rather than polynomial in dimension number.


answer 2
using the usual extra 2 stones for each line of the wall, we have 5*8 -4 + 10 = 46 stones for B. W has perhaps 5 * 3 + 4 = 19. By this crude estimate, B+27 is expected which is reasonable as B is out on both sides and W isn't alive. If we ignore W's local life and death, it seems that locally B can threaten either from P7 and Q8, or from S7, (or R6/R7 with support).

The meaning of overconcentration is that extra defences don't help until the last boundary is sealed. Basically B always has at least R6 unless blocked. Although W can block, B still has 2nd line strength. This means 1 stone jumping S7 can go ahead 2 spaces with 2 lines of territory minus one weak point is 3 stones. Then 1st line and 2nd line development are miai, so opp has to play further to surround, after which B normally has at least the equivalent of another 2nd line move. Probably we just add 3-4 stones without halving for this potential, and maybe another for W not being alive.

However, W also expects a little more than this on the lower side perhaps because M3 threatens P2. Perhaps we subtract a (3*3-2)/4 (if W can play M3 with just 2 moves) and another 6/16 for P2 as that probably needs another move even if M3 is there to be played securely. This is then another 2 stones.

Overall B+28 seems about right.


centre evaluation and aggression
I think this has something to do each other. How to evaluate marginal expected profit from an area. If aggressive, it seems taking 4th line can be a good idea, trying to attack 3rd line with it "working".

Such areas are most "interesting" because the least moves have the highest mistake value. that is, they are close enough to death that it is valuable if the opponent makes a mistake.

I think this means allow the opponent weakish stones to give you strong but eyeless shape, then counterattack or kill when they attack your stones.

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