Predicted ownership heatmaps

[lightvector]

Edit: See also this post below for some real-time videos of ownership on a 9x9 board during selfplay!

In case Uberdude or anyone else is interested based on his earlier post in that other thread about how different corner moves have very distinctive effects on corner ownership that normal influence maps don't necessarily capture well - I have a 15-block neural net now that is perhaps on-par with LZ120 in strength. One of the things it's trained to do is directly predict who owns each spot on the board at the end of the game.

Here are colored maps of its predicted ownership of points on the board for a few corner positions. For the ones with a single black stone, I always had white take 4-4 in reply before screenshotting. For the ones with two black stones, I always had white take both 4-4s on the right in reply before screenshotting.

The brightest pinks, which you see under the black stones themselves, correspond to about a 90% probability of ownership. Also keep in mind this ownership is also not actually too much of the overall weight of what the net is told to "care about" in training (it cares a lot more about things directly affecting playing strength), so it might not be entirely accurate.

Anyways, here we go:

44

A much weaker hold on the corner than 3-4 or 3-3.

44.png (82.99 KiB) Viewed 10442 times

34

The orange spot at E17 indicating probable *white* ownership is because in the current metagame the net prefers the low approach to 3-4 points, and this reflects the probability that white will approach there in the future and end up owning that spot on the board. It looks like white also likes playing the 4-4 point attachment.

34.png (83.23 KiB) Viewed 10442 times

33

The orange spot at at D16 indicating probable *white* ownership is because in the current metagame the net often likes shoulder-hitting 3-3, and this reflects the probability that white will do so in the future and end up owning that spot on the board.

33.png (83.1 KiB) Viewed 10442 times

[lightvector]

34 small knight

Strong hold on the corner. The light spot at C15 is because in the current metagame the net likes that attachment against this enclosure for white, so this reflects the probability that white will do that in the future and end up owning that spot on the board.

34knight.png (84.41 KiB) Viewed 10441 times

44 big knight

Weaker hold on the corner. The light spot at D16 is because in the current metagame the net likes that attachment against this enclosure for white, so this reflects the probability that white will do that in the future and end up owning that spot on the board.

34longknight.png (84.17 KiB) Viewed 10441 times

44 small knight

Generally doesn't hold the corner territory as well as 34 small knight.

44knight.png (84.06 KiB) Viewed 10441 times

[lightvector]

34 small jump

It's not very pronounced, but D17 and G17 appear to be slightly lighter than what would fit the general gradient, presumably reflecting the fact that in the current metagame, white is slightly more likely to play those points than arbitrary points against this corner enclosure.

34jump.png (84.05 KiB) Viewed 10441 times

34 long jump

34longjump.png (83.93 KiB) Viewed 10441 times

44 short jump

The 3-3 point is a bit lighter, white might invade there later and own that point.

44jump.png (84 KiB) Viewed 10441 times

[lightvector]

44 long knight

The 3-3 point is more a possible future invasion spot for white now than with smaller enclosures.

44longknight.png (84.16 KiB) Viewed 10441 times

44 long jump

Now the 3-3 point is even more likely for white to invade in the future.

44longjump.png (83.92 KiB) Viewed 10441 times

[ez4u]

Interesting! Three quick questions:
1. What are the 'pure' colors for Black and White? You mention the 'pink' under the 4-4 stone as 90% probability. On my screen, the 4-4 under the white stone appears light blue. Yet overall blue/purple seems to indicate Black ownership rather than White.

2. On the Black side of the 4-4 map, C17 is a lighter blue than B18. Does this mean that the net predicts a higher probability that White will own C17 than B18? If so, how might that be possible?

3. On the 4-4 map K17 and K18 (under the middle star point) are more blue than not, i.e. the map is not symmetrical. Does this reflect the fact that Black plays first?

[lightvector]

Interesting! Three quick questions:
1. What are the 'pure' colors for Black and White? You mention the 'pink' under the 4-4 stone as 90% probability. On my screen, the 4-4 under the white stone appears light blue. Yet overall blue/purple seems to indicate Black ownership rather than White.

2. On the Black side of the 4-4 map, C17 is a lighter blue than B18. Does this mean that the net predicts a higher probability that White will own C17 than B18? If so, how might that be possible?

3. On the 4-4 map K17 and K18 (under the middle star point) are more blue than not, i.e. the map is not symmetrical. Does this reflect the fact that Black plays first?

1. The pure colors are very bright pink (not far from white), and very bright teal (not far from white). The color scheme started with only as a mapping from positive numbers (red to orange to yellow to green to teal and bright teal), which is great and intuitive for looking things like probabilities of moves, and then later I realized that some of the other heatmaps you'd want to display also contain negative numbers, so I sort of just arbitrarily picked another curve that winds through the blues and purples and pinks.

2. Yes. It isn't surprising to me that sequences where white owns 3-3 but not 2-2 could be more common than ones where white owns 2-2 but not 3-3. If white invades 3-3, it should be pretty rare that this stone will sacrificed, but some sequences still lead to black owning 2-2 even though 3-3 survives. For example, see one of the middle diagrams in Uberdude's post in https://www.lifein19x19.com/viewtopic.p ... 0&p=225807

3. Neat observation. Yes, I think there is generally a very slight and diffuse bias towards blue (black ownership) in the opening due to black going first. White gets komi, but komi of course is not ownership on the board. I wouldn't be necessarily sure that the neural net is correct about where those points manifest on average though, it's a pretty subtle signal for the neural net to try to fit better than simply a slight overall bias towards blue given all the other demands on the net's capacity.

[Uberdude]

This pattern of reduced influence at points the opponent is likely to approach/invade/attach in actual play, and the same shape shimari different distance from the edge of the board have drastically different heatmap rather than just translations, is exactly the sort of thing I wanted to see which a static decaying lines of force type of influence map can't do. Great work, thanks.

[ez4u]

...

2. On the Black side of the 4-4 map, C17 is a lighter blue than B18. Does this mean that the net predicts a higher probability that White will own C17 than B18? If so, how might that be possible?

...

...

2. Yes. It isn't surprising to me that sequences where white owns 3-3 but not 2-2 could be more common than ones where white owns 2-2 but not 3-3. If white invades 3-3, it should be pretty rare that this stone will sacrificed, but some sequences still lead to black owning 2-2 even though 3-3 survives. For example, see one of the middle diagrams in Uberdude's post in https://www.lifein19x19.com/viewtopic.p ... 0&p=225807

...

Of course! My crufty, pre-AI knowledge is showing through.

[pnprog]

In case Uberdude or anyone else is interested based on his earlier post in that other thread about how different corner moves have very distinctive effects on corner ownership that normal influence maps don't necessarily capture well - I have a 15-block neural net now that is perhaps on-par with LZ120 in strength. One of the things it's trained to do is directly predict who owns each spot on the board at the end of the game.

This is interesting, thanks for sharing!

Could you elaborate a bit more on how you trained that network?

I am curious about something: if you sum up those percentage values for each free intersection of the board, will that give you the estimated score? (you would need values between -1 and 1, but that's a detail).
Estimated score (like B+3.25469887) without the ownership heatmap is already a valuable information

[lightvector]

Training via self-play.

Yes, you'd get a score estimate, but it wouldn't be necessarily that good, because unless you explicitly make the neural net care also about getting the sum of all points right (rather than only caring about predicting each individual point right), the small errors could sometimes accumulate into a large error as you sum across the board, and wouldn't necessarily always cancel out.

It wouldn't be that hard to add a bit more scaffolding to make that work though. I'm working on it...

[pnprog]

Hi lightvector!

Have you make some progress on this project? or new development?

[lightvector]

Ah, thanks for the bump! Yeah, for ownership heatmaps and score reporting, there is a bit of news, which I forgot that I never posted to this forum.

Mostly still doing ground-level research on KataGo (and finding some things that could give another factor of 2 or 3 speedup!). So far haven't spent a lot of time on UI and tools. I figure I want to try to get things a bit more competitive with other bots first in terms of the actual final strength of the network. LZ130-level, while quite strong, is still quite a ways below the best networks out there that have been trained with greatly more resources.

Despite that, not too long ago, I did add a "kata-analyze" GTP command to the GTP engine, which works very similarly to "lz-analyze", except that it also has the ability to report in real time during the search:
* A prediction of the mean final score at the end of the game (i.e. "how many points is the player ahead or behind by")
* A heatmap of predicted final ownership across the board.

If tools like Lizzie could pull that in, that would be really fun. And I also made one-off visualization for a local demo I was doing (sadly, not a review tool, just a visualization). I posted the resulting videos here, showing examples of the real-time ownership during some self-play games.

https://www.dropbox.com/s/svoybd565u6qf ... 1.mp4?dl=0
https://www.dropbox.com/s/dmrs8rgzzukeo ... 2.mp4?dl=0
https://www.dropbox.com/s/is7xsc1839guk ... 3.mp4?dl=0

ownershipmoviescreenshot.png (210.98 KiB) Viewed 9435 times

I'd be very happy if someone who works on one of the many existing GUIs or analysis tools out there wanted to go ahead and add support in their tool for this.

[Rémi]

Note that gogui can simply display such color maps:
https://www.kayufu.com/gogui/analyze.html
(see "cboard" analyze command)

https://github.com/Remi-Coulom/gogui/releases