Number of nodes needed to LC0 reach an average human play level

[Zeta]

In this artilce https://arstechnica.com/science/2018/12/move-over-alphago-alphazero-taught-itself-to-play-three-different-games/ there is a very interesting image: 

I'd like to know if somebody knows how many moves (nodes visited per move) are needed so LC0 can play with an average Elo of 1800+ reaching in this way an average human player level. 

This may seem a fool question but I think it's interesting from the point of view of the neurology and the possible similarity (or not) of this (NN) approach with the way our own brain works in order to play chess.

In other words: if you limit the LC0 nodes to, let's say, 500 nodes per move (and I don't mean 500 nodes per second but per move) what's the approximate Elo she reaches in comparison to a human player?

 

[svoi s]

I think one node is enough

воскресенье, 23 июня 2019 г., 11:08:08 UTC+3 пользователь Zeta написал:

In this artilce https://arstechnica.com/science/2018/12/move-over-alphago-alphazero-taught-itself-to-play-three-different-games/ there is a very interesting image:

[Zeta]

1) What's the Elo reached with only 1 node? Is there any study about?

2) With only one node is basically the Value head the only involved in the process, isn't it?

3) Well, how many nodes so to reach a grand master human play level 2300+?

[glbchess64]

• +2300 ELO is FIDE master level
• IM if 3 IM norms
• GM if 3 GM norms and +2500 ELO

seems late T40 nets at 1 node/move has FIDE master level

[Zeta]

Absolutely incredible!

1) So 1 node/per move is already enough to beat a FIDE GM even if the human is thinking its moves long time, for example in 120 min. matches?

2) I still wonder if at 1 node per movement it is only the Value head the one involved in the MCTS process. I.e.; whether or not there only occurs an evaluation (Value Head) of the root node and then the more promising legal move is selected (without the Policy head acting at all). Does anybody know?

Regards,

Samu.

[Stephen Bell]

I thought 1 node would be policy head only (move with highest probability). Depth 1 would be value head only (highest value among all positions 1 ply hence). Perhaps that's too simplistic or I've misunderstood.

[Zeta]

Ok, I see it's a little tricky question.

1) So one node per movement (in the configuration) means the root is explored using the Policy head and the engine simply selects the higher probable legal move returned by this policy (without the use of the Value head in any moment)? Is that correct? 

2) And in this way LC0 is able to beat a FIDE GM even if the human is thinking its moves long time (for example in 120 min. matches)?

[glbchess64]

A GM had an ELO > 2500 a least once in his life (he must reach this level after he made his 3 GM norms). A GM at just 2300 should probably a very old one. And T40 nets are just above 2300 at 1 node/move. It is the level of FIDE master (not IM or GM : generally IM are above 2400 and GM above 2500). Kingscrusher (that comments Leela games, see youtube) for example is a FIDE master.

[Zeta]

Ok, but that's not the main point I would like to understand. I change my question accordly:

1) So one node per movement (in the configuration) means the root is explored using the Policy head and the engine simply selects the higher probable legal move returned by this policy (without the use of the Value head in any moment)? Is that correct? 

2) And in this way LC0 is able to beat a FIDE master even if the human is thinking its moves long time (for example in 120 min. matches)?

[glbchess64]

I don't now if someone play such match at this TC. But Leela at 1 node/move beat FIDE master at rapid chess and GM at bullet chess.

And at correspondence TC human are still better than computers.

[Stephen Timothy McHenry]

Also, in the original post, 1800+ is definitely NOT the average human player. The average tournament player is somewhere in 1300 to 1400 range I think. 

[Zeta]

Ok, average is 1300-1400. My fault. 

And it's already clear the TC for that wins against FIDE master are rapid and bullet (and there seems not to exist any study for more time matches between over-average humans and LC0 at very low nodes).

1) The only question remaining is whether at 1 node/per movement is the Value head or the Policy head the one at charge of this great efficiency (or if both act even if we configure LC0 to 1 node per movement). How does MCTS act in this situation normally (with or without NN)?

 

2) Also I think it would be very interesting to study how many nodes are required in order to equal the human skill level at high TC. That could have some interest in relation to the similarity of this NN and our own brain (see the image I pasted in my first commentary).

Regards. 

[Dietrich Kappe]

You’re talking boundary conditions here. 1 node can play very strong chess, but will sometimes miss obvious tactics. The engine is, after all, not just the network but the mcts algorithm it’s trained to drive. Somewhere between 5 and 30 nodes is the magic point for a strong network. For a different style of play, maybe a net trained against human games would give one something more satisfying.

I do have a 48x5 distilled net playing on lichess on a raspberry pi 3 at 8 nodes per move (MiniHuman). It probably stronger than 1800+.

[M MUSTERMANN]

glbchess64:

A GM had an ELO > 2500 a least once in his life (he must reach this level after he made his 3 GM norms). A GM at just 2300 should probably a very old one. And T40 nets are just above 2300 at 1 node/move. It is the level of FIDE master (not IM or GM : generally IM are above 2400 and GM above 2500). Kingscrusher (that comments Leela games, see youtube) for example is a FIDE master.

It could be very interesting to use LC0 with SquareOff Board.

Should be no problem to run it like playing online LC0 or to run it on mobile phone and play on the board. 

[Zeta]

Great and very interesting response.

"5 and 30 nodes is the magic point for a strong network"

So like the image of my first comment shows it's probable our brain works in a very similar way to this NN models when playing chess. I guess it's a neurologically interesting result.

[Shah]

The fact that a 1-node search can easily miss obvious tactics, as Dietrich says, makes perfect sense to me.

But how can we explain that a 5-node search helps in finding those obvious missed tactics?

I mean, if a 1-node search can miss a mate in one, so can 5 node search, with a somewhat lower probability.

A 30 node search, if we continue to follow this line of thought, may miss a mate in two just as easily.

[Shah]

And should I add? that no 2400+ player would ever miss a mate in one or a mate in two...

[Dietrich Kappe]

Now you’re moving the goalposts. We’re shooting for average play. A few months ago an IM and GM tried their hand against a low node leela. They had some luck at 10 nodes. At 30 nodes it was over.

The search will “see” tactics. The net will evaluate win chances and suggest promising moves. As you weaken the engine by allowing fewer nodes, tactics drop off more quickly than positional smarts.

If you want a net that is weaker positionally but still good at tactics by virtue of searching more nodes. Different goal for different nets.

[Shah]

Not sure if I can translate what you are saying into strict numbers.

So would it be correct to say that:

1. One-node-search Leela may occasionally miss trivial one-move tactics (like a mate in one)

2. Five-node-search Leela will never miss trivial one-move tactics (like a mate in one)

??

[Alexandre]

even if it is only master FIDE must take into account that it is on long part.
Clear middle part at a rate of 20 minutes KO it must be at least 100 elo more minimum compared to humans it is very possible that it is great master at this rate.
But in time blitz she is clearly BIG MASTER and must have more than 2500 elo minimum
and in bullet it must compete with the world's top 20.

Everything I say deserves verification but it is obvious that it has the advantage of the machine and it is much easier than humans.
remember FRITZ 3 and 4 which rivaled KASPAROV partly semi-fast (it seems to me) while FRITZ 3 was only 2400 2500max  elo partly long.

[Robert Filter]

@Dietrich: do you have more distilled nets and know approximately their strength scaling in network size and/or nodes?
Thank you!

[Zeta]

@Dietrich: "IM and GM tried their hand against a low node leela. They had some luck at 10 nodes. At 30 nodes it was over. "

It's incredible that LC0 can beat with only 30 nodes a GM. That has neurologically perfect sense with this: 

It seems both our brain and these NN work in a very similar way after all.

[Юрий Павлович]

One node is a policy network only, no search.

воскресенье, 23 июня 2019 г., 21:36:18 UTC+5 пользователь Zeta написал:

[Vladimir Medvedev]

понедельник, 24 июня 2019 г., 0:15:52 UTC+3 пользователь Shah написал:

And should I add? that no 2400+ player would ever miss a mate in one or a mate in two...

Except he is Vladimir Kramnik vs. Fritz in 2006.

[Zeta]

"One node is a policy network only, no search."

Ok! That was my last doubt. 

It's incredible how only the Policy head without any search can beat average humans player and even FIDE masters. These NN are without doubt a good approximation to the way our brain works. No one classical AI engine could archive such a thing no matter how well we try to implement the evaluation function. Without search only a NN can imitate our skills (and in the end, a NN is just adds and mult tensor operations: that's probably also our mind in essence).

[Jim Glass]

"no 2400+ player would ever miss a mate in one or a mate in two"

Well Ivanchuk famously missed mate in one against Anand, and that's hardly the only time...

https://chess24.com/en/read/news/5-incredible-missed-mates

A quick Google search finds a lot more.

[Shah]

Well... ok... But the point is that when not under time pressure, such an event is extremely rate.
Rare enough to statistically ignore it.
I think.