There Might Exist Simple Rules For Accurate Position Evaluation

[towforce]

The GPU (more exactly the NN) evaluation contain the result of the many millions games played during self learning. Enhancing the number of played games and the measure of NN we can gain engines playing better and better games.
It is pity but bigger NN needs more powerful hardware.

What does "GPU" mean in this context?

For solving specific problems, a big NN can be worse than a small one. When a human has done a task enough times, they can do it quickly without conscious thought because fast NN pathways for doing that task get built. However, chimps have much smaller brains than us, but they can still learn simple video games, and when they do, they can easily beat humans because their reaction times are MASSIVELY faster than ours.

More tasks where monkeys outperform humans: the matching pennies game (link), and willingness to change tactics (link).

Going even more extreme, a housefly has complex behaviours in terms of flight control (including landing), walking on six legs, feeding, mating and living life before it can fly (among others), but has a brain size of only around 100,000 neurons (the human brain has around 100,000,000,000 neurons). This shows that good behaviour for solving some complex problems can be encoded in a more simple algorithm than you'd expect.

[towforce]

2. Codify a set of linear relationships between the pieces, then use linear programming algorithms to generate expressions for these from a correctly evaluated set of samples. If doing this at the surface level isn't good enough, iteratively deepen it by adding relationships between relationships using the method of divided differences to keep it linear (in order to be able to find optimal solutions quickly).

Having done this, if the resulting expression has a large number of parts, there would be an easy way to simplify it: run the optimisation again, requiring (as a linear programming condition) that it get the same result, but this time, instead of optimising for the result, optimise for the maximum number of weights in the result which are zero. Parts of the expression with a zero weight could then be discarded from the solution, hopefully making the final expression much simpler.

[towforce]

A quick thought experiment which, admittedly, entails a combination of optimism and plucking numbers out of the air.

Suppose that, using methods discussed in this thread, a set of 100,000 linear expressions could evaluate a chess position quite accurately. There are, on average, 30 legal moves in a chess position. This would mean that choosing a move would entail calculating 30 x 100,000 = 3 million linear expressions. A computer could do this as quickly as human perception, making move selection, from a human perspective, instantaneous.

[towforce]

Talking about static evaluation, I think it's a shame that AlphaZero uses a combination of minimax search and well-trained NN (though admittedly it generated a much smaller game tree than its opponent, Stockfish). To REALLY demonstrate their prowess in the field of NN, they should make a NN that can beat StockFish in a 1 ply search - evaluating only the legal moves in the current position.

Has anyone ever done a rough plot of number of neurons v elo rating in a static evaluation? Maybe the graph rises exponentially (or is "S" shaped), meaning that the next 1 elo point increase requires more extra neurons than the last one did.

[corres]

The GPU (more exactly the NN) evaluation contain the result of the many millions games played during self learning. Enhancing the number of played games and the measure of NN we can gain engines playing better and better games.
It is pity but bigger NN needs more powerful hardware.

What does "GPU" mean in this context?

For solving specific problems, a big NN can be worse than a small one. When a human has done a task enough times, they can do it quickly without conscious thought because fast NN pathways for doing that task get built. However, chimps have much smaller brains than us, but they can still learn simple video games, and when they do, they can easily beat humans because their reaction times are MASSIVELY faster than ours.

More tasks where monkeys outperform humans: the matching pennies game (link), and willingness to change tactics (link).

Going even more extreme, a housefly has complex behaviours in terms of flight control (including landing), walking on six legs, feeding, mating and living life before it can fly (among others), but has a brain size of only around 100,000 neurons (the human brain has around 100,000,000,000 neurons). This shows that good behaviour for solving some complex problems can be encoded in a more simple algorithm than you'd expect.

Please, show me a chimp or a housefly knowing chess.
This would be the exact evidence for your minimalistic idea.
Btw. NN is such a "black box" what has non-linear connection between its input and its output.
So it is not an ideal object for a linear math.

[towforce]

The GPU (more exactly the NN) evaluation contain the result of the many millions games played during self learning. Enhancing the number of played games and the measure of NN we can gain engines playing better and better games.
It is pity but bigger NN needs more powerful hardware.

For solving specific problems, a big NN can be worse than a small one. When a human has done a task enough times, they can do it quickly without conscious thought because fast NN pathways for doing that task get built. However, chimps have much smaller brains than us, but they can still learn simple video games, and when they do, they can easily beat humans because their reaction times are MASSIVELY faster than ours.

More tasks where monkeys outperform humans: the matching pennies game (link), and willingness to change tactics (link).

Going even more extreme, a housefly has complex behaviours in terms of flight control (including landing), walking on six legs, feeding, mating and living life before it can fly (among others), but has a brain size of only around 100,000 neurons (the human brain has around 100,000,000,000 neurons). This shows that good behaviour for solving some complex problems can be encoded in a more simple algorithm than you'd expect.

Please, show me a chimp or a housefly knowing chess.

Obviously there are no such examples. This is why I called to analogy from other areas.

This would be the exact evidence for your minimalistic idea.

My core idea is to use mathematical optimisation of weightings in linear expressions, which is analogous to, but different from, NNs. It looks as though most people won't believe it unless somebody builds it out.

Btw. NN is such a "black box" what has non-linear connection between its input and its output. So it is not an ideal object for a linear math.

It is possible to convert trained NNs into mathematical expression - link. Will be a big expression for a deep NN.

[Zenmastur]

The GPU (more exactly the NN) evaluation contain the result of the many millions games played during self learning. Enhancing the number of played games and the measure of NN we can gain engines playing better and better games.
It is pity but bigger NN needs more powerful hardware.

For solving specific problems, a big NN can be worse than a small one. When a human has done a task enough times, they can do it quickly without conscious thought because fast NN pathways for doing that task get built. However, chimps have much smaller brains than us, but they can still learn simple video games, and when they do, they can easily beat humans because their reaction times are MASSIVELY faster than ours.

More tasks where monkeys outperform humans: the matching pennies game (link), and willingness to change tactics (link).

Going even more extreme, a housefly has complex behaviours in terms of flight control (including landing), walking on six legs, feeding, mating and living life before it can fly (among others), but has a brain size of only around 100,000 neurons (the human brain has around 100,000,000,000 neurons). This shows that good behaviour for solving some complex problems can be encoded in a more simple algorithm than you'd expect.

Please, show me a chimp or a housefly knowing chess.

Obviously there are no such examples. This is why I called to analogy from other areas.

This would be the exact evidence for your minimalistic idea.

My core idea is to use mathematical optimisation of weightings in linear expressions, which is analogous to, but different from, NNs. It looks as though most people won't believe it unless somebody builds it out.

Btw. NN is such a "black box" what has non-linear connection between its input and its output. So it is not an ideal object for a linear math.

It is possible to convert trained NNs into mathematical expression - link. Will be a big expression for a deep NN.

My guess would be that on smaller problems the expression(s) can be reduced to a manageable size without too much loss in accuracy. There are many methods used to analyze complex systems in which the math used is theoretically unsuitable for the type of analysis being performed. It doesn't stop the analysis from being useful. E.g look at para-axial ray-tracing used in lens design. It's based on a false equation. Namely sin(u)=u. And yet it has been used to design the most powerful optical systems man has ever built!

Regards,

Zenmastur

[corres]

The main issue is the chess is not a solved game. If we would know the exact solution of chess we could make a mathematical model for chess and we could plan an ideal chess engine basing on this model
Without knowing the solution we can only use the experience yielded from programming tricks, parameter modification and from the tests of modified engine to gain stronger engine.

[towforce]

The main issue is the chess is not a solved game.

It seems unlikely that chess will be solved by exhaustive game tree search from the starting position as other games have, so it will have to be solved by a combination of mathematics and computing, like the four colour theorem was.

If we would know the exact solution of chess we could make a mathematical model for chess and we could plan an ideal chess engine basing on this model

There are two criteria that a perfect chess engine has to meet:

1. in a drawn position, avoid a move that results in a losing position

2. in a winning position, choose the move on the shortest path to the win

Without knowing the solution we can only use the experience yielded from programming tricks, parameter modification and from the tests of modified engine to gain stronger engine.

This is the hill climbing optimisation technique, and is unlikely to lead to optimisation due to local maxima, ridges, alleys, and plateau (link).

There are many rules about how to play good chess in certain types of position. There is every reason to suppose that there probably exist more complex rules that can be applied in a wider variety of position types. More complex rules still may exist that could apply in most position types. If they do exist, then they can be found, and it is my opinion that mathematical optimisation techniques would be a better tool for finding them than methods like NNs or genetic algorithms. However, I am happy to be proven wrong about this.

[corres]

The main issue is the chess is not a solved game.

It seems unlikely that chess will be solved by exhaustive game tree search from the starting position as other games have, so it will have to be solved by a combination of mathematics and computing, like the four colour theorem was.

If we would know the exact solution of chess we could make a mathematical model for chess and we could plan an ideal chess engine basing on this model

There are two criteria that a perfect chess engine has to meet:
1. in a drawn position, avoid a move that results in a losing position
2. in a winning position, choose the move on the shortest path to the win

Without knowing the solution we can only use the experience yielded from programming tricks, parameter modification and from the tests of modified engine to gain stronger engine.

This is the hill climbing optimisation technique, and is unlikely to lead to optimisation due to local maxima, ridges, alleys, and plateau (link).
There are many rules about how to play good chess in certain types of position. There is every reason to suppose that there probably exist more complex rules that can be applied in a wider variety of position types. More complex rules still may exist that could apply in most position types. If they do exist, then they can be found, and it is my opinion that mathematical optimisation techniques would be a better tool for finding them than methods like NNs or genetic algorithms. However, I am happy to be proven wrong about this.

There were some experience to make exact rule for evaluating chess positions.
If you think you can solve the problem go ahead and we will be the fans of you.