The future of Human vs Computer Go in a post-AG world.

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Re: The future of Human vs Computer Go in a post-AG world.

Post by dfan »

Uberdude wrote:I was under the impression that if you are a 2200 chess player and want to be a 2500 chess player you need to sit down with big books of openings and memorise them, is this true?

No. There are plenty of 2500 players with quite a narrow repertoire, and some that largely play rather offbeat lines.

Something like "the L group is dead" is a fact I have remembered, but the actual sequences to kill I have not, though being standard applications of life-and-death principles of hanes and then placements are moves I can generate in a few seconds.

That is interesting. I have spent some time memorizing life-and-death sequences but perhaps this time is somewhat misplaced.

Here's an example: have you memorized how to kill the J group, or do you work it out from first principles, or somewhere in between? It ends with what I consider a tesuji so it's not something that's easy for me to plan from the start unless I have the roadmap.
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Re: The future of Human vs Computer Go in a post-AG world.

Post by Uberdude »

dfan wrote:
Uberdude wrote:I was under the impression that if you are a 2200 chess player and want to be a 2500 chess player you need to sit down with big books of openings and memorise them, is this true?

No. There are plenty of 2500 players with quite a narrow repertoire, and some that largely play rather offbeat lines.

Interesting.

dfan wrote:
Uberdude wrote:Something like "the L group is dead" is a fact I have remembered, but the actual sequences to kill I have not, though being standard applications of life-and-death principles of hanes and then placements are moves I can generate in a few seconds.

That is interesting. I have spent some time memorizing life-and-death sequences but perhaps this time is somewhat misplaced.
Here's an example: have you memorized how to kill the J group, or do you work it out from first principles, or somewhere in between? It ends with what I consider a tesuji so it's not something that's easy for me to plan from the start unless I have the roadmap.

For the J group I remember hane and placement at 2-1, and now that I read it in my head I suppose you consider that descent to first line and throw-in the finishing tesuji but wouldn't say those moves are remembered as "this is the sequence to kill a j group", they are part of my general go vocabulary that fit here; and if they try to live another way I'd have to read. For the carpenter's square I know the attach on 2-1 after their vital point, but the following sequences are one of those things on my "I should study these when I'm a dan player" list that I've never got round to doing ;-).
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Re: The future of Human vs Computer Go in a post-AG world.

Post by Bill Spight »

Kirby wrote:
Tapani wrote:To me go has two games in one. There is a top level game deciding where to invade, reduce, strengthen, build or whatever. Then there the second game the tactical execution of those options - includes playing out memorized sequences.


What you refer to as "memorization", I'd refer to as "chunking". When you first learn go, you know only the rules and think move-by-move. As you gain experience, do problems, review games, your mind becomes aware of larger sequences/chunks that you can think of as a single unit. While some may be able to attempt to memorize chunks, a more natural process is to acquire the skill naturally through training.


So far, I agree. :D

The same phenomenon happens in language. At first you learn letter-by-letter. Then you get to know words. Then common phrases become apparent. As you gain proficiency, your mind chunks the information. To me, this differs greatly from memorization.


I think that there is pretty good evidence that children first learn the melodies of their language. (A major difference between British and American English, BTW. American English is more monotone.) I suppose that by letter-by-letter you mean learning phonemes. Babies do babble, but I am not sure that phoneme by phoneme is the best way to describe what is going on. And certainly when they start speaking words, they do not construct them phoneme by phoneme. E. g., Iss instead of ich in German, tuck instead of truck in English, dest instead of desk in English, and where I grew up, Saredy instead of Saturday, Febuary instead of February, lieberry instead of library, and Missippi instead of Mississippi. But, regardless of the details, it seems clear that children do not learn their language by memorization. :)
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Re: The future of Human vs Computer Go in a post-AG world.

Post by Bill Spight »

OK, here is a pretty easy life and death problem.

Click Here To Show Diagram Code
[go]$$W White to play
$$ -----------------------
$$ . . . . X . X O . . . .
$$ . . . O X O X X O . O .
$$ . . O . O X C X O . . .
$$ . . . . O X C X O . . .
$$ . . . . O . X O . . . .
$$ . . . . . O O O . . . .
$$ . . . . . . . . . . . .[/go]


Because of damezumari White can throw in a stone and take away a potential Black eye on the marked points. This kind of half eye is fairly common in tsumego problems, and occasionally occurs in real life. After you do enough tsumego, it becomes a pretty easy shape to see, even if you do not memorize it. :)

Here is my little joke. ;)

Click Here To Show Diagram Code
[go]$$W White to play
$$ ---------------
$$ | . X O . . . .
$$ | O X X O . O .
$$ | X C X O . . .
$$ | X C X O . . .
$$ | . X O . . . .
$$ | O O O . . . .
$$ | . . . . . . .[/go]


Voilà! Le groupe J. (Or whatever they say in French. :))

I have nothing against memorization, per se. And it may be the best way to learn a lot of go, especially as an adult. But the problem with it, it seems to me, is that it is not enough. Is memorization enough to generalize how to take away the potential eye?

IMO, even though you can learn how to kill the J group by memorizing enough of the game tree, starting with the hane, it is better to start with taking away the potential eye, perhaps with the little problem I showed above. Or like so:

Click Here To Show Diagram Code
[go]$$W White to play
$$ ---------------
$$ | . . . . . . .
$$ | 1 2 X O . O .
$$ | 4 . X O . . .
$$ | X 5 X O . . .
$$ | . X O . . . .
$$ | 3 O O . . . .
$$ | . . . . . . .
$$ | . O . . . . .
$$ | . . . . . . .[/go]


Then you show why that does not work.

Click Here To Show Diagram Code
[go]$$W White to play
$$ ---------------
$$ | 6 . 8 . . . .
$$ | 1 2 X O . O .
$$ | 4 . X O . . .
$$ | X 5 X O . . .
$$ | 7 X O . . . .
$$ | 3 O O . . . .
$$ | . . . . . . .
$$ | . O . . . . .
$$ | . . . . . . .[/go]


Now the hane is not just the first move in a memorized sequence, but the play that prevents :b8:. :D
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Re: The future of Human vs Computer Go in a post-AG world.

Post by Cassandra »

Dear Bill, you surely know that still "open" formations have other dependencies to consider than already "closed" formations.

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

Black's potential eye space consists of seven empty points in a quite bulky shape.

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

You can see three vital points inside (each is a central point of a dead bulky five-point eye shape).

Click Here To Show Diagram Code
[go]$$W
$$ ---------------
$$ | . . . . . . .
$$ | 1 2 X O . O .
$$ | . . X O . . .
$$ | X . X O . . .
$$ | . X O . . . .
$$ | . O O . . . .
$$ | . . . . . . .
$$ | . O . . . . .
$$ | . . . . . . .[/go]

Playing inside forces your opponent ...

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

... to transform their potential eye space into a snaky line of six points.

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

You can see four vital points inside (each is the central point of a dead three-point eye shape), one of which is already occupied by White.
The number of unoccupied vital points is the same as before the move pair played, but Black's shape has become much better.

Of course, the hane is not lost, but that's another dependency's story ...

Click Here To Show Diagram Code
[go]$$W
$$ ---------------
$$ | . 2 1 . . . .
$$ | . . X O . O .
$$ | . . X O . . .
$$ | X . X O . . .
$$ | . X O . . . .
$$ | . O O . . . .
$$ | . . . . . . .
$$ | . O . . . . .
$$ | . . . . . . .[/go]

Playing from the outside, however, assuming that Black's wants to maximize his potential eye space, ...

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

... results in only two vital points after the move pair played, one less than in the very beginning.
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Re: The future of Human vs Computer Go in a post-AG world.

Post by dfan »

I do indeed know the "J group tesuji" from tsumego (for reasons I can't reconstruct, I think of it as "the fishhook") but although I would recognize it in a tsumego problem or after the first 4 moves of the J-killing sequence, I wouldn't intuitively see it from the start when presented with a J group, as I would with, say, a more vanilla throw-in. So I need to remember the first couple of moves by hand; after that, I remember there is a trick at the end, and once I know it's there, it's not hard to find. I don't doubt that stronger players can just use their intuition to read the whole thing out from scratch every time (although of course they are applying a lot of learned patterns).
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Re: The future of Human vs Computer Go in a post-AG world.

Post by Bill Spight »

Cassandra wrote:
Click Here To Show Diagram Code
[go]$$Wc
$$ ---------------
$$ | . . . . . . .
$$ | S S X O . O .
$$ | . S X O . . .
$$ | X . X O . . .
$$ | . X O . . . .
$$ | . O O . . . .
$$ | . . . . . . .
$$ | . O . . . . .
$$ | . . . . . . .[/go]

You can see three vital points inside (each is a central point of a dead bulky five-point eye shape).


That's an interesting perspective. :) I have my doubts about the B-18 point, however.

Click Here To Show Diagram Code
[go]$$Wc
$$ ---------------
$$ | . . . . . . .
$$ | 1 2 X O . O .
$$ | . . X O . . .
$$ | X . X O . . .
$$ | . X O . . . .
$$ | . O O . . . .
$$ | . . . . . . .
$$ | . O . . . . .
$$ | . . . . . . .[/go]

Playing inside forces your opponent ...

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

... to transform their potential eye space into a snaky line of six points.

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

You can see four vital points inside (each is the central point of a dead three-point eye shape), one of which is already occupied by White.
The number of unoccupied vital points is the same as before the move pair played, but Black's shape has become much better.


FWIW, :b2: is also played (hypothetically) at A-17, which, IIUC, leaves only 2 vital points at B-17 and B-18.

Of course, the hane is not lost, but that's another dependency's story ...


I was going to quibble about the question of shape, but, in fact, after the above exchange, the hane has become the only killing play. The descent to A-14, while it does prevent the eye at B-16 - B-17, does not kill.

OTOH:

Click Here To Show Diagram Code
[go]$$Wc
$$ ---------------
$$ | . 2 1 . . . .
$$ | . . X O . O .
$$ | . . X O . . .
$$ | X . X O . . .
$$ | . X O . . . .
$$ | . O O . . . .
$$ | . . . . . . .
$$ | . O . . . . .
$$ | . . . . . . .[/go]

Playing from the outside, however, assuming that Black's wants to maximize his potential eye space, ...

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

... results in only two vital points after the move pair played, one less than in the very beginning.


After the hane and atari, only A-18 kills. So whatever you may think of the different Black eye shapes, only one move kills in each.

BTW, this Life and Death position is an example where, even in a restricted region of the board, there is more than one correct play. White can start with either the hane or A-18, leaving the other play as a follow-up. Playing go is not like threading a needle. :)
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Re: The future of Human vs Computer Go in a post-AG world.

Post by Cassandra »

Bill Spight wrote:I have my doubts about the B-18 point, however.

Don't you think that a black move at this point results in a living shape ?

Bill Spight wrote:So whatever you may think of the different Black eye shapes, only one move kills in each.

Go would be much too simple if every central point of a dead eye shape was also a vital point of the problem.

There exist also other shape issues besides
-- Can be filled with a dead eye shape.
-- Can be almost filled with a dead eye shape.
-- Cannot be even almost filled with a dead eye shape.

Having a hole in your own encirclement that can be exploited by the opponent is an example ...
;-)
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Re: The future of Human vs Computer Go in a post-AG world.

Post by Tapani »

Kirby wrote:The same phenomenon happens in language. At first you learn letter-by-letter. Then you get to know words. Then common phrases become apparent. As you gain proficiency, your mind chunks the information. To me, this differs greatly from memorization.

Did you memorize the phrases in your post here on L19? Or did you construct the sentences yourself? Maybe you studied English by memorizing conversations. But I hardly think it's a necessary method for learning, as there are many other ways to gain proficiency and "chunk" techniques naturally.

I think the language analogy is a brilliant one.

So how do you start when you study a new language? By memorizing! Cramming vocabulary and sample sentences. Memorizing them since the sounds have no inherent meaning initially. The meaning comes from using them.

So yes, at some point, long ago, I did learn sentences in English by heart. It is not sufficient to become fluent, but it helps to bootstrap the process. And still there are rare words in English I know from memory and not from associations formed by usage.

Bill Spight wrote:
Kirby wrote:The same phenomenon happens in language. At first you learn letter-by-letter. Then you get to know words. Then common phrases become apparent. As you gain proficiency, your mind chunks the information. To me, this differs greatly from memorization.


I think that there is pretty good evidence that children first learn the melodies of their language. (A major difference between British and American English, BTW. American English is more monotone.) I suppose that by letter-by-letter you mean learning phonemes. Babies do babble, but I am not sure that phoneme by phoneme is the best way to describe what is going on. And certainly when they start speaking words, they do not construct them phoneme by phoneme. E. g., Iss instead of ich in German, tuck instead of truck in English, dest instead of desk in English, and where I grew up, Saredy instead of Saturday, Febuary instead of February, lieberry instead of library, and Missippi instead of Mississippi. But, regardless of the details, it seems clear that children do not learn their language by memorization. :)


This is interesting! I guess the method of learning a language before you have one must differ from learning your second language? Or has it to do with age of learning?
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Re: The future of Human vs Computer Go in a post-AG world.

Post by Alyssa05 »

hydrogenpi7 wrote:In or around 2015, Google's AlphaGo was the original impetus that started a sort of evolutionary "Cambrian explosion" in the world of Computer Go AI. At this point it is fair to say the genie is out of the bottle and there is no going back. Go has existed in some form or another for roughly 5000 years, and it was only in the last year and a half that computers have suddenly reached a level that surpassed top pros. So while AlphaGo was the first, it will certainly not be the last. In a few years, more and more AI programs will proliferation their way to besting and beating the top pros at this ancient game. From the grand scheme of things, a few years compared to a few thousand years is but a blink of an eye. AI has won, forever, and there is no going back.

But that is not to say that in the future Human vs Computer Go games would be futile or meaningless. We must merely adapt and evolve the nature of the competition and the structure of the dynamic to make things more interesting and to put things on more common ground without giving a handicap or a surplus of moves or stones.

One way to naturally do this is to compete on energy parity. Kudos that the AG version that has won against Kie Je is reported to only use 10% of the total power requirement compared to the AG19 version of Lee Sedol games a year or so back. This is a huge step forwards but still it uses far more power than the human brain or even the entire human body. So as computers get stronger and stronger at Go, ultimately and eventually one metric to target would be the first computer AI Go program that can beat a top pro while using same equivalent to the top pro himself. This can be in the form of scaling down the AI to use less and less resources, or to artificially cap the thinking time of the AI, to give it less time and thus forcing it to use less total energy consumption, in order to match that of the human, so that at the end of the game the AI used no more total power or energy than its human counterpart. This would be an interesting goal post and qualitative challenge.

Another way to make human vs computer matches more intriguing is to give the human a limited number of redos or undos. To essentially allow the human to go back to a particular move, to play out a different branch to see if that new path or new route might entail a better end result or maybe even end up in a winning game. While this may seem like “cheating” at first glance, it is really not. Let me explain.

Computers have always been better than humans at brute force calculations. This has been decided since the days of the very first pocket calculator. Your mobile phone can calculate arithmetic operations orders of magnitude faster than all the top mathematicians in the world added together could do in terms of team mental math or group pencil and paper. But we should not confuse brute force calculations as “artificial intelligence” any more than we would say that a rudimentary autopilot program capable of holding an airplanes altitude without deviation is more “intellectual” than the human pilot. Likewise we would not attribute “artificial intelligence” to a fast calculator.

Everything from brains to computers are actually higher level emulators, at least second order or higher computers. It is the laws of physics and the individual quantum effects, the atoms and molecules and forces of the universe that combine together in such and such a way as to actually do the “calculation” and the “computer”. Everything else is a virtualization and symbolic computing layer on top of that. So be it an abacus or pocket calculator or slide ruler or human brain or silicon processor, these are all second/higher order computers within a computer, virtual emulators of processing, if you will. The reason Intel processors are faster than the abacus is because the integrated circuit is far smaller and thus more efficient than the larger macro-sized beads, but make no mistake, these are all symbolic representations of calculations, the smaller we can make these representations the more powerful of a processor we can have. But at the end of the day, the universe is the only true computer, and everything else is a higher level emulator, the only question is how efficient is the emulation and the symbolic emulation.

Humans are better than computers at some things while computers are much better than humans at a lot of other things. The question is fundamentally why?

It is akin to building a virtual CPU inside of Minecraft. It would be much more efficient not to have to have these higher order virtualizations which actually add to the symbolic unnecessities by artificially increasing computational overhead by orders of magnitudes and for no good reasons. This is why the human brain cannot compute arithmetic faster than a crude calculator. Because the brain was not hardwired to directly manipulate so closely with efficiency level the way a silicon processor can symbolically reduce numbers to more atomic bits of binary zeros and ones and thus calculate them much faster, and without error. It is not because the calculator is more advanced than the human brain, but that the human brain has to visualize and add symbolic layers to concept such as numbers (and cannot directly manipulate them on the molecular level) and thus just like in the earlier virtual CPU inside of Minecraft example, this is why humans cannot outdo computers when it comes to things like brute force arithmetic calculations.

Coming back to Go games, MCTS is akin to brute force calculation and not the sort of “intuitive artificial Intelligence” people think of when they think of AI outsmarting human intuition. Traditionally humans have had the advantage against computer Go programs of the past due to the large search tree of the Go game made it not possible to do an exhaustive brute force search. Therefore to a large degree this thing we call “human intuition” came into play, and without computers being able to emulate that intuition, there was no way computers were ever going to catch up by sheer scaling up of brute force searches. Modern AI Go programs have changed all of that because for the very time in human history, computer programs are now starting to catch up with human intuition when it comes to the game of Go. And with the advantageousness of brute force calculations that are not afforded to humans, the MCTS and other “brute force” simple algorithmic methods help carry Alpha Go and DeepZen and others the “last miles” to the “finish line”, finally boosting it above superhuman levels of overall effective play.

So the question is one of how do we highlight the true “intelligence” aspect of artificial intelligence and bring that real AI to the forefront and diminish the whole brute force aspect of modern “GO AI”, which in truth is actually a hybrid of AI and that of good old fashioned brute force calculations which humans were never good at and never had a chance or a hope against computers anyway.

A way to do that would be to give human players “redo” attempts. Since by definition Go is not a ‘brute force-able’ game anyway, (ironically, otherwise computers would have beat humans at Go back in the 1960’s without need for DCNN etc) a 25kyu player could have unlimited redo’s and could spend the rest of his life and would never win a single game against something like AlphaGo 2017. But on the other hand it is fair to say that someone like Ke Jie and Lee Sedol, given sufficient redos, might find a particular branch in which they win out against AG and the likes of top AI Go programs in the future.

Since humans are by definition fallible and machines are by definition do not get tired or sleepy and do not slip up and make “miscalculations” etc, it would only actually be “fair” for a human vs computer competition to allow the humans to have a set number of attempts per game.

Or if that is not acceptable, then a more natural way to level the playing field to be fundamentally more equitable would be for AI programs to rely ONLY on the neural network component for play and not use any MCTS or anything remotely like it. Another possibility would be to allow the human to have a real board to do analysis, to let him put down stones and to analyze the different variations in a manner that does not prone to victimize him to the fallibility of his own mind and memory and visualization which cannot ever compare to the brute force ‘speed of light’ search that a computer could instantly perform.

Finally, once GO AI programs have cast aside the MCTS and other functional equals to the MCTS methods and the brute force components that humans could never compete against and was never really ‘artificial intelligence’ anyway and then to rely solely and exclusively on the emulation of neural networks instead, transfers paris airports then the next step would be to reduce the dataset the AI has access to in a way that is quantitatively fair to the human counterpart. Train an AI from scratch and only give it access to play a very limited number of games, on par with what a human would be exposed to in his lifetime.

What is intuition? It is ability to extrapolate and learn from a subset of data. AlphaGo has played hundreds of millions of games within the span of a year or two. Is this true intuition when a top pro could only ever hope to play a tiny fraction of a fraction of that in his entire lifetime?

So the ultimate goal in AI would be to reach energy parity with human brain itself, to only use Nueral Network and no other brute force searching and whatnot, and exposing it to a limited dataset of games, comparable to what a human would be exposed to.

In human vs computer games, humans should be given a generous number of redo’s. The human should be given much more time than the computer, the computer should be capped to only a few seconds thinking per move, and not allowed to think on human time, no komi should be given to the computer, human should be allowed to pick which color, and finally the human should be given access and ability to consult with other humans during the game, and as well as ability to use a real go board in live match to physically play out and experiment with variations.

Hi, thank you for these informations :)
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Re: The future of Human vs Computer Go in a post-AG world.

Post by moha »

Tapani wrote:So how do you start when you study a new language? By memorizing!

No intelligent activity is possible without having some memory, so the question is if this (and the "rote" part) is more characteristic in go than in other activities?

I think that instead of memorization, sequences (not joseki) that often repeat are a result of directed or hinted minimaxing. Many players only look out for some key moves and dangers which makes "reading" (if this can still be called) out the sequence much easier and maybe even unnoticeable. OC you can still say that those key moves or patterns were memorized, but I doubt this leads to the right direction.

Incidentally, this is similar to what made computer go so strong by now. Although (random) MC alone is not really useful in go (it measures something completely different than the value of a position), the addition of the extra networks made it possible to do meaningful minimaxing for the first time. And the power of a reasonable global reading can be overwhelming!

Tapani wrote:Cramming vocabulary and sample sentences.
...
I guess the method of learning a language before you have one must differ from learning your second language? Or has it to do with age of learning?

Mostly with the method of learning you choose. There are language learning systems that aim at a more child-like learning process (but these have their own problems as grownups' brain works a bit differently than children).
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Re: The future of Human vs Computer Go in a post-AG world.

Post by Bill Spight »

Sorry, I did not see this earlier. :(

Cassandra wrote:
Bill Spight wrote:I have my doubts about the B-18 point, however.

Don't you think that a black move at this point results in a living shape ?


So would a sagari. We have different perspectives. :)
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Re: The future of Human vs Computer Go in a post-AG world.

Post by Cassandra »

Bill Spight wrote:So would a sagari. We have different perspectives. :)

I don't think so. At a special moment, we are just looking at different sections of the whole shape issues' picture (or have these in mind).

Of course, there is more to consider than only the central points of dead shapes inside. Holes and defects in the outer encirclement are also important. As are potential lines of false eyes. And the 1-2-points in the corner. And the number of liberties. ...

However, you will have to excuse that I am not really fit for the "J-group". My current work on tsume-go is restricted to groups with a potential eye space up to six points ...
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Re: The future of Human vs Computer Go in a post-AG world.

Post by Bill Spight »

Cassandra wrote:However, you will have to excuse that I am not really fit for the "J-group".


Oh, it's not like I am, either. ;)
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.
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