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Comment by cyberferret | Hacker News Reader

Amazing. I assume AlphaZero knew the basic moves of the pieces, but had to figure out defensive moves etc. against the other computer 'on the fly'? Are those learning games included in the statistics (which include ZERO losses)?? If so, it is a remarkable learning engine.

Shades of WOPR. "This is a game nobody can win..."

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Yes, it got a set of all legal moves, of which it had to choose one. It was trained for 8 hours where it only played against itself, only using the knowledge of which moves are legal. After self-playing for 8 hours, it played 100 times against stockfish. In those 8 hours, it was apparently able to infer all human knowledge on chess acquired over centuries, and surpass it.

And, when the legal moves are replaced with the moves of other games (like Go for which it was actually written, or Shogi), it did exactly the same thing. Redevelop millennia of human knowledge and go beyond, all within 8 hours of compute.

Makes you wonder what will happen when instead of the rules of chess, you put in the axioms of logic and natural numbers. And give it 8 months of compute.

Amazing achievement. Still, "eight hours" is a bit misleading. That's eight hours on thousands of parallel TPUs.

Let me reformulate. I'm just saying that there is at least one obvious way in which Google could scale this at least 2 to 3 orders of magnitude if they would want to, for the cost of the electricity bill. Just run it for 8 months instead of 8 hours. And I wonder which problems are feasible when you look at it that way. I mean, they just solved chess in what looks like a warming-up.

More interesting would be how many games it has played in that time.

44 million, according to their paper, and they used 5000 TPUs, which are capable of 4.6×10^17 operations per second.

(The operations the TPU can run are far simpler than what supercomputers can do, but just for the sake of comparison, the current top supercomputer in the world can do 1.25×10^17 floating point operations per second)

I haven't seen any details from AlphaZero, but when they were training AlphaGo Zero they drastically reduced the amount of hardware and only used a single node taking about a killowatt of power. If we assume AlphaZero uses the same hardware, then given that a brain uses about 10w that would be equivalent to 800 hours. Which is still amazing.

>That's eight hours on thousands of parallel TPUs.

But it's not really misleading at all. The ability to produce massive amount of power and product is the pinnacle of our society. The fact is we can make thousand, if not millions or even billions of TPUs if we desired, and it is a relatively easy engineering problem at that. And that these things may solve all kinds of problems mankind has had for millennia in hours should be a wakeup call to a future that will be hard to predict.

Humans take 9 months to gestate, no amount of parallelism will speed that up, after that it takes 18 years for them not to be completely stupid all the time attempting to hammer an education in them. Even after that it takes more years to become a specialist.

> Makes you wonder what will happen when instead of the rules of chess, you put in the axioms of logic and natural numbers. And give it 8 months of compute.

How do you score this computation? What's your goal? There's no checkmate here.

> How do you score this computation? What's your goal?

Maybe give it a list of problems of varying degree of hardness, and tell it to either prove or disprove as many as possible?

You could even train it with random theorem expressions run through a conventional theorem prover. And then let it loose on the problems that are left.

I would assume you have to come up with some scoring function.

For example, give it a number and tell it to factor it into the prime factors. The score might be the solution with the smallest time or storage requirements. Or maybe find a way to generate a hash where the last n digits are zero.

I also remember a RadioLab episode where they talked about electronic theorem solvers and they would do something like show it a video of a double pendulum and it would come up with equations to model the behavior of that system.

I think the idea here is for life to imitate art.

> Makes you wonder what will happen when instead of the rules of chess, you put in the axioms of logic and natural numbers.

If you're talking about formal proofs or maths, I'm not sure how this would apply in general as the branching factor for each 'move' in a proof is efficiently infinite. It would be interesting to see it applied to more constrained proof domains though.

It's inferred a different chess knowledge though, not necessarily including all human knowledge on chess.

Seems like it learned by only playing against itself, and for only 4 hours (for the chess component).

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