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Comment by gus_massa | Hacker News Reader

They can see the last 4 results, not only the last result. That's somewhat equivalent of partially seeing the secret internal state.

As a bad metaphor: Let's suppose that you enter a lifter and a NN without internal state must predict which button you will press, but now consider the case where the NN can see a video of everything you have done during the last year. Do you think it's possible?

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> That's somewhat equivalent of partially seeing the secret internal state

Not just partially, xorshift128 is designed such that the output depends only on the last 4 results. So this is "just" learning the output function of xorshift as a neural network.

Perhaps you might consider how big that output function ideally is, then compare to the capacity of the neural network they used and the number of samples provided.

My reading of it is that it's essentially one-to-one (up to minor constant factors), they took the binary circuit for xorshift128 and replace the xor gates by functionally equivalent NN blocks, and then trained the weights.

That's only ~365 values. XORshift32 has a period of 2^32-1, a good portion of that (I'd imagine) unique. If XORshift had really good randomness properties, at the extreme we'd expect that the NN would have to special case all of them. What this implies is that XORshift has easily cracked, nonrandom, repeatable patterns (which we suspect of course since it fails certain tests) and that the NN has identified them.

We knew that before the two ML attempts. You just need to look at the source. There are several other trivial PRNG's with the exact same properties. Never use a trivial PRNG for security or seeding.

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