this post was submitted on 09 Feb 2025
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Programming
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Idk about Barliman but just logically speaking, why would it generate a prime number lookup when a parabola (or even an exponential) fits those values just as well? Apart from an AI using pattern matching to recognize that the inputs being given "look like" a list of primes (in which case the AI is just going to be outputting someone else's pre-programmed prime number generating algorithm, not one that it came up with itself), the problem with inputting any N number of data points and asking for the function that generated them is that there is always ambiguity, and the simplest solution conceptually will just be an N-1 order polynomial.
Well just add more data points (7, 11, 13, etc) until the simplest solution is a prime solution. Would this program be smart enough to generate the right algorithm?
Of course, an AI would just generate a prime algorithm because it's well known, but not all problems are well known. In fact, most problems I'm solving everyday are not. So for the AI, it may as well be the prime lookup problem for Barliman.
That's the problem with "AI" isn't it? At least at the stage it is today. It can only really solve the kinds of problems that have already been solved. Maybe with some variations in the parameters, but the general structure of a problem needs to be one that it has already encountered in its training.
If we define "the simplest solution" as "the solution with the shortest program computing it", then this problem is literally uncomputable, because it is equivalent to the halting problem. Moreover, it is proven that there is no algorithm that can in general case achieve results meaningfully better than "print the number from the lookup table".
As i said, i don't know anything about this program, but conceptually i think you first need to define what you mean by "simplest solution". Because at least for me a polynomial is the simplest solution regardless how many data points there are because then the problem is reducible to a set of linear equations that a computer can easily solve.
However if we specify that the solution needs to be one with the lowest number of parameters possible, then it gets interesting. Then you can have an algorithm start to iteratively test solutions, and try to reduce complexity until it hopefully arrives at something resembling a prime number generator. Or it may not. I don't know if this is even possible because one well known problem with the "gradient descent" approach is that your algorithm can get stuck in a local valley. It thinks it's found the optimal solution but it's stuck in a false minimum because it does not have the "imagination" to start to test an entirely different class of solutions that may at first be much less efficient.