Today (2024), generative artificial intelligence allows us to generate infinite solutions, but the problem is that we cannot prove that these solutions are related to a particular real output. We can, correlate them and approximate the solution as a function of a given distance in a latent space, but we cannot prove this as a fact.

To me, this is a problem whenever we want to apply this to deterministic systems, where we need to prove that a given solution is the correct one no matter what.

Now, let us imagine a system that can generate us a set of infinite solutions \(X\); for these, we take them and assign to each a probability of success given by its correlation with the actual output \(Y\).

Let us now imagine a solver, logically deterministic, that allows us to prove that \(X\) is really related to \(Y\), no likelihood involved.

The solver should be designed in such a way as to allow us to make from generic inputs and outputs, a discrete result.

This system should work as a pipeline that ingests random values and from there reduce the entropy of the set to obtain a finite result.

This is a multi-million dollar problem.