That's what machine learning is. We build these systems we don't fully understand, and set them on solving problems we don't understand. It's revolutionary because it lets us solve problems we don't understand. We don't really fully understand what they do or how, but it does still work.
Technically that's what deep learning accepts. Other forms of machine learning have greater or lesser degrees of explicit statistical basis.
It's revolutionary because it lets us solve problems we don't understand
It's certainly a change! I would submit that an approach like that also is often limited in it's understanding of to what degree it has solved a given problem. That's not too bad when you have human verifying the end result but can problematic if one turns a machine of this sort loose to make it's own decisions.
We can and do explicitly explain their inner workings in math.
I certainly don't! I don't know of anyone who understands how and why they work. Granted there are many who write code that "works" but where's the proof that the code actually "works properly"? And if you don't know where you are then it is difficult to determine a path to a better place.
I see few attempts to explicitly explain their inner workings in math. I do see lots of programs/code, however but that isn't math.
Similar dramatic moments have likely occurred before many times. The bare facts lie before us but we do not understand. I'm thinking of late 1800s-1900 just before Einstein published his works on special relativity. We knew Maxwell's equations and their relationship to the speed of light. We even had Lorentz's equations but we did not understand what they meant. Einstein interpreted the math and gave us special relativity.
Perhaps there is an Einstein (or two, or three, ...) working with LLMs now but they are quiet so far.
We do, of course, understand ML models at a pretty deep level. What you can't do is identify the weight values that encode all information about squirrels. You can't point to a particular neuron and say this is why it hallucinates. We do not grok these models. I severely doubt that it's even possible for a human to grok a 13B parameter LLM
Isn't that easy to debunk?
I'd be hard pressed to implement an algorithm that can control a double-jointed inverted pendulum without reading up on control theory again.
But I can instead read up on neural networks and implement one that can be trained to control the pendulum.
For a more advanced example, I would never be able implement speech recognition explicitly by writing a regular program. But I could probably implement a passable one using neural networks and lots of training material.
How is this not "engineer something one doesn't understand"?
The basic description is "a computer system that can do all relevant things a human being can do". And sure, we don't have a very codified definition of what those things are but we, human beings, exist and so even if we can't define our own capacities, we have an strong idea they exist.
The implicit argument is that one can't engineer something one doesn't understand. I tend to agree in the case of full capacities but LLMs seem to have some capacities that their creator don't understand, so the claim doesn't seem a "slam dunk" anymore.