I did not have the impression the proof uses a surprising and novel contribution of fields. I think the proof uses standard application techniques of algebraic number theory towards discrete geometry. If you have a quote substantiating what you said I would be curious.
I know these articles write that it used deep algebraic number theory techniques, which is true, but it may also just be the standard in the field.
You are believing a very unlikely scenario. I think the reason is that you have been convinced of a claim which is unlikely and indeed not true. That is:
>the model seems so capable at doing things like refuting fundamental theorems of mathematics
That is not true and a complete misrepresentation of recent progress of AI in math. It is therefore not necessary to believe the conspiracy theory you described in order to explain recent progress of AI in math.
You should believe that the proof works at least as much as any ither paper in mathematics. The proof has been scrutinized by experts and simplified and improved. If you don't believe that then I'm sorry but you are deluding yourself.
No it is not Leibniz/Euler/Galois. More like writing good papers that contribute to the broader understanding of a theory. I think if one evaluated a mathematicians research output and it consisted of mostly the kinds of problems AI has solved so far, it would give the impression that this person is somehow very good at picking accessible problems to target, but has not made a larger impact on the field.
I am pushing the optimism a bit of course, but currently we can see many demos of robots doing basic tasks, and it seems like it is quite easy nowadays to do this with the data driven approach.
Say you want to steer an android to walk forward. You need to provide angles or forces or voltages for all the actuators for every moment in time, so that's high dimensional. If you already have certain control models, neural or not, you can instead just press forward on a joystick. So what I mean low dimensional input is when someone steers a robot using a controller. That's got like, idk, 10-20 dimensions max. And my understanding is that SIMA 2 when it plays No Man's Sky or whatever basically provides such low dimensional controls, like a video game. Companies like Figure and Tesla are training models that can do tasks like folding clothes or emptying the dishwasher given low dimensional inputs like "move in this direction and tidy up". SIMA has the understanding to provide these inputs.
The gap between high level and low level control of robots is closing. Right now thousands of hours of task specific training data is being collected and trained on to create models that can control robots to execute specific tasks in specific contexts. This essentially turns the operation of a robot into a kind of video game, where inputs are only needed a in low-dimensional abstract form, such as "empty the dishwasher" or "repeat what I do" or "put your finger in the loop and pull the string".
This will be combined with high-level control agents like SIMA 2 to create useful real-world robots.
This is pretty cool. I have several points to make.
1. We all know that Cellular automata or more generally any dynamical system of sufficient complexity (and maybe not too much complexity) will be Turing complete, will have complicated "uncomputable" behavior, will have perhaps pattern formation, or gliders, solitons etc.
So what is a valuable addition to this these computational investigations? I think when studying emergent computational behavior we really care about dynamics complexity / rules complexity. It's not impressive to get complicated dynamics out of a complicated system but the simplicity of game of life made it really impressive.
I think in that regard LACE is pretty nice: the rule still feels very simple/natural and you can get much more structured/complex behavior with fewer cells.
2. Nevertheless in the end this blog shows mostly pretty pictures of computational, complex, emergent, chaotic behavior, which we've all seen before. And the key features that make the difference go something I would call physics-like are still missing.
And I guess that would be complex stable patterns that can have complex stable interactions. Who knows maybe there are 10^16-celled patterns that have this but we don't know.
3. If I were you I would cut the whole preamble. It will make people take you less seriously than they should. You don't want to look like a crank.
Well yes, you can "hack" the pseudorandom number generator, but... that's not really the point when talking about determinism in LLMs is it? I mean the mathematical idea of the standard LLM is certainly truly random.
Hold on a second. A transformer produces deterministically a probability distribution over the token alphabet from the context. Then one samples from this distribution. This is random and meant to be random.