As I understand it, the advantages of AI have not just been speed of processing.

Humans have cognitive limits. Humans hold a specific slice of all knowledge at a time and necessarily limits what correlations can be leveraged. This is similar to "context windows" in modern AI. Human minds are wildly variable in efficiency. AI is has constant inefficiency, largely controlled by the speed of light, physical RAM, and processing power, with superior (no cost) "thought" context switching. The AI also has superior accuracy without the need for "concentration" because the AI is processing on a Turing machine with the limited operations that it's superior at in terms of time and energy - eg find an element in a list of 1 million elements.

> a finite number of neurons in a finite number of configurations

Neurons and synapses change, especially synapses (the connections between neurons). Some neurons have a few connections to other neurons. Others have hundreds of thousands of connections to other neurons. These grow and change. "Estimates are between 100 trillion and 1,000 trillion neural connections" Is it finite? Depends on your definition of finite. If anything countable is finite, then it is finite but the number may be practically uncountable. Is it fixed? No.

model collapse seems to say that "AI" cannot train on itself.

I would be curious to see the end result of letting it endlessly update its inputs from its own outputs. I was under the impression that eventually this would cause delusions and if you let it do this long enough and it is solving problems that no humans can verify as correct that it isn't useful.

Maybe that is the limits of my imagination, but it seems unwise to take humans completely out of the loop. Having mathematicians around that can understand what it is doing so that we can utilize that knowledge in a way that we can have some confidence in seems important.

Typical thought experiment - go back to the early years of humanity, even before we've created language itself. Communication is basic grunts and other such things, cutting edge knowledge is 'poke him with the pointy end'. Compile all of this knowledge into the training set for an LLM, let it run with infinite processing power and infinite time. It'll just continually remix the knowledge of that snapshot of time. You're certainly not getting to the Moon, discovering the secrets of the atom, or even discovering mathematics.

It sounds increasingly dumb to bring this up given how advanced models have become, but it remains true - they are still fundamentally token prediction algorithms. And that imposes hard constraints on their potential. These constraints are relatively academic in our current world because there's just so absurdly much information and no human can hold more than a negligible amount in his mind at once. So they'll certainly be able to connect many 'obvious' dots that we don't see simply for a lack of carrying capacity, but they're not going to discover concepts that do not clearly follow from the comprehensive knowledge of an era.

Perhaps they could some day. I'm basing my understanding on the current day capabilities. Once that changes I will update what I think.