It's relevant to the "thousand monkeys on a thousand typewriters".

'Always free' does not sound like an opinion.

Especially since, by the "reasonable person standard," they have been offering it for free, so a reasonable person would conclude that they will continue to do so as promised.

The ratio of AI startups at YC surprised me... (slide 48). This is a clear trend.

> Probabilistic analysis can carry you very, very far in doing something that looks like logical inference at the surface level, but it is nonetheless not logical inference.

A statistical approximation of logical inference (as vague as I state it) could (and will) very well pass for logical inference, at least for the common people, whose logic skills are far from perfect.

Also, humans are certainly not capable of the perfect logical inference you speak of. And I get the irony of what I'm saying with such certitude. Logic is still framed in axioms that are framed in languages, we'll never truly get there. Ah, but absoluteness gets in the way of practicality.

Yet, here we are with a tool, that is maybe not at its prime yet, that equals and beat many human beings at logical inference on some problems that are pragmatically relevant. Should I say symptoms of logical inference at that point?

As to why LLMs capacity for (apparent) logical inference is only limited to specific use cases, I don't have a clue. But I'd like to argue that, humans are like that too.

> nobody understands the fundamentals

Funny statement to be found in the discussion about... research results on the fundamentals.

Asymptotics has been used to validate tons of statistical tools. This is just another tool being validated.

If you have a tool that you don't know works when data increases (n-> infinity), then you shouldn't use it.

So practicaly, I believe it has serious implications.

It's very much necessary but not sufficient. In real life the sample complexity matters a lot too, which is also asymptotics, but a more important one. E.g. how the central limit theorem is far more powerful than the law of large numbers.

I don't think that this is true. You need an infinite number of dimensions for this (think Taylor's expansion, Fourier expansion, infinitely wide or deep NNs..)

Yes, you do linear interpolation between an infinite number of data points.

As someone who worked with Nadaraya-Watson regression in the pass, the result that infinitely wide NNs converges to kernel regression baffles me.

Add the feature of doing a high five for the rare cases when it's actually good.

> instantly

Shor's and Grover's still are algorithm that require a massive amount of steps...

I don't think they meant "in O(1) steps", I think they meant "the day someone figures out how to keep many thousands of qubits entangled while operating on them with gates will be the same day we have the first QC that can start breaking encryption in reasonable time". Where, of course, same day is also an exaggeration. But the general point is that we need a single breakthrough to achieve this, and it's very hard to estimate how long a breakthrough might take to appear.

Exactly

You could say it'd be a quantum jump in capabilities.