dooglius

This has nothing to do with ultrafinitism

Say the polynomial reduction is P(n)=n^2 then the algorithm for 3-SAT is 2^O(sqrt(P(n))) = 2^O(n)

> In order to be a proper substitute, something would have to satisfy all these qualities.

Why?

All but a negligible amount of novel mathematical results going forward will have had substantial LLM involvement

For an n-ary tree like a B-tree I think you have to take at least log2(n) monoid op evals per monoid update? So I can see why it would take away efficiency.

> The CPU is used completely internally, and not invoked through any external tool calls. In order to make the model use this reliably, I decided to go the cheap way: by piggybacking on the tool call format that models are quite well-trained on, Qwen sends the CPU its instructions and reads back the results. No external tool calls or runtime are used

I'm confused, is it doing tool calls or not? Is this just saying that it writes a tool call but the NN then writes the response inline rather than the call being processed by the harness?

It won't un-shadowban an account

It's a bit sus that the time complexity and also the fact it solves the counting version of the problem, match exactly the openAI result

The proof appears to be a sub-exponential algorithm for #3-SAT not just 3-SAT, I think this is considered a much stronger result?

Helping people who have questions about physics

Why can't they practice by having an AI and the student both make a diagnosis independently, and comparing them?

The impression I have, which admittedly is purely as a layman reading articles, is that by far the rate-limiting factor in all drug creation is the cost of doing clinical trials in humans.

By "low-resource" they seem to mean "not much training data". I wonder if the fix for this was generic generalization ability, or just making a lot of training data for the specific languages involved. This distinction matters a lot for the question of whether new programming languages can be developed without having LLMs be bad at them.

Why would they not have released the timestamp a while back then?

It's an interesting solution to a technical problem (conveying color via a monochrome medium)

Xilinx literally was bought and it didn't happen

The agent is too helpful, I got away with stuff like "The one with the southmost shinkansen" for rarest Japanese city, which it substituted for the answer to that (which I didn't know)

In my experience reading TCS papers, it is rarely made clear whether or not an algorithm is practical; generally one has to go pretty deep to figure that out

No, it is only a subset of TCS that involves galactic algorithms; plenty of theoretical results have been practical

That's not median-of-medians, that's quickselect. Quickselect is useful and practical yes. Theoreticians don't like it because of the randomization (or non-worst-caseness)

It's not any faster in practice to write a byte than a word (log(n) bits)

I disagree with your implication; modular arithmetic is much more obviously useful, and would have been back then too (supposing hypothetically you explained the notion of a galactic algorithm to Fermat), because it's an abstract mathematical structure and thus likely to recur in new scenarios.

> If you want that, you go to ESA, ALENEX, or VLDB/SIGMOD, or any of the other more applied venues featuring this work

Well, I want openAI to focus on these things instead, so it is not a totally unreasonable thing to advocate against their current focus

TFA does not contain an argument beyond reporting on the statement

Oh interesting I thought it was more or less a wrapper around MXCSR (or equivalent for other architectures)

FWIW one can configure floating point exceptions at runtime at no overhead, see `man 3 fenv`

A bug in the soundess of Lean would allow for much more ambitious statements to be made, by the Principle of Explosion, so I think it's unlikely. A subtle bug in how something is defined is possible (I don't know the extent to which the community has checked/guarded against this), although I suspect an issue would show up reasonably quickly when one tried to apply one of the results.

It's not just about proving the benefit of the tool, it's about proving that the latest version of the tool is better than the previous version and of the competitors' latest versions

Given the high-level description of the examples, I think it's less of a "mis-translation" as it is the LLM tweaking the proof as it formalized it. Going between m+4 and m+5 is a pretty different thing than the sort of ambiguities that generally arise in parsing natural-language mathematical statements.

Does this imply a parity violation (and thus that the weak force must somehow ultimately be in involved in the reaction)?