Edward Lockhart

Researcher / Engineer at @GoogleDeepMind
Co-led our IMO 🥇 effort
Now working at the intersection of formal math and LLMs

[Edward Lockhart @freeetext]

@JimDodgy @runthinkwrite @Simi_2210_ There could be thousands of holes on the back

[Jill Foster @JournalistJill]

@mehrubawan The audacity of you arriving on my timeline and not having the faintest idea that this is an entirely accurate account of what happened to the son of Susie Green, former boss of trans charity Mermaids. It's all there in her own Ted Talk on it.

[Edward Lockhart @freeetext]

@SVPhillimore @mar2vickers @Andrews1850 "theft is wrong" is also a philosophical belief, and also enshrined in statute and enforced by courts. Those aren't mutually exclusive things

[Edward Lockhart @freeetext]

@MerriamWebster @dumbahey The sound changes occuring in the evolution from PIE to modern IE languages are systematic and consistent. This is a profound fact about language evolution first articulated in the late C19. And is why a coincidence in PIE gives multiple coincidences in modern IE languages.

[Edward Lockhart @freeetext]

@katlianik Generally I like the framing, but "the quickest way to get more homes built is ...." somewhat presupposes that speed is the main criterion. Replacing "quickest" with"best" might be more neutral and more preference-revealing.

[Edward Lockhart @freeetext]

@therealcyrillej @morphilibrium @AhhereLIO @elonmusk The difference is that human labour is mostly not required to produce the goods that are distributed

[Edward Lockhart @freeetext]

@rivermillion @grahamscheper Also minuend and subtrahend for subtraction

[Edward Lockhart @freeetext]

@samth @finn_hulse You could use ~abs(popcount - log2 n) but the distribution isn't so easy to work with, and you get less resolution. Eg for 4 bits, the freqs are 2 8 6 vs 1 1 2 4 8 for trailing zeroes

[Edward Lockhart @freeetext]

@_Mira___Mira_ I think there may be too many theorems for retrieval on its own to be a useful general strategy.

[Edward Lockhart @freeetext]

@Imported_Fun @IMAO_ Also on a single drive machine, A and B were potentially two different removable floppy disks time-sharing the same drive.

[Edward Lockhart @freeetext]

@paul_wilson_nz @garylfrancione @MForstater Closer, but still not exact

[Edward Lockhart @freeetext]

@CatGodSandHive @HarmonicMath @zjasper Having an LLM compute the entropy / information content is one option

[Edward Lockhart @freeetext]

@HarmonicMath @zjasper A proof with many obvious steps may be simpler than a shorter proof where some steps require non-obvious insight. My guess is that some measure of the time taken to find the proof would be more informative. Information content / entropy might also be revealing.

[Edward Lockhart @freeetext]

@ChShersh Run 100 tasks in parallel, each scanning 1/100th of the file.

[Edward Lockhart @freeetext]

@alexolegimas @alz_zyd_ @danielrock The reasoning approach effectively includes iteration and backtracking in the generation process. The models can (and do) spot mistakes and fix them.

[Edward Lockhart @freeetext]

@xzai259 @CarinaLHong @axiommathai Yup, the Putnam problems require more background knowledge but seem to be easier to solve (for reasoning LLMs).

[Edward Lockhart @freeetext]

@DoozerDiffuser @TMcirony22088 @pickover Nonstandard models are only equivalent inside PA. From the outside they're clear different.

They're generally excluded by moving to second-order logic and a stronger induction axiom.

[Edward Lockhart @freeetext]

@DoozerDiffuser @TMcirony22088 @pickover PA is defined in terms of first-order logic, which requires formulae to be finite. See for example https://t.co/aWVz40JJPg

You could look at what happens when you remove that restriction, but it won't be the natural numbers any more.

[Edward Lockhart @freeetext]

@DoozerDiffuser @TMcirony22088 @pickover The natural numbers are by definition each defined by a finite formula, i.e. a finitely many applications of the successor function.

If you want to infinitely many applications of successor you need a different type of logic and what you get won't be the natural numbers.

[Edward Lockhart @freeetext]

@DoozerDiffuser @TMcirony22088 @pickover What does the arrow mean there? I don't think what you're doing is well-defined.