soVeryTired

Probably true for the dedicated problem solvers (of which Tao is one IMO). But I doubt there's ever been a better time to be a theory builder (more like Peter Scholze, or Grothendieck).

Some up with an idea and leave the system to check it 15 different ways, and see whether you can simplify an existing body of theory. It'd be like having an army of lightning-fast grad students.

What's an example of your belief system conflicting with a motivated example? I'd love to understand that a bit more.

Wintermute and neuromancer!

Was it a marketing win though? My takeaway is: if you're doing groundbreaking work with openAI's models and they find out, at best they'll outspend you and scoop you. At worst they'll steal your chat history.

Yeah - I think he’s worried that we have a tool that’s almost an oracle that can just get straight to the heart of a given problem.

The problems aren’t always that interesting in their own right. But the quest to solve them is often what drives the invention of new techniques.

We ultimately got the Langlands program and a large amount of algebraic number theory out of attempts to solve fermat’s last theorem. A “clever” approach using techniques from the 1800s wouldn’t have been anywhere near as fruitful for mathematics as a discipline.

Out of interest, would you call BERT an LLM? It’s pre trained but not particularly large.

It’s neither large nor language-based. ARC-AGI-1 is grid-based and nonverbal.

Use of a transformer is not necessary or sufficient to qualify as an LLM.

Undetectable by a human reader. Come on, give the post a charitable reading.

Yeah - otherwise it’s bizarre to have row vectors and column vectors.

To that point, given a corpus of writing from person A and another from person B, I have no doubt it’s easy to train a classifier to determine who wrote what. In fact I believe law enforcement agencies already have these classifiers.

The only difference here is that Anthropic is actively trying to make the watermark undetectable.

Out of interest, do Musk's politics impact your decision on whether or not to use Grok? I'd be interested to know where folks lie on the (Agree / Disagree) and (Use / Don't use) axes.

0000 in base pi. Oh Jeff.

I mean yes but where does that get us? The great oxygenation event wasn't exactly good for the organisms that were alive at the time.

No way is vocab size zipfian. Word counts from a corpus follow zipf's law, but not vocab sizes themselves.

Otherwise the most common vocab size would be equal to one.

Can anyone explain to me why Q and K are both needed? They only ever appear as a pair, so why can’t you just define a matrix A = QK and learn that directly?

> On March 12, 2025, a search warrant was executed at Sohaib’s home in Alexandria. Agents grabbed plenty of tech gear but also turned up seven firearms and 370 rounds of .30 caliber ammunition. Given his former crimes, Sohaib should have had none of this.

For god's sake, don't commit crimes while you're committing crimes.

I have a feeling taxes are possible to circumvent only because a government tends to have one arm that wants to collect taxes, and another that wants to reduce them to encourage certain outcomes (like having a business setting up shop within its borders).

The US may have this dual incentive structure since it wants to build its tech giants while limiting their control, but the EU doesn't. The arrival of a foreign tech social media giant might make the legislation a bit more palatable to pass.

It will undoubtedly be complex to regulate all dark patterns away. But there are a few obvious, easy wins. It'd be a shame to make perfect the enemy of good.

Us consumers don't want moats. But to understand the investment you need to understand the moat: no sensible investor will throw this much money around without one. If you don't understand what is keeping new players from entering the market, then either you've missed something or we're in bubble territory.

That's why it's interesting to try to pick apart where the moat is.

Whenever people bring this up I like to remind them that linear interpolation is a universal function approximator.

The company is named after the evil telepathic orbs from lord of the rings. Wasn't that the first clue that everything might not be hunky dory?

I'm sure some python devs care about cache misses too. I guess my point was that the big results will be picked over again and again to understand _exactly_ which conditions are needed for them to hold.

In my experience those debates are usually between experts who deeply understand the difference between ABC and XYZ widgets (the example I'm thinking of in my head is whether manifolds should be paracompact). The decision between the two is usually an aesthetic one. For example, certain theorems might be streamlined if you use the ABC definition instead of the XYZ one, at the cost of generality.

But the key is that proponents of both definitions can convert freely between the two in their understandings.

IMO it's not far off how most python or javascript devs don't care about registers or cache misses. Someone's thought deeply about those things so you don't have to.

Mathematicians do care about how much "black magic" they're invoking, and like to use simple constructions where possible (the field of reverse mathematics makes the central object of study). For example, Wiles' initial proof of Fermat's last theorem used quite exotic machinery called "inaccessible cardinals", which lie outside of ZFC. Subsequent work showed they weren't needed.

Another good example of mathematicians caring which 'house of cards' their results are built on is the search for an "elementary" proof of the prime number theorem (i.e. showing it doesn't rely on complex analysis).

Edit: here's a great related discussion on MathOverflow, bringing in analogies from CS: https://mathoverflow.net/questions/90820/set-theories-withou...

Anyone have a good explanation for why elliptic curves have a 'natural' group law? I've seen the definition of the group law in R before, where you draw a line through two points, find the third point, and mirror-image. I feel like there's something deeper going on though.

As far as I've seen, the group law is what makes elliptic curves special. Are they the _only_ flavour of curve that has a nice geometric group law? (let's say aside from really simple cases like lines through the origin, where you can just port over the additive group from R)

The average density of matter in the universe is one proton per five cubic meters or so. We're very much the outlier!

That's more like the false positive rate and false negative rate.

If we're being literal, accuracy is (number correct guesses) / (total number of guesses). Maybe the folks at turnitin don't actually mean 'accuracy', but if they're selling an AI/ML product they should at least know their metrics.

The word “some” in the quote from Box is doing a lot of heavy lifting.

If a model is useful, I’d like to see it being used (outside academia, where there’s minimal penalty for complexity and a high emphasis on novelty).

If models like these are widely adopted at social media companies or news agencies, it’s fair to say OP’s take isn’t valid. Otherwise they may have a point.

There's no place for you here you lunatic

I didn't say it wasn't alarming, I said it wasn't civilization- or nation-ending. Unless you're a tiny island nation, in which case I'll happily retract what I'm saying.

There are degrees of awfulness between "the end of all mankind" and "nothing to see here", but it seems like there's a taboo on calling those shades of grey out when it comes to climate change.

Ports get retrofitted, redesigned, and rebuilt. The AMOC collapsing is a serious thing, but I'm not saying climate change isn't real or isn't a threat. My original point is that three feet of sea level rise is manageable, if expensive. Simply that, nothing else.

If you draw the line at the year 2100, things are uncomfortable but maneagable. If your horizon is 2300 or 2500, you get a different story. But you would hope that in tha sort of time frame, we have time to adapt.