> When you write things you just need to think about what you want to say and write it. It's not hard.

At least for technical writing at work (internal docs for example), i typically have an extended back and forth conversation with claude refining my ideas, then I have it sketch out the outline which saves _so much time_. Then all I have to do is fix what it got wrong or add things that it missed.

I am not doing this as a creative expression that I find personal fulfillment in, I am doing it to check off a box on a jira issue.

They're also allowed to use wikipedia to use research. It has similar sorts of problems.

My wife is on a school board in a large district that is trying to cut spending. The problem is not really how much money they have and giving them more money doesn't help. The problem at least in our state is:

Public schools are subsidizing charter schools

Public schools have many legal requirements to provide services that charter schools don't have to deal with. Charter schools also have a lot of freedom to refuse problematic kids, that public schools have to take.

Parents who don't need those services keep taking their kids out of public schools and putting them into charter schools, charter schools kick out problem kids. Public schools end up having a higher cost per student because of that.

Schools have to finance an entire security apparatus because assholes keep doing mass shootings.

Public school systems _also_ are terrible at spending money on bullshit that has absolutely nothing to do with schools. The amount of money spent on administration is way way out of line. There are so many layers between the top and teachers and so many people with their hands out. Big school systems could probably fire half of their administration and literally nobody would notice. They would probably run better. When they do internal reports on how to save money, it always comes back to the most trivial shit or even worse, pulling it out of _education_ and is _never_ 'you need to fire a bunch of people collecting a paycheck for doing nothing'.

I genuinely think most big school systems would be vastly improved by firing half of the administration at random and doubling teacher salaries.

Public schools are not subsidizing charter schools. Rather per-student money travels with those kids to the school they are actually attending. So since the kids don't go to those schools, neither does the money.

I don't know what state you are in, and there are a number of them where the charter systems are absolute messes and have become fraud paradises (looking at you Florida), but other states things are much better.

Fo instance my kids are in charter schools in California. All charter schools here are required to have tiered lotteries to get in, and after siblings and teachers' kids, the first tier is always kids with an IEP (the problematic/expensive ones). And at my kids school we know one of the kids with a severe problems that the school has bent over backwards to provide the best environment for that little girl.

And every 4 years they have to re-apply for their charter, and one of the front-and-center numbers required for that is how many kids they kick out. And they got grilled on that (which our school passed with flying colors). The charters absolutely had to prove that they are doing things better than the local schools, and our school worked very hard to prove that (and had the numbers to do so). If they didn't, then their charter would have been cut (we heard about other schools that failed this grade).

So I am experiencing a well run charter school, inside a well policed system (California). If you are not, then make that one of the things you cast your vote on: regulations on where your school dollars flow to.

I will note that there is one important advantage that charter schools have: you have to make a choice to get into them. That means that the parents tend to be more involved in their kids' education (if only minority so), and so you get kids that are a bit more motivated to do well. This one area is unfair to the public schools.

> This one area is unfair to the public schools.

One could say it's the entire point of them existing to begin with. Self-selection of the student body is the only thing that actually matters. The rest is a bunch of minor details. Everyone more or less intuitively understands this point but doesn't want to admit it in public.

And no, I do not see that as a bad thing. I see it as a great thing. It's the closest thing to public school academic tracking as we are likely to get. Other western democracies have this one figured out. They don't throw endless amounts of money into bottomless pits with zero expectation of a payback to society.

I would be nothing today if my very working class parents didn't have the ability to opt me out of the local urban school system. I likely would be dead or in prison. What they had going for them was "giving a shit" and a still-functional system where motivated highly engaged parents could opt out of the status quo. Most of my peers would have had similar stories if not for tracking and academically based magnet schools and the like. The system I was able to use to get ahead has since been torn down.

If it had been the choice of "pay for private school" or "go to the local public school" I'd have been forced into the latter with almost zero chance to succeed in life. I ended up back in that system my final year I attended K-12, and the education offered was laughable and perhaps 6-7 year behind what I had become used to. Plus a moderately violent environment on top of it all.

> Public schools are not subsidizing charter schools.

That is a blanket statement that is not true everywhere. There is, yes the money going with the student, but there is also money from the general funds that goes to subsidize various aspects of running charter schools.

> I don't know what state you are in, and there are a number of them where the charter systems are absolute messes and have become fraud paradises (looking at you Florida)

you guessed the one :)

I don't understand your comment. Charter schools are public schools. Are you confusing charter schools with private schools? Charter schools generally can't pick and choose students the way private schools do.

They don't do it the way that private schools do, but they do have a variety of mechanisms for weeding out undesirable students, which they use, even though they are not legal. There is almost no enforcement for any of it.

What is the transition state where people start using open source models that you imagine actually happening?

Play out a scenario. An open source model is released that is capable as Mythos. Presumably it requires hardware big enough that running it at home is unfeasible. You are imagining that individuals can run it in the cloud themselves for cheaper than api tokens would cost? Or even small companies? And that Anthropic and OpenAI won't be able to cut costs deeper than their competitors while staying profitable?

If it is fundamentally a commodity, that means "running it yourself" also isn't really interesting as a proposition. Many of the world's biggest companies sell commodities. It's a great business to be in if you can sell them cheaper than anyone else.

The value add here isn't the model, it is "having a bunch of compute and using it more efficiently than anyone else".

> I mostly see their products as commodity at this point, with strong open source contenders.

I have seen this argument made a lot, but llm serving being a commodity makes it _better_ for them not worse.

If it's a commodity, then you are entirely competing on price, and the players that will win on price will be the largest ones, because they can find efficiencies that smaller competitors won't have.

It's actually the small LLM companies that are in trouble if LLM serving commoditizes. They will need to distinguish themselves on features, because they can't compete on price. And even there the big labs will have an advantage.

His derivations are genuinely pretty, but it isn’t a result when everything he claims is actually just wrong.

It has more problems. See my other comment in this thread.

I wish i had seen this a few days ago i spent days on this before arriving at the following:

It’s completely wrong, for multiple reasons.

First, and immediately, none of the derived total functions are the functions they appear to be, because they are all partial functions.

Worse than that the domain over which these trees are defined is undecidable by Richardson. You can encode Hilbert’s 10th with elementary functions. Which means you can’t algorithmically decide if a tree evaluates to zero so you never know if ln(y) is undefined

So the central claim is done right off the bat.

Secondly and probably more importantly, these trees have exponential blow up problems because even fairly shallow trees involve tetrations of e that don’t cancel. Even in float64 you can‘t add 800+800 without overflow. Clamping it just gives you wrong answers and clamped exp A) isn’t elementary and B) gives bounded growth so can’t generate all elementary functions.

The consequences for his claimed practical application is disastrous. the loss function is NaN everywhere once you get to around depth 6 in his trees. If you clamp it you just get a flat plateau. Even if you had infinite precision the gradient would be unusable and wouldn’t converge.

As a second note, he frequently in the paper talks about using positive reals as inputs. First, positive reals aren’t even part of his generating set (and if they are his whole central claim is wrong, it has uncountably many constants), but even if they are, fundamentally his operations are complex, and you have subtraction so it is not hard to construct trees that should be total but which never the less are undefined at undecideably many points.

Using extended reals doesn’t save it either. There are just different undefined values that lead to undecideability.

None of these arguments are really specific to EML either. Any binary operator that hopes to generate elementary functions must include exp and ln, must be partial and must be able to encode hilbert’s 10th. There is no fix for this.

You might ask why his tests didn’t find any of this but if you look at his code, they do. He just carefully restricts them to a narrow domain where they happen to work and even then he does things like drop imaginary components and filters out undefined results. He doesn‘t even really hide this in the paper, he just dismisses them as implementation details that can be fixed but the problems are structural

So what we are left with is a generator that can generate exp(x) cleanly and essentially nothing else.

So here is the problem -- we have two constructions of -z.

Whether or not this shows up in a tree somewhere if you try to compose functions together is probably undecideable.

Either they aren't equal and you've broken any tree that includes that construction of -z anywhere in it, _or_ you have two trees which _are_ equal, but disagree on their value at every point

Any rule that tries to rewrite one form to the other is unsound

The lack of any equational theory makes a lot of claims about it fairly nonsensical.

I spent a few days playing around with this work in Lean and his central claim is provably wrong..

The main problem is that singularities infect everything, and you can't have an equational theory without rewrite/substitution rules that aren't grounded unless you can decide if an arbitrary EML tree is zero, which is undecidable in elementary functions (because of sine).

Basically it's only valid on a undecideable subset. All of his numerical tests are carefully crafted to avoid singularities which are exactly where it fails, and the singularities are all over the place -- in particular in subtraction (which shouldn't have any!). He wants to sort of compile it to actually computable functions and use those instead, but there is no equational theory possible that you can build with this.

You can't restrict it to the positive reals either or it's not closed, it's trivially easy to get to complex or negative numbers.

Using extended reals doesn't fix it, you just get different undefined terms (-inf + inf = 0).

It's quite pretty! I love the idea or I wouldn't have spent so much time on it. It just doesn't work, and none of his other candidates will work either because they all have ln(0).

The only sense in which it's true which is that it can generate the elementary functions that it can generate, which is just tautological. It can in no sense generate all of them.

Even his verification doesn't work because they set it up to check the narrow bands where it's valid, outside of that it's a mess.

Thinking about this some more. It having a NAND style combinator for elementary functions is probably impossible. ln(x) is inescapable as part of the composition in the generator somewhere, and you can't generate subtraction without passing through it which means the whole thing doomed as a project.