That's why you should prefer LPIPS to PSNR. LPIPS is a learned metric that uses subjective human input.
That said, it's limited due to the training set, iirc. So we still use PSNR regularly — it's an easily-understood metric with widely-understood limitations, which is in practice not too bad. Devil you know, etc.
Ironically when we did compression quality evaluations, me and my colleague found that PSNR way better matches our perception of quality, than LPIPS or FLIP. Our assumption is that LPIPS is biased towards quality artifacts that is not representative of compression quality artifacts.
Curious if the authors are hanging around here and how they feel about the recent Leiden Statement. (Late in the article it’s clear that this is at least partially a publicity effort around a new AI math tool, if I’m reading it correctly.)
On a personal level I’m very excited about AI getting good at math, but I’m a consumer of math, not a creator. My job gets easier as AI gets better on this front, so I can’t fully empathize with mathematicians who feel threatened or are worried about the sanctity of the discipline.
I am a producer of math. But I feel two ways about AI math.
First I fear slop-math. People producing LLM “proofs” and prose with no value. I do not want to review something the author has spend lies energy on than I will spend reviewing.
Two, I am excited about formal machine-checked proofs. I love formalisation, and if the llm can prove my lemmas I will be a happy camper!
I think my optimism here is coloured by the fact that I am a theory builder, not a problem solver. I will be happy to create beautiful theory, writing (myself) wonderful articles explaining them, but letting the ugly details be formally verified by an LLM.
A problem solver kind of mathematician might feel cheated of all the fun of the llm did all the problem solving.
The root cause of the collapse in math education in California is one bad researcher's work, combined with politics.
Briefly, a Stanford-affiliated "researcher" named Jo Boaler produced two deeply underpowered studies claiming to show that putting all students in the same grade-level math course led to better outcomes for everyone — even the kids that would've normally been tracked into advanced math. But she only tested results on grade-level math — of course the would-be advanced kids did better on "grade level" math if they've taken it recently. The loss is the advanced math they didn't take.
I fought with my son's middle school administration about this precise issue. It is the stated policy of CA's state level education department to de-emphasize advanced math and tracking, in favor of these deeply suspect ideas. I'm pretty progressive in general, but this is braindead stupid, alarming, and self-defeating. (If you care about equity, you NEED to have options in the public school for the underprivileged gifted kids! the rich kids have lots of options and will be fine.)
It's deeply depressing, but education has long been a weak spot for California; since Prop 13 in the 1970s, California has been 49th or 50th in per-pupil funding for public education (excluding college, I think). But to compound that with this wrongheaded, moronic, politically suspect and quantitatively incorrect policy is... infuriating.
I agree with everything you wrote about maladministration of California's math curricula, but:
> since Prop 13 in the 1970s, California has been 49th or 50th in per-pupil
funding for public education (excluding college, I think).
This is totally incorrect. California ranked 6th in total per-pupil spending in 2023[0].
California has a formulaic mandate on K-12 funding amounts (Prop 98) and schools are funded through both property taxes (affected by Prop 13) and general funds via the LCFF, which directs extra funds towards schools with more disadvantaged students.
In fact, funding levels keep hitting record after record, with only mandatory Prop 98 spending rising from $59B in 2013-14[1] to $127.1B in 2026-27[2], despite an enrollment decline of ~7% over that period[3].
This is interesting news to me, thank you. I'm curious if the per-pupil spending includes locally raised funds; the reality in California is that the state level funding is poor, and districts that are above some threshold don't get enough funding to operate. So public schools function as local charities and inevitably have fundraising arms to make up the shortfall. This has been true since at least the 1980s when I was in school, and is definitely still true today.
> the reality in California is that the state level funding is poor
No, it really isn't. Again, just mandated Prop 98 state spending on K-12 is $127.1B for next year, with this year's enrollment at just about 5.8 million students. That works out to $21k per pupil not including all discretionary state spending, federal spending, and other local funding (like the fundraising you're talking about).
> districts that are above some threshold don't get enough funding to operate
Since 2013, under the LCFF, districts with a very high amount of property tax revenue only get "basic aid" from the state, but this is only a small fraction of school districts. Anyway the funding disparity is the entire point of the LCFF: The idea is to give rich districts less and poor districts more.
It's frustratingly difficult to get my fellow Californians to understand that our schools are, if anything, over-funded, and that throwing ever more money into the black hole is unlikely to improve our abysmal outcomes.
Well I live in a basic aid district; Bay Area but firmly middle class. We’re just above the cutoff for federally subsidized school lunches iirc, and the schools are chronically short on money.
Part of it is declining enrollment, part of it is Baumol’s cost disease (a living wage is pretty high here! Teachers get paid well on a national scale and very poorly on a local scale).
But yeah… education is simply not well-run in California. I find that pretty indisputable.
Your situation is a good argument against the equity-focused LCFF. It's such a HCOL area that despite having high property tax revenue vs. the rest of the state, your district really should be funded at a higher level. Unfortunately I have little hope of Californians abandoning their zeal for punitive equity any time soon.
It is indeed indisputable that education is not well-run here. But it's not going to be easy to fix. For starters, nearly 100% of the people I talk to about this issue believe, like you, that the problem is Prop 13 and underfunded schools. I don't know where this idea came from but it's remarkably pervasive and consistent across demographics.
But the biggest problem IMO is that the education administration mafia has a stranglehold on our one-party state and things are broken just the way they like it.
Your comment prompted to look into this further, thank you. The funding situation in California is complicated and weird, but yes, CA does spend a lot of money on public education.
There are weird relics of the underfunded past, but you can’t blame the educational failures on lack of budget.
This already happens — my district when I was in school, and my son's district now, both have / had "alternative" high schools that kids get transferred to when they're struggling. Kids who are dropping out inevitably get transferred as part of the process; the high school they were originally attending has stellar graduation rates. The alternative high school has miserable graduation rates, but no one really cares.
A lot of people believe in Musk and will invest in anything he wants to do. Is this rational? It depends on how it plays out.
I think we may be seeing a new type of capitalism that maybe Steve Jobs and Warren Buffet hinted at: A business empire built around the outsized ambitions of a single charismatic individual. The valuations of Tesla and SpaceX only make sense if you attach an enormous premium to Musk the individual.
I hate semantic arguments but have a thought. I don't think "charismatic" is the right word. Musk is more vilified than celebrated. He's like a human traffic accident, an amoral black hole of social media attention. I am not sure the English language has a word for this.
In his interview on the Hard Fork podcast, Palo Alto Networks’ CEO described the capability change from Opus to Mythos being more about availability; evidently it runs in a very compute-intensive, always-on mode. Unclear if the base model is significantly different, but Arora ascribed the difference mostly to that change.
In case anyone is wondering why this is important: the spherical harmonics are frequently most of the data in a Gaussian splat data set — as much as 80% of the data for good quality scenes.
The magic of Gaussian splats is their ability to render photorealistic outputs without material properties, explicit ray tracing, etc. They do this by synthesizing complex light transfer in the scene via these fuzzy blobs overlapping — but they need to be able to change color and transparency with view angle to recreate much of that light transport. Hence, relatively heavyweight data.
There are many approaches to reducing the data volume, and they get increasingly complex when you add a time component. Not even worth listing publications here because it's changing so quickly, just plan to look at the SIGGRAPH pre-prints in a couple of months. Exciting times!
It's worth signing up for Levine's free newsletter and listening to the podcast (though there is substantial overlap in the content, it's still fun to hear what you've already read).
His take on this, crypto, all things Elon Musk, and the current 'predictions market' are funny and insightful.
I wish he interviewed more for his podcast. The Cliff Asness episode was great (and he knows it because they keep on rereleasing it ever month or two) as was Boaz Weinstein
Because it acquires an asset worth roughly that much, it’s neutral. GME is (probably!) not doing a huge at-the-market offering, they’re creating the shares and immediately giving them to eBay shareholders.
In practice the price paid for the company being acquired is usually a bit higher than the market value (so the shareholders take the deal), and the market usually punishes the acquirer a bit and the resulting entity’s stock will fall a bit. (This is most definitely not investing advice.)
That said, it's limited due to the training set, iirc. So we still use PSNR regularly — it's an easily-understood metric with widely-understood limitations, which is in practice not too bad. Devil you know, etc.