Max Hopkins

Postdoc @Princeton-@the_IAS. PhD '24 @UCSanDiego theory.

Inputs sushi. Occasionally outputs combinatorics. Likes learning things (mostly halfspaces). He/Him.

[Max Hopkins @MHop_Theory]

For those that couldn't make it, we've uploaded our full STOC workshop on High Dimensional Expanders to Youtube!

Hopefully a useful resource for learning the basics of HDX and how they're applied in TCS.

Talk 1: An introduction to HDX
https://t.co/IaVj4M4yok

[Max Hopkins @MHop_Theory]

@marikgoldstein I miss it -- Princeton coffee scene is... lacking.

[Max Hopkins @MHop_Theory]

@marikgoldstein Can't speak to the locations downtown, but I was a big fan of the bird rock coffee roasters on UCSD campus.

[Max Hopkins @MHop_Theory]

HMS instead keep the labels of S and run A across *all subsets* of the sample.

Since (w.h.p) there's a large subset of S consistent with h_{OPT}, running A on this subset will output a good hypothesis.

This completely sidesteps dependency on the label space -- Nice!

[Max Hopkins @MHop_Theory]

Hanneke, Meng, and Shaeiri give a simple resolution to a core open question in our work "Realizable Learning is All You Need".

We did not know how to adapt our algorithm to the infinite multiclass setting. They give a simple variant resolving this!

https://t.co/jp89OOsSZL

[Max Hopkins @MHop_Theory]

Our reduction works as follows. Given a realizable learner A:

1. Draw a sample S, and throw out its labels
2. Run A over all possible labelings of S
3. Learn the best hypothesis output in Step 2 (e.g. via ERM)

This doesn't work when there are infinite possible labelings!

[Max Hopkins @MHop_Theory]

See also our website, which contains extra information/helpful material!

https://t.co/e48afPPSB2

[Max Hopkins @MHop_Theory]

For those that couldn't make it, we've uploaded our full STOC workshop on High Dimensional Expanders to Youtube!

Hopefully a useful resource for learning the basics of HDX and how they're applied in TCS.

Talk 1: An introduction to HDX
https://t.co/IaVj4M4yok

[Max Hopkins @MHop_Theory]

Talk 6: The Impact of HDX in Quantum Coding

https://t.co/GUvi1H3TKz

[Noah Singer @singerng_]

my article (with some spanish language quotations) drawing parallels between some of Jorge Luis Borges' fiction and computational complexity theory, published ~2 years ago in Variaciones Borges, is now online on JSTOR!

https://t.co/aKxazokvYS

[Max Hopkins @MHop_Theory]

So in the end, I guess the take-away is there really isn't much algorithmic difference between approximate sampling a (dense enough) distribution mu efficiently, and "perfectly" sampling it efficiently in expectation.

Obvious in hindsight but hadn't occurred to me at least :)

[Max Hopkins @MHop_Theory]

Came across a cool result by Göbel and Pappik (https://t.co/yoaQaWX8pQ) this morning.

They show any (nice enough) distribution mu with an efficient MCMC approximate sampling scheme can be converted into an efficient *perfect* sampling scheme

[Max Hopkins @MHop_Theory]

Of course one might say this is cheating:

I'm just running the chain and doing a "correction" by computing the real value of mu(s) with exponentially small probability. So in reality I'm pretty much always just running the chain and doing nothing else.

[Max Hopkins @MHop_Theory]

@GregBodwin "Nat'rals"

[Max Hopkins @MHop_Theory]

Thanks Tom :) -- this paper was inspired by an elegant proof of hypercontractivity due to Yu Zhao and @BooleanAnalysis appearing in Yu's PhD thesis.

My hope is the techniques will eventually extend to weak HDX and beyond simplicial complexes -- still much to be done!

[Tom Gur @TomGur]

A fabulous result by @MHop_Theory, extending Bourgain’s symmetrisation theorem to high dimensional expanders, yielding optimal global hypercontractivity for partite HDX. This resolves the main open problem in my paper with Lifshitz&Liu. Congrats Max!
https://t.co/TjDGwxPFqv