Sunay Joshi

PhD student @Penn. AB @Princeton. #Stats #ML #AI. Grateful to be advised by @EdgarDobriban and @HamedSHassani

[dandelion georgism 🔰🏗 @DolphinMossad]

1995: oh cool you can buy books online now

2026: the company that owns Whole Foods and Lord of the Rings is experiencing setbacks with its space program

[Simo Ryu @cloneofsimo]

I have to admit, Kimi folks cooked like crazy and this aged like absolute yogurt. Stupid cat.
Competition is on, it seems.

[Behrad Moniri @bemoniri]

Just astonishing! If actually implemented as is, this policy will destroy Ph.D. programs in the US.

I don't think the policy makers understood the severe devastating long term impact that is policy is going to have on science and technology in the US.

[Greg Brockman @gdb]

GPT-5.6 Sol Pro for resolving an important open question in statistics:

[Noam Brown @polynoamial]

2023: LLMs struggle with 4th grade word problems
2024: LLMs can do high school math
2025: LLMs get a gold medal at the IMO

Now, GPT-5.6 solves famous frontier math/stat questions. The IMO is today and 5.6 one-shotting a perfect score isn't even news.

Where will we be next year?

[Ben Golub @ben_golub]

Congratulations to Hong Wang, Yu Deng, John Pardon, and Jacob Tsimerman on the Fields Medal!

(It seems the winners were revealed early because they were on the ICM website in "hidden" fields.)

[Nature Biotechnology @NatureBiotech]

The FDA’s drive to reduce animal testing in drug development has coincided with a boom in AI-powered biosimulation techniques such as multi-agent virtual scientists and digital twins, while organoids and other mature methods embrace AI to ramp up predictive power https://t.co/r04a9Ykqkb

[Pravesh K. Kothari @praveshkkothari]

Huge news: Bandeira, Kunisky, Nizic-Nikolac, Pesenti, and Wang finally get rid of all the log factors in the hypergraph Moore bound! One of my all-time favorite questions that GPT 5.6 Sol helps resolve!!! Check out the neat proof. https://t.co/JsIZAXZhTO

[Jason Lee @jasondeanlee]

My impression https://t.co/UIpj0hDRMi based on 300c (emmanuel's class , which I think @EdgarDobriban and I took together back in 2013 ) is that if you do BH-q , we kind of expect that you control at \approx q but probably >q. FDR experts feel free too correct me, @wfithian @yuvalbenj @lihua_lei_stat @weijie444 . BY already says C(n) < \log n if we define it as FDR(BH)< C(n) q. This example shows sup_n C(n)>1.04 (?) .

More formally , define C(n) = max_{m<=n, q<= 1/2} \max_{\mu \in R^n, \Sigma\succ 0 ,diag(\Sigma) =1} FDR_{\mu,\Sigma}(BH) /q The interesting research question would be to show C(n) << \log n (positive result). BY already gives log n, and anything o(log n) is theoretically interesting. Probably to justify BH use in practice you really need C(n) < (1+\epsilon), not that studying it in Gaussian really justifies it anyways.

Given that AI is better problem-solvers than us or will be in 6 months for sure, all we have left is our taste and ability to propose/synthesize problems, may as well write down what I think is the real question here.

[Ulugbek S. Kamilov @prof_kamilov]

Descartes moved to Sweden to tutor Queen Christina. She insisted on lessons at 5am in unheated, freezing rooms.

Descartes, who preferred working in bed until late morning, soon fell ill and died.

So now you know why I don’t teach until I’ve had my coffee and a fresh croissant.

[Ronnie Chatterji @RonnieChatterji]

So many wow moments in just reading this tweet about AI solving a major open question in stats. He couldn’t do this with 5.5 and it took just 90 mins with 5.6—capabilities growing fast! Also great to see it promptly turned into a paper we can all learn from.

[OpenAI @OpenAI]

Introducing GPT-Red

An internal automated red teamer on a mission to find our models’ prompt injection vulnerabilities at scale, helping us build stronger defenses before wider deployment.

https://t.co/GxnmxxcpSk

[Alex Robey @AlexRobey23]

Safety is at the core of the work we're doing @thinkymachines🦺

And if you're interested in working on safeguards for future models, please reach out!

[Jared Duker Lichtman @jdlichtman]

"GPT-5.6 one-shot the problem after 90 minutes of reasoning"

"Emmanuel Candes of Stanford University once called the false discovery rate and the Benjamini-Hochberg procedure 'one of the two most important developments in statistics after 1950' "

My rule of thumb:
if a problem has a short proof or disproof with existing methods (albeit cleverly executed), then current frontier AI can likely find it.

The definition of "short" is lengthening over time, and seems to be currently around ~15 pages.

This may also help explain why stories of counterexamples are popping up, since they often can be constructed by a short argument.

[Sunay Joshi @sunay_joshi]

Exciting AI-aided breakthru by @EdgarDobriban on BH method: BH *fails* to control FDR, in simple gauss'n location model w/ carefully-chosen coeffs! Excited for follow-ups: distilling example to essence, bding excess FDR for gen dependencies, study impact on apps. Check it out!

[Edgar Dobriban @EdgarDobriban]

AI has helped resolve an important question in statistics. In the area of multiple hypothesis testing, the goal of controlling the false discovery rate (FDR) has been introduced in a seminal paper by Benjamini and Hochberg (1995). They also introduced a method (the Benjamini-Hochberg or BH method) and proved it controls the FDR. This method has been widely adopted in modern high-throughput science, including in genomics, astronomy, economics, etc. The paper has has garnered more than 130,000 citations to date.

However Benjamini and Hochberg showed FDR control only when the data for the individual tests are *independent*. In practice, these data are often dependent; a good example is data on genetic variants due to linkage disequilibrium. Later work has focused on extending the validity of the BH procedure, e.g., to a form of positive dependence by Benjamini and Yekutieli (2001).

The question of when the BH procedure controls the FDR has remained open. Over the last twenty years, many authors, including Reiner-Benaim (2007), Kim and van de Wiel (2008), Benjamini (2010), Sarkar (2023), Sarkar and Zhang (2025), have conjectured that the BH procedure controls the FDR for two-sided tests using any correlated Gaussian data. These authors have presented both theoretical and empirical evidence supporting, but not directly showing, the conjecture.

With the help of AI (specifically GPT-5.6 Sol Pro), I have settled the question in the negative: The Benjamini-Hochberg procedure does *not* generally control the false discovery rate at the desired level for correlated two-sided Gaussian tests. This was done by exhibiting a Gaussian factor model for which, at a nominal level alpha=0.01, the false discovery rate is proved to be FDR>0.0104.

There is a lot of interesting commentary to be made:

1. This result should be of interest to everybody in the field of statistics. Emmanuel Candes of Stanford University once called the false discovery rate and the Benjamini-Hochberg procedure "one of the two most important developments in statistics after 1950" (the other being James-Stein shrinkage). The present conjecture is probably the most central question about FDR/BH that was unresolved to date.

2. GPT-5.6 one-shot the problem after 90 minutes of reasoning, whereas with 5.5 I was not able to solve it even after iterating with multiple parallel agents for perhaps 20 hours. So the capability improvement is quite real. Exciting times to live in!

3. The argument is not especially surprising, but it does combine an asymptotic approach (standard for FDR analysis, see e.g., Genovese and Wasserman, Efron, etc) with a numerical certificate in a way that would be pretty non-standard in the field. Once we have the specific example, then straightforward simulations also support that the false discovery rate is indeed higher than the nominal value (see attached fig).

4. The current degree of violation over the nominal level is relatively small (0.104 vs 0.1). So the importance of this result is mainly conceptual. The practical implications remain to be determined.

Overall, an exciting development! Preprint is available here (https://t.co/YgiwgDF2qr) and will be on arxiv tonight; supporting code is here (https://t.co/KZhj15qDXC).

[Edgar Dobriban @EdgarDobriban]

AI has helped resolve an important question in statistics. In the area of multiple hypothesis testing, the goal of controlling the false discovery rate (FDR) has been introduced in a seminal paper by Benjamini and Hochberg (1995). They also introduced a method (the Benjamini-Hochberg or BH method) and proved it controls the FDR. This method has been widely adopted in modern high-throughput science, including in genomics, astronomy, economics, etc. The paper has has garnered more than 130,000 citations to date.

However Benjamini and Hochberg showed FDR control only when the data for the individual tests are *independent*. In practice, these data are often dependent; a good example is data on genetic variants due to linkage disequilibrium. Later work has focused on extending the validity of the BH procedure, e.g., to a form of positive dependence by Benjamini and Yekutieli (2001).

The question of when the BH procedure controls the FDR has remained open. Over the last twenty years, many authors, including Reiner-Benaim (2007), Kim and van de Wiel (2008), Benjamini (2010), Sarkar (2023), Sarkar and Zhang (2025), have conjectured that the BH procedure controls the FDR for two-sided tests using any correlated Gaussian data. These authors have presented both theoretical and empirical evidence supporting, but not directly showing, the conjecture.

With the help of AI (specifically GPT-5.6 Sol Pro), I have settled the question in the negative: The Benjamini-Hochberg procedure does *not* generally control the false discovery rate at the desired level for correlated two-sided Gaussian tests. This was done by exhibiting a Gaussian factor model for which, at a nominal level alpha=0.01, the false discovery rate is proved to be FDR>0.0104.

There is a lot of interesting commentary to be made:

1. This result should be of interest to everybody in the field of statistics. Emmanuel Candes of Stanford University once called the false discovery rate and the Benjamini-Hochberg procedure "one of the two most important developments in statistics after 1950" (the other being James-Stein shrinkage). The present conjecture is probably the most central question about FDR/BH that was unresolved to date.

2. GPT-5.6 one-shot the problem after 90 minutes of reasoning, whereas with 5.5 I was not able to solve it even after iterating with multiple parallel agents for perhaps 20 hours. So the capability improvement is quite real. Exciting times to live in!

3. The argument is not especially surprising, but it does combine an asymptotic approach (standard for FDR analysis, see e.g., Genovese and Wasserman, Efron, etc) with a numerical certificate in a way that would be pretty non-standard in the field. Once we have the specific example, then straightforward simulations also support that the false discovery rate is indeed higher than the nominal value (see attached fig).

4. The current degree of violation over the nominal level is relatively small (0.104 vs 0.1). So the importance of this result is mainly conceptual. The practical implications remain to be determined.

Overall, an exciting development! Preprint is available here (https://t.co/YgiwgDF2qr) and will be on arxiv tonight; supporting code is here (https://t.co/KZhj15qDXC).

[Sunay Joshi @sunay_joshi]

@sama There are too many degrees of freedom (chat/work, 1.5x speed or not, selecting the thinking effort). Why can't the model set these by itself? Too much burden on user

[Sunay Joshi @sunay_joshi]

@davisbrownr @HenryKvinge @davisbrownr Some MELD pairs are of form ("express in language of field X", "express in lang of subfield Y of X"); e.g., (modules, vec spaces). Are these as informative as expressing a thm in two *disjoint* fields? E.g., viewing thm abt Brownian motion thru (probability, PDE)?

[Physics In History @PhysInHistory]

We waited until the blast had passed, walked out of the shelter and then it was extremely solemn. We knew the world would not be the same. A few people laughed, a few people cried. Most people were silent. I remembered the line from the Hindu scripture, the Bhagavad-Gita:

Vishnu is trying to persuade the Prince that he should do his duty and, to impress him, he takes on his multi-armed form and says, "Now I am become Death, the destroyer of worlds." I suppose we all thought that, one way or another.

-- interview in The Decision to Drop the Bomb (1965)

[Francesco Orabona @bremen79]

If you are at ICML, the poster (spotlight) will be at 2pm.
Come to say hi and talk with Tuo