7/ 5:30–5:35 PM — Closing Remarks 5:35–7:30 PM — Poster Session & Reception That's a wrap on STAI-X 2026! Thanks to our speakers, panelists, award winners & everyone who joined us this week 🎉 #STAIX2026# #Statistics# #AI# @WenyiWang4 @XihongLin @linjunz_stat @EdgarDobriban @tz33cu

We recently conducted an evaluation of algorithmic reasoning — the inputs are generated by executing an algorithm on a graph, and we ask whether existing neural network models (e.g., graph neural nets, transformers) can memorize or predict the execution outputs. Here are our findings from this evaluation: 1) Depth-first search (DFS) is notably hard to “learn” as compared to breadth-first search (BFS): for input sequences generated on Erdos-Renyi random graph inputs with 16 nodes, existing neural net architectures predict DFS with less than 40% accuracy, whereas for BFS, the accuracy is nearly 100%. This is also consistent with earlier findings from the CLRS benchmark. Our explanation is that, for a model to predict DFS, it must first identify the node IDs; if the IDs are randomly assigned in the input graph, it’s hard to learn this permutation. For BFS, on the other hand, at each step, given a node, the search process pushes to the entire neighborhood of that node. 2) Learning multiple algorithms is as easy as learning a single algorithm: for all twelve algorithms tested in this evaluation, on average, training a shared base encoder with a separate prediction head for each algorithm turned out to perform as well as, or even slightly better than, training a separate model for each algorithm. 3) For text description versions of the same problem, fine-tuning open-source LLMs follows similar patterns as 1) and 2), but the evaluation is a lot more difficult. Link to arXiv paper: (Tables 4 and 5 in particular) Tagging a few co-authors @life_olivers @ZhenshuoZhang @EdgarDobriban who are on this paper. Ideas for this work are also based on prior work with @Wu_Sen.

Episode3️⃣ of the FDR(BHq) saga: we now have promising lower bounds for ONE-sided Gaussian tests: The wild part: GPT-5.6 Sol got the correct answer in ONE SHOT 🥳 I attached my exact prompt. It took me 1.5h to verify and another 6h to edit. 🧵(1/4)

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.

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 ( and will be on arxiv tonight; supporting code is here (

Check out our #ICML# 2026 workshop, AI as a Tool for Mathematics, Computer Science, and Machine Learning! Happening now in the Auditorium at COEX Drop by anytime during the day if you are around, or follow online. Exciting kickoff talk by Sergei Gukov!

Final version of my book (with a new title) Online Learning: A Modern Introduction Using Convex Optimization Especially proud of the Foreword by @NicoloCB! It'll be printed by Cambridge University Press. The end of 7 years of updates :)

I was invited to review for NeurIPS 2026 and assigned 4 papers. 2 of 4 are complete AI slop and deserve strong rejects. They study homework-level problems, use overly lengthy yet uninformative language, and include obviously AI-generated method figures that are not even vector graphics. I just found an interesting shortcut for identifying these papers: check the number of references. The authors obviously did not systematically survey the area, and many of these papers cite fewer than 20 works in total.

I solved an open problem in optimization with ChatGPT Pro. Consider min-max problems, where we have to minimize with respect to some variable and maximize with respect to other variables to find a saddle-point.

This was surprising to me. But AI risks can also be surprising. In our recent work on prompt injection, we found that even frontier models can be vulnerable to attacks, and lead to security risks, when messages come from certain channels, such as group chats:

GPT-5.5 (the one available right now to everyone) can also disprove the sum-product conjecture: . I didn't reveal it before because I think it is good to give some space to the community to absorb these new capabilities. In particular the humans involved in the discovery should get all the credit for this amazing breakthrough. We all have some work to do to align on cultural norms in this new world.

Which post-hoc calibration method should you actually use? We ran thousands of experiments to find out. We introduce CalArena, the largest empirical study on post-hoc calibration to date, together with @DHolzmueller, @BachFrancis and Michael I. Jordan.

🚀 The STAI-X 2026 speaker lineup is live! Hear from top AI minds from 07/31–08/01. ⏳ Deadline: Challenge team & early-bird registration ends June 1. 👉 View the program & secure your spot: #STAIX2026# #AI# #MachineLearning#

5.5 Pro one-shot settled the tight localization of electrical flows w/ a cute proof. This improves the log^2 n result of Schild-Rao-Srivastava. Many excellent researchers and myself had thought about this q for a long time.