Rohan Varma
1.5K posts
@rvarm1
@reflection_ai | prev: Jump Trading, Meta Superintelligence, @PyTorch
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 (faculty.wharton.upenn.edu/wp-content/upl…) and will be on arxiv tonight; supporting code is here (github.com/dobriban/BH).
New blackboard lecture w @reinerpope How do chips actually work – starting with basic logic gates, and working up to why GPUs, TPUs, FPGAs, and the human brain each look the way they do. 0:00:00 – Building a multiply-accumulate from logic gates 0:16:20 – Muxes and the cost of data movement 0:25:59 – How systolic arrays work 0:39:00 – Clock cycles and pipeline registers 0:51:40 – FPGAs vs ASICs 1:03:14 – Cache vs scratchpad 1:07:16 – Why CPU cores are much bigger than GPU cores 1:11:49 – Brains vs chips 1:15:22 – A GPU is just a bunch of tiny TPUs Look up Dwarkesh Podcast on YouTube/Spotify/etc to watch. Enjoy!
The vibes in SF feel pretty frenetic right now. The divide in outcomes is the worst I've ever seen. Over the last 5yrs, a group of ~10k people - employees at Anthropic, OpenAI, xAI, Nvidia, Meta TBD, founders - have hit retirement wealth of well above $20M (back of the envelope AI estimation). Everyone outside that group feels like they can work their well-paying (but <$500k) job for their whole life and never get there. Worse yet, layoffs are in full swing. Many software engineers feel like their life's skill is no longer useful. The day to day role of most jobs has changed overnight with AI. As a result, 1. The corporate ladder looks like the wrong building to climb. Everyone's trying to align with a new set of career "paths": should I be a founder? Is it too late to join Anthropic / OpenAI? should I get into AI? what company stock will 10x next? People are demanding higher salaries and switching jobs more and more. 2. There’s a deep malaise about work (and its future). Why even work at all for “peanuts”? Will my job even exist in a few years? Many feel helpless. You hear the “permanent underclass” conversation a lot, esp from young people. It's hard to focus on doing good work when you think "man, if I joined Anthropic 2yrs ago, I could retire" 3. The mid to late middle managers feel paralyzed. Many have families and don't feel like they have the energy or network to just "start a company". They don't particularly have any AI skills. They see the writing on the wall: middle management is being hollowed out in many companies. 4. The rich aren’t particularly happy either. No one is shedding tears for them (and rightfully so). But those who have "made it" experience a profound lack of purpose too. Some have gone from <$150k to >$50M in a few years with no ramp. It flips your life plans upside down. For some, comparison is the thief of joy. For some, they escape to NYC to "live life". For others still, they start companies "just cuz", often to win status points. They never imagined that by age 30, they'd be set. I once asked a post-economic founder friend why they didn't just sell the co and they said "and do what? right now, everyone wants to talk to me. if i sell, I will only have money." I understand that many reading this scoff at the champagne problems of the valley. Society is warped in this tech bubble. What is often well-off anywhere else in the world is bang average here. Unlike many other places, tenure, intelligence and hard work can be loosely correlated with outcomes in the Bay. Living through a societally transformative gold rush in that environment can be paralyzing. "Am I in the right place? Should I move? Is there time still left? Am I gonna make it?" It psychologically torments many who have moved here in search of "success". Ironically, a frequent side effect of this torment is to spin up the very products making everyone rich in hopes that you too can vibecode your path to economic enlightenment.
Full video of the ICCV '25 presentation
