Proud to have contributed to Gemini 4 Argon’s much improved math capabilities. It’s been an intense few months!

Official apology to Google from me, they cooked with Carbon. It's spikier in terms of domains and capabilities, but it's really good in a few areas.

The expert in signal prop in large neural nets is weighing in.

Yesterday, I left Microsoft which of course feels rather bittersweet after 14.5 years. Nevertheless, the logic that it's the right decision for me seems inescapable.

Sharing early evals on Gemini 4 Carbon. Strongest model that we've seen so far for long-form research and answer quality, with a new SoTA on the Wide-And-Deep-Research (WANDR) benchmark. Coming soon to all Perplexity Pro and Max users inside Computer, once we have sufficient token capacity. Congrats @GoogleDeepMind!

And Gemini 4 isn't even done cooking, so...

Elliptic curves are not generic. Long time coming. Congrats @crypto_theory and collaborators github.com/bochum-crypto/sub… What I said a week ago: It wouldn't surprise me in the least bit if there were a better factoring or discrete logarithm alg. For factoring: what is the chance that exp(n^1/3) is the right bound? who are we kidding? For discrete log over finite fields: better algorithms over Z_p have followed a decade or so behind those for small-char fields (Coppersmith'84 vs NFS a decade-ish later). Joux gave a quasi-poly alg over small-char fields in the 2010s. Porting to finite fields long overdue. For discrete log over elliptic curves: assuming that elliptic curve groups were "generic" is particularly preposterous given the rich structure they have. All of these ripe for disruption. Unstructured LPN would take me by real surprise, also unstructured LWE to a slightly lesser extent.

Spoooky Macchiato.

carbon

Formally verify SystemVerilog and SVA (or autoforamlized properties). Prove memory safety about your C programs. Prove a C model is equivalent to its SystemVerilog implementation. Our AI theorem prover is now publicly available. Try it out at harmonic.fun

Strange new world.

The question of information complexity of VC classes kept me busy for a year. In 2021, we made some progress: arxiv.org/abs/2111.05275 🎉 Now, it’s great to see Steve Hanneke and Juexiao Wang close the gap with a positive result in their FOCS ’26 paper: arxiv.org/abs/2610.10600

This bug was first found and fixed by Gemini Flash 3.7, and most experiments in the paper were done by Flash 3.8. Gemini 4 Argon wrote the first draft of the paper and figures, which I aggressively nitpicked until the content was solid but the writing was not. Then I fed Argon a handful of my first-author papers from the last few years and had it do a rewrite in my style (which worked astonishingly well), and then I manually did a rewrite (the hands + keyboard variety) after that. I really liked this workflow! If you like my writing style feel free to throw some of my old papers in your context window and do the same.

How many algorithms (that were discarded) actually work? If you have your algorithmic loves that didn’t pan out, time to go back and double check?

Beautiful new result in statistical learning theory and probability: arxiv.org/abs/2610.24336

If you'd like to come work with me and my amazing colleagues as a full-time researcher @MSFTResearch @MSRNE, please apply here: apply.careers.microsoft.com/… apply.careers.microsoft.com/…

Now for some well earned vacation.

1500W output(!) laser installation for the Frieze Art Show in Regents Park. Insane to see.

Today @GoogleResearch is launching Deep Review — an agentic system designed to stress-test manuscripts, design docs, and complex proposals before submission or publication. After pilot partnerships analyzing over 15,000 research papers, we’re making Deep Review globally accessible to help researchers, engineers, and professionals bring structured critique to their daily workflows.