Dan Roy

Just some personal thoughts now that the AI co-mathematician tech report is public... First, I'm so excited to see the co-mathematician team's hard work out for the world to preview. 💪+🦾=🔥 The team has built a system for mathematicians, with mathematicians. The fact it's now top of the FrontierMath leaderboard is a cherry on top, not the goal. Vibes and utility >> benchmarks. The system is currently being tested with a small number of professional mathematicians. It is not widely available, but I personally hope that, one day, we can get even more capable systems into the hands of all mathematicians. It's been a privilege working with this team at Google DeepMind since January. Props to @dhhzheng, @ADaviesAI, and @pushmeet for their leadership. Give them all a follow to not miss exciting upcoming work.

When we started the podcast, we wanted a place to share our own opinions about AI, so we decided to record an episode every two weeks. Then we said, let's bring on some guests - so we went weekly. But then we realized we still wanted time to say what we think about AI, so we added a special no-guest episode once in a while. Somehow, today we're at two episodes per week, with guests in each one. I really don't have time for a third 😬

Today I messaged someone to ask if he wants to be on the podcast. After 3 minutes, he responded with a yes and a link to his calendar. Be this person

Back from ICML and brimming with new ideas and a new profile photo so people can actually recognize me in person ;-)

@SebastienBubeck @brianryhuang Rereading your post, I realize I misunderstood that the last set of improvements are also unpublished. Nice progress indeed!

@roydanroy @brianryhuang I do not understand the question, can you rephrase it?

@__eknight__ No chain of thought? 😉

You can find the proof here: cdn.openai.com/pdf/04d1d1e4-b… And the full text of the prompt used to produce the proof here: cdn.openai.com/pdf/04d1d1e4-b…

Yesterday, we made GPT-5.6 Sol Ultra generally available. Today, we're sharing that it produced a proof of the 50-year-old Cycle Double Cover Conjecture using 64 subagents in just under one hour. We're sharing the prompt and proof below. We're excited to see what you all do with Ultra!

@jasondeanlee Are you on a shitty bandit arm in some OpenAI experiment?

Tried this and burned through subscription in about 2 minutes

J-space is really something we have been exploring since 2022. Glad to see it continues to work well at scale! Some of the related work along this direction: - How to recover the latent process using Jacobians (Identifiability of nonlinear ICA): arxiv.org/pdf/2206.07751 - How to handle dependent latents and assumption violations (again, through Jacobians): arxiv.org/pdf/2311.00866 - For general latent variable models, what remains recoverable with guarantees, and why Jacobians are universally helpful? (We could generalize SAEs to the general nonlinear case, with Jacobians!): arxiv.org/pdf/2604.17568 Feels like we're still only beginning to uncover what Jacobian structure can tell us about representations.

Nice theory for an empirical phenomenon.

Fascinating finding. I hear there are antecedents in the literature and I’m glad I now know about this line of work.

my paper won an award at icml 😁 some thoughts: • this work was rejected from NeurIPS. i cleaned it up a small amount and it got great reviews from ICML! don't give up • ICML received 24k submissions and only gives out 7 awards, which is crazy. feeling grateful • i distinctly remember sitting at my desk two winters ago wondering if i would ever finish this project. most of all this is the product of sitting down and forcing myself to keep working for several months straight. the results emerged from running the experiments over and over and fixing a long sequence of tiny details. eventually, the curves looked like that 👇 • also happy that the insights in this paper are becoming more widely accepted: 3.3 bits/param, thinking about capacity "LLM as flashdrive" mentality • the method here is used successfully for selecting midtraining data at least one frontier lab, which is cool! • i am grateful to my collaborators, but Meta is no longer a great place for academic research imo and this almost never got published for a number of reasons. i shall not elaborate further • for future work, i think analyzing the implications of on-policy algorithms on capacity, as well as LoRA and things like it, are fruitful potential research directions • sadly i'm not in Korea but am following the conference online from california and happy to chat! a nice end to one phase of my research career :)

So much interesting work. Got through only 20% of the poster session.

This is the right setting to study unlearning just as it is the right setting to study privacy.

How does public data affect unlearning guarantees? Come find out RIGHT NOW in HALL A #3110 (10:30 AM) "Unlearning with Asymmetric Sources: Improved Unlearning-Utility Trade-off with Public Data," Can't come? Enjoy this ICML'26 Seoul🇰🇷 tweet 🧵...

Arrived into Seoul. If you see me, say hi!

@konstmish Would be cleaner to state this in terms of the language of adaption theory.

The gaps between upper and lower bounds for something as basic as deterministic gradient descent with no momentum are still pretty wide. Basically we still don't know what can be achieved by choosing the stepsizes optimally.

@max_simchowitz Serious conflict of interest potential. Would nearly all of my students have become faculty?

pro or con: frontier labs who hire a phd student should pay the student’s advisor commission for their mentorship 🙃

@prfsanjeevarora 👀

This is not impressive compared to current models on the leaderboard trishullab.github.io/PutnamBench/le…

@jalajupadhyay @kasperglarsen Where will you spend your retirement?

A beautiful result just dropped. I often joked that they day someone resolved this problem, I will retire from DP. Guess, it is time :) Congratulations to @kasperglarsen and Konstantina! arxiv.org/abs/2607.00876

@tejasdkulkarni Jealous I’m away for the launch of the new building. How’s it!??

Summer vibes at DeepMind in London