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100% agree on the productivity boost. One just needs patience to correct mistakes, which are more subtle than before imo.
I had a nice interaction with GPT-5-pro while proving a convex analysis lemma: arxiv.org/abs/2510.26647
The model didn’t write the full proof, but the ting enough for me to write a short report about it. The report illustrates both the productivity gain and the need for careful proof-checking. The model’s contributions are in blue, and the full chat is in the Appendix. You will see my prompts and how I think, so, no judgement please :)
The problem itself has an history in optimal transport (see intro) and comes from a question I was discussing with some UCLA math professors last summer. Simpler than @ErnestRyu's recent result imo, but still very useful in optimal transport!
I had a nice interaction with GPT-5-pro while proving a convex analysis lemma: arxiv.org/abs/2510.26647
The model didn’t write the full proof, but the ting enough for me to write a short report about it. The report illustrates both the productivity gain and the need for careful proof-checking. The model’s contributions are in blue, and the full chat is in the Appendix. You will see my prompts and how I think, so, no judgement please :)
The problem itself has an history in optimal transport (see intro) and comes from a question I was discussing with some UCLA math professors last summer. Simpler than @ErnestRyu's recent result imo, but still very useful in optimal transport!
Totally agree with @ErnestRyu that AI helpers will become very useful for research. But in the near future the biggest help will be with *informal* math, the kind we work out with our collaborators/grad students on a whiteboard. I already use frontier models to help write/debug lemmas for my papers and lectures. AI is fast, but can also misunderstand. So have to still carefully check the lemma statements and proofs. But already a big productivity boost. (Lean provers will automate the proof checking, but the human will still need to check that the lean formalization accurately captures their intent, which humans will be doing for a while.)
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Adil Salim retweeted
🚨 Thrilled to be co-organizing a Simons Institute semester-long program on diffusions and flows with @joanbruna, Sinho Chewi, @KonstDaskalakis, @ArnaudDoucet1 in Fall '27!
The call for Simons postdoctoral research fellowships for the program is out now, more info below ⬇️ 1/3
The call for Simons postdoctoral research fellowships for the program is out now, more info below ⬇️ 1/3
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Adil Salim retweeted
KLS conjecture is true:
link to paper (in arxiv tomorrow (hopefully)): github.com/kriznakumar/pa…
link to a worked out example: kriznakumar.github.io/blog/
Joint work with Shiva Kasiviswanathan (@kasivisw18)
link to paper (in arxiv tomorrow (hopefully)): github.com/kriznakumar/pa…
link to a worked out example: kriznakumar.github.io/blog/
Joint work with Shiva Kasiviswanathan (@kasivisw18)
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Okay here is another (certainly less dramatic) "concurrent efforts" story about @icmlconf 2026 outstanding paper awards.
Peter’s post below refers to our ICML paper with Khashayar and @sitanch. He raised this point because another ICML paper, “High-accuracy sampling for diffusion models and log-concave distributions” by Chen et al., which independently and concurrently established a result similar to ours, received an Outstanding Paper Award.
The story starts on January 15, when we uploaded a paper to arxiv achieving high-accuracy (polylog(1/ε)) complexity for diffusion models.
Since Chen et al. are colleagues, they reached out shortly after: "We will soon upload a paper to arXiv with a similar high-accuracy result."
We discussed the relationship between the two works and agreed that the papers should be described as concurrent and independent.
So they added a section to their paper acknowledging that the two works are indeed concurrent and independent, and then uploaded their paper to arXiv.
Then, both papers were submitted to ICML 2026, received identical scores on OpenReview, and were accepted as oral presentations.
Chen et al. also received an outstanding paper award for "settling a long-standing conjecture in the theory of score-based sampling" (see the ICML award blog post), namely achieving high-accuracy sampling for diffusion models. Congrats to them! This award is well deserved imo, and their solution is quite elegant.
At ICML in Seoul, I was asked several times, "Why didn't your paper also receive the same recognition, since both papers resolved the conjecture independently?"
That's why one of the godfathers of our community (not @peter_richtarik) reached out to the committee to ask for the VAR 😂
I will paraphrase the committee's reply because those emails are private. Essentially, they said that it was unfortunate if there had been an omission, but that they could not revisit the decision because the selection process was too complex...
Which I understand, since they chose 2 papers out of 6,000+. On the other hand, I hope we can find a way to prevent situations like this from happening again.
Peter’s post below refers to our ICML paper with Khashayar and @sitanch. He raised this point because another ICML paper, “High-accuracy sampling for diffusion models and log-concave distributions” by Chen et al., which independently and concurrently established a result similar to ours, received an Outstanding Paper Award.
The story starts on January 15, when we uploaded a paper to arxiv achieving high-accuracy (polylog(1/ε)) complexity for diffusion models.
Since Chen et al. are colleagues, they reached out shortly after: "We will soon upload a paper to arXiv with a similar high-accuracy result."
We discussed the relationship between the two works and agreed that the papers should be described as concurrent and independent.
So they added a section to their paper acknowledging that the two works are indeed concurrent and independent, and then uploaded their paper to arXiv.
Then, both papers were submitted to ICML 2026, received identical scores on OpenReview, and were accepted as oral presentations.
Chen et al. also received an outstanding paper award for "settling a long-standing conjecture in the theory of score-based sampling" (see the ICML award blog post), namely achieving high-accuracy sampling for diffusion models. Congrats to them! This award is well deserved imo, and their solution is quite elegant.
At ICML in Seoul, I was asked several times, "Why didn't your paper also receive the same recognition, since both papers resolved the conjecture independently?"
That's why one of the godfathers of our community (not @peter_richtarik) reached out to the committee to ask for the VAR 😂
I will paraphrase the committee's reply because those emails are private. Essentially, they said that it was unfortunate if there had been an omission, but that they could not revisit the decision because the selection process was too complex...
Which I understand, since they chose 2 papers out of 6,000+. On the other hand, I hope we can find a way to prevent situations like this from happening again.
This paper should have received the ICML 2026 best paper prize (alongside the other two that did). I am serious.
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Adil Salim retweeted
yes, nonsofic groups exist: this statement is one of many new beautiful results proved by Astra, our next major model.
We're releasing 10 such Astra proofs, complete with lean certificates and CoT walkthroughs for each of them. The results are wide-ranging, from von Neumann algebras (disproof of Connes' Rigidity Conjecture) to better bounds for high dimensional sphere packing, for circuit complexity, for monochromatic triangles in multicolored graphs, and more.
More thoughts here: openai.com/index/ten-adva…
We're releasing 10 such Astra proofs, complete with lean certificates and CoT walkthroughs for each of them. The results are wide-ranging, from von Neumann algebras (disproof of Connes' Rigidity Conjecture) to better bounds for high dimensional sphere packing, for circuit complexity, for monochromatic triangles in multicolored graphs, and more.
More thoughts here: openai.com/index/ten-adva…
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Adil Salim retweeted
Nesterov wins the Carl Friedrich Gauss Prize 2026
mathunion.org/imu-awards/car…
The Gauss Prize is awarded to Yurii Nesterov for his groundbreaking work on mathematical optimization that provided the theoretical foundation and algorithmic backbone for many numerical and data-driven cal computations that were previously too time-consuming to be feasible.
mathunion.org/imu-awards/car…
The Gauss Prize is awarded to Yurii Nesterov for his groundbreaking work on mathematical optimization that provided the theoretical foundation and algorithmic backbone for many numerical and data-driven cal computations that were previously too time-consuming to be feasible.
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Nice @AdenIshaq!!
A unique experience in mathematics is being told that one has carried the "wrong perspective" on one's own work. GPT 5.5, prompted by Ishaq Aden-Ali, just resolved a very well-known open problem in discrepancy theory of giving an optimal bound of oblivious online vector balancing "quickly". (1/4)
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Adil Salim retweeted
hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend fable for working during the world cup final
((1+xy)^3 z + y^2 (1+xy) (4+3xy), y + 3 x (1+xy)^2 z + 3 x y^2 (4+3xy), 2 x - 3 x^2 y - x^3 z): \C^3\to \C^3, has jacobian determinant -2, and sends (0, 0, -1/4), (1, -3/2, 13/2), and (-1, 3/2, 13/2) to (-1/4, 0, 0)
((1+xy)^3 z + y^2 (1+xy) (4+3xy), y + 3 x (1+xy)^2 z + 3 x y^2 (4+3xy), 2 x - 3 x^2 y - x^3 z): \C^3\to \C^3, has jacobian determinant -2, and sends (0, 0, -1/4), (1, -3/2, 13/2), and (-1, 3/2, 13/2) to (-1/4, 0, 0)
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Today at #ICML 2026, I'll be presenting our paper on score-based sampling that achieves both high-accuracy and dimension-free guarantees.
ORAL
Wed, Jul 8, 2026 • 10:30–10:45 AM KST • Hall C
POSTER
Wed, Jul 8, 2026 • 2:30–4:15 PM KST • Hall A #2507
Please join us if you're around!
ORAL
Wed, Jul 8, 2026 • 10:30–10:45 AM KST • Hall C
POSTER
Wed, Jul 8, 2026 • 2:30–4:15 PM KST • Hall A #2507
Please join us if you're around!
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Adil Salim retweeted
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 :)
arxiv.org/pdf/1912.13213
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 :)
arxiv.org/pdf/1912.13213
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Adil Salim retweeted
So, I tried ChatGPT.
But ChatGPT 5.5 Pro failed, no matter what I tried.
So, I used a different strategy: I wrote a pdf with everything I knew about this problem, including results that were not immediately useful, and told ChatGPT to complete the proof. This time it worked!
But ChatGPT 5.5 Pro failed, no matter what I tried.
So, I used a different strategy: I wrote a pdf with everything I knew about this problem, including results that were not immediately useful, and told ChatGPT to complete the proof. This time it worked!
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Adil Salim retweeted
ChatGPT solved an optimization problem that puzzled me for a very long time. Back in summer 2020, I started to work with coauthors on algorithms for optimal transport. We then invented a very simple and elegant algorithm: Bregman Douglas-Rachford splitting method (BDRS).
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Very elegant
Imagine that projected gradient descent (PGD) was a new method, discovered today. How would that feel? This is a textbook algorithm... What further research, extensions, improvements and variants would this enable?
In fact, together with Kaja Gruntkowska and Hanmin Li, we have r method to projected gradient descent -- one of equal conceptual importance.
Our method admits the same or very similar guarantees as PGD. However, instead of relying on projections onto the constraint, it relies on linear minimization!
You may say: Did you rediscover Frank-Wolfe?
No.
In contrast to Frank-Wolfe, which uses a global linear minimization oracle (global LMO), our method relies on a local minimization oracle (local LMO). For this reason, we simply call the method "Local LMO" (admittedly, conflating the oracle name with the method name).
Frank-Wolfe theory is much more limited to the theory of Local LMO. Here are some key differences:
1) Frank-Wolfe only works if the constraint is bounded, and its convergence theory depends in the diameter of the constraint set. Local LMO works even for unbounded constraints, and its theory does not depend on the diameter of the constraint set.
2) In fact, Local LMO reduces to gradient descent (GD) in the unconstrained case. If the constraint is affine, Local LMO reduces to (preconditioned) GD in the affine space.
3) While Frank-Wolfe does not converge linearly for smooth strongly convex functions, Local LMO does.
4) While Frank-Wolfe does not converge for non-smooth convex problems (its theory depends on a curvature assumption), Local LMO does.
arxiv.org/abs/2605.08850
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Adil Salim retweeted
🎉 Applications are open for MLSS 2026 — the 50th edition of the Machine Learning Summer School!
Join us in Tübingen for world-class lectures, hands-on sessions, and an amazing ML community. 🧠
Apply now 👉 mlss2026.is.tuebingen.mpg.de
#MLSS2026 #MachineLearning #SummerSchool #ML
Join us in Tübingen for world-class lectures, hands-on sessions, and an amazing ML community. 🧠
Apply now 👉 mlss2026.is.tuebingen.mpg.de
#MLSS2026 #MachineLearning #SummerSchool #ML
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Adil Salim retweeted
We'll be organizing the Machine Learning Summer School in Tübingen to be held Aug 31st-Sept 11th, featuring top speakers across academia and industry. If you are a student or ML researcher, save those dates and stay tuned for updates! 🚀
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Adil Salim retweeted
Following my visit last month, I've just arrived to Berkeley again!
At 9:30am PT today, I am giving the opening keynote talk at the Simons Institute workshop "Learning from Heterogeneous Sources".
simons.berkeley.edu/workshops/lear…
Title of my talk: "From the Ball-proximal (Broximal) nt Training of LLM". Abstract: simons.berkeley.edu/talks/peter-ri…
During my February visit, I gave a tutorial on "Federated Optimization" at the "Federated and Collaborative Learning Boot Camp". Recordings of my lectures are available on the Simons Institute YouTube channel:
Part 1: youtube.com/live/WcHUu08CL…
Part 2: simons.berkeley.edu/talks/peter-ri…
Part 3: youtube.com/live/oT02lHX6s…
At 9:30am PT today, I am giving the opening keynote talk at the Simons Institute workshop "Learning from Heterogeneous Sources".
simons.berkeley.edu/workshops/lear…
Title of my talk: "From the Ball-proximal (Broximal) nt Training of LLM". Abstract: simons.berkeley.edu/talks/peter-ri…
During my February visit, I gave a tutorial on "Federated Optimization" at the "Federated and Collaborative Learning Boot Camp". Recordings of my lectures are available on the Simons Institute YouTube channel:
Part 1: youtube.com/live/WcHUu08CL…
Part 2: simons.berkeley.edu/talks/peter-ri…
Part 3: youtube.com/live/oT02lHX6s…
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📢New paper out!
We propose an inference algorithm for diffusion models that does not explicitly depend on the ambient dimension and converges exponentially fast. That’s because, unlike most of the competition, we solve the reverse ODE via Picard and not via Euler discretization
We propose an inference algorithm for diffusion models that does not explicitly depend on the ambient dimension and converges exponentially fast. That’s because, unlike most of the competition, we solve the reverse ODE via Picard and not via Euler discretization
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Kudos to Khashayar Gatmiry who led this project (that was part of his 2024 internship at MSR) and to @sitanch
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