Aaron Roth

Aaron Roth

@aaroth.bsky.social

Professor at Penn, Amazon Scholar at AWS. Interested in machine learning, uncertainty quantification, game theory, privacy, fairness, and most of the intersections therein

4.4K followers392 following480 posts

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It was fun giving this tutorial. If you missed it, check out calibration-tutorial.github.io where all of our materials are available, including slides, hundreds of pages of lecture notes, an interactive demo, and an annotated reading list.

Aaron Roth@aaroth.bsky.social

On Monday @ncollina.bsky.social @iraglobusharris.bsky.social and I are giving a tutorial at ICML on (multi)calibration and its applications. You can find slides and an annotated bibliography on the website: calibration-tutorial.github.io as well as an interactive demo of online calibration algs.

Aaron Roth reposted

The #FORC2027 Call for Papers is up! Submit your best work on the foundations of responsible computing, including, e.g., privacy, robustness, fairness, and (for the first time!) safety and alignment! First deadline: November 11 Conf: June 2-4 at Stanford responsiblecomputing.org/forc-2027-ca...

responsiblecomputing.orgFORC 2027: Call for PapersA call for papers for the 8th annual Symposium on Foundations of Responsible Computing.

Aaron Roth reposted

Anthropic system prompt change that shows how careful you need to be with words: Opus 4.1: "Claude never curses unless the human asks for it" Opus 4.5: "Claude never curses unless the person asks Claude to curse"

There are two papers we decided to submit to journals rather than ICLR to avoid the anticipated mess of this years review process. (But last time we submitted something to a Journal - GEB - the review process took so long that the journal collapsed before we ever got a decision)

An annoying part of the twitter/bluesky discussion of whether LLMs are "only" "next token predictor"/stochastic parrots is that "next token predictor" is contentless - all mappings from inputs to output strings can be factored into a sequence of "next token" distributions.

In this sense you, or any other system that can output text can be written as a "next token predictor". This isn't making any statement about whether brains function similarly to LLMs or not at an internal level, its just a boring syntactic fact about probability distributions.

The interesting question a decade ago about representing output distributions as next token distributions was computational: maybe this would introduce computational difficulties that would make it hard to learn useful behaviors. It turned out it didn't (at least given what was spent)!

AI tools are very useful for mathematical research. But at present, producing good work requires a labor intensive step that I have been calling "deslopping" - making the thing readable. Please do not skip this step; even if the theorem is great an unreadable paper is worthless.

Codex and Claude Code have a neat auto approve feature where 1) it doesn't ask for permissions, but 2) you get to feel safe. Well --- do you? The premise is it is asking an agent for permission. But if you don't trust the driver agent, why should you trust the review agent?

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But despite being weaker it is not guaranteed to be satisfied. Still, we find some preliminary evidence of non-trivial safety/completeness tradeoffs among real reward models, and these effects come from coallitional rather than individual alignment.

Codex and Claude Code have a neat auto approve feature where 1) it doesn't ask for permissions, but 2) you get to feel safe. Well --- do you? The premise is it is asking an agent for permission. But if you don't trust the driver agent, why should you trust the review agent?

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What about strategic agents? Let both the driver agent and the reviewers be fully strategic and optimizing for their long run discounted payoff. Under the same non-negative span condition, every Nash equilibrium of the game is safe for the Principal--i.e. no worse than baseline.

We call this condition "coalitional alignment" -- it is very similar to the market alignment condition that drives our earlier work: arxiv.org/abs/2509.15090 It is a substantially weaker condition than individual alignment (That the reviewer agents have your utility exactly)

arxiv.orgEmergent Alignment via CompetitionAligning AI systems with human values remains a fundamental challenge, but does our inability to create perfectly aligned models preclude obtaining the benefits of alignment? We study a strategic sett...

Codex and Claude Code have a neat auto approve feature where 1) it doesn't ask for permissions, but 2) you get to feel safe. Well --- do you? The premise is it is asking an agent for permission. But if you don't trust the driver agent, why should you trust the review agent?

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There is a remarkably clean characterization of when you can. We start with a simple one-decision model. A system is safe if and only if the Principal's utility is in the non-negative span of the reviewer's utilities. The forward direction is elementary; backwards is LP duality.

What about long running agents? We study an MDP model where utilities depend on action and state and actions change state. We again get a characterization The performance difference identity lets us lift the one-shot conic-hull characterization (on Q values) to the full MDP.

Codex and Claude Code have a neat auto approve feature where 1) it doesn't ask for permissions, but 2) you get to feel safe. Well --- do you? The premise is it is asking an agent for permission. But if you don't trust the driver agent, why should you trust the review agent?

We study this and model both you (the principal) and the reviewer agent(s) as having utility functions you are trying to maximize. The driver agent repeatedly proposes actions. The reviewer agents compare them to a baseline and vote to approve or deny based on perceived utility.

The difficulty is reviewer agents are misaligned - their utility functions differ from yours. Can you still guarantee that the system is safe, even with an arbitrary driver agent? Safe means that principal utility is guaranteed to be no worse than following the baseline policy.

A world without open problems Here are some that fell today: K-server: arxiv.org/abs/2609.15979 Matroid Secretary: arxiv.org/abs/2609.145... Matrix Spencer: arxiv.org/abs/2609.15025 (Well Matrix Spencer was maybe also a few weeks ago, but who's counting? arxiv.org/abs/2608.28816 )

arxiv.orgThe $k$-server conjecture is trueThe $k$-server conjecture states that a deterministic online algorithm can achieve competitive ratio $k$ on every metric space. We prove the conjecture. Specifically, we show that the work function al...
Aaron Roth@aaroth.bsky.social

So we are clearly moving to a world that will be without open problems, but this doesn't mean math is going away. Interesting work will correspond to discovering new questions and coherent theoretical frameworks. Well defined agreed-to-be-interesting problems won't last long.

I sometimes see people trying to use complexity theory to argue that building "true" AI is impossible. I find this unreasonably annoying. It requires ignoring what is in front of your face and it ignores that worst-case complexity has been an awful guide in machine learning.

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Applying this kind of argument to more general intelligence would have been wrong a decade ago but now requires ignoring the obvious success of AI and particularly the reasoning models from the last few years. A decade ago we could have said it denies computationalism:

i.e. that the laws of computation bind human cognition just as much as they bind silicon. This is merely a conjecture --- maybe its not true and we have some non-computational secret sauce. But now making this argument requires ignoring evidence in silico (and in browser tab)

I sometimes see people trying to use complexity theory to argue that building "true" AI is impossible. I find this unreasonably annoying. It requires ignoring what is in front of your face and it ignores that worst-case complexity has been an awful guide in machine learning.

For example, the simplest problem in machine learning - learning a linear classifier to minimize classification error --is NP hard even to approximate (to distinguish the ability to get 51% accuracy from 99% accuracy). epubs.siam.org/doi/10.1137/... and thus everything more general too.

epubs.siam.orgHardness of Learning Halfspaces with Noise | SIAM Journal on ComputingLearning an unknown halfspace (also called a perceptron) from labeled examples is one of the classic problems in machine learning. In the noise-free case, when a halfspace consistent with all the trai...

But of course this has been no obstacle to solving almost every real-world statistical learning problem of this sort. The model of worst-case complexity is elegant but turns out to be a poor guide for what is possible (or even easy and reliable) on naturally occuring problems.

Aaron Roth reposted

Years of iterating against the same benchmarks should, by textbook logic, produce overfitting. It largely doesn't. New research explains why: strategies that generalize can be expressed in too compact a form to allow memorization, while the ones that overfit don't survive a compression.

amazon.scienceWhy don’t machine learning research agents overfit?New research indicates that AI agents learn compressible models of data, which don’t have enough space to enable memorization.

We have a new online boosting algorithm which is very efficient and effective. Unlike prior algorithms which maintain many weak learners and ensemble them, we operationalize the "dual view" of boosting. We don't maintain an ensemble. We try to construct an online hard core distribution.

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In the end we're putting a bunch of existing pieces together. The fact that multiaccuracy implies weights for a hard core distribution was noticed by @sicapu.bsky.social , Dwork, and Vadhan. Lots of good prior work gave online adversarial algorithms for multiaccuracy and related notions.

We have a new online boosting algorithm which is very efficient and effective. Unlike prior algorithms which maintain many weak learners and ensemble them, we operationalize the "dual view" of boosting. We don't maintain an ensemble. We try to construct an online hard core distribution.

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So we get two incomparable boosting guarantees in one. And the algorithm works well, matching or beating the best comparator on real and synthetic datasets. Since we don't maintain an ensemble we run ~ 50x faster than these competitor algorithms as well.

Online learning tricks let us make this guarantee adaptive - i.e. we get the boosting guarantee on every sub-interval on which the weak learning condition holds, even if it doesn't on others. This works through an adaptive version of a hard core distribution which seems like an interesting object.

We have a new online boosting algorithm which is very efficient and effective. Unlike prior algorithms which maintain many weak learners and ensemble them, we operationalize the "dual view" of boosting. We don't maintain an ensemble. We try to construct an online hard core distribution.

We make probabilistic forecasts that are multiaccurate with respect to the weak class---i.e. with residuals orthogonal to the weak class. If we have high error, then ex-post transcript reweighting by our own residual error gives a smooth distribution on which no weak learner has non-trivial edge.

The weak learning assumption is that there is no such distribution - so if it holds, by contrapositive, our error was low. Adding one more orthogonality condition also lets us compete with any predictor in the span of the weak class - the usual gradient boosting guarantee.

People used to be able to impress and intimidate reviewers with complicated proofs. This will change. In the age of AI inscrutable proofs are cheap. It is understandable proofs that are valuable. Opaque complexity is now it is a sign of laziness or lack of insight.

Aaron Roth reposted

"We're all worried," as what it means to do research (in my field, Theoretical CS) seems to be shifting, and shifting fast. What to do? Senior researchers must lead by example, knowing that not everything will pan out. What I'm suggesting below may not work everywhere, but here's my own advice: 1/

Right now we have "problem overhang" - lots of problems we as a community are interested in because smart and charismatic people thought about them and convinced us that these problems are important. So we are happy/interested to see them solved by AI.

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Could it be that once AI models exhaust the overhang of existing problems we care about, no new such problems emerge? There will be plenty of true statements with difficult proofs, but we may stop caring about (any of) them.

So we are clearly moving to a world that will be without open problems, but this doesn't mean math is going away. Interesting work will correspond to discovering new questions and coherent theoretical frameworks. Well defined agreed-to-be-interesting problems won't last long.

Right now we have "problem overhang" - lots of problems we as a community are interested in because smart and charismatic people thought about them and convinced us that these problems are important. So we are happy/interested to see them solved by AI.

But as we move to a world in which well defined "open problems" are solved by AI, will we find new problems that we as a community care about? We don't care about most true statements, even if they are difficult to prove. The process of agreeing on interesting problems is social.

Aaron Roth reposted

I've been referring people to this perspective every day for the last couple weeks. As we work together to determine new norms, we should not tolerate pure AI or otherwise bad writing. Tell your friends if they fall into this trap.

Aaron Roth@aaroth.bsky.social

AI is getting good at math. What are our jobs as researchers now that we have proof machines? The raw proofs that come from LLMs are difficult to understand, even if correct. So its now easy to quickly write many badly written papers that nevertheless contain correct proofs of interesting theorems.

Aaron Roth reposted

Reminder, this is in a few hours!! j o i n u s

Aaron Roth@aaroth.bsky.social

On Monday @ncollina.bsky.social @iraglobusharris.bsky.social and I are giving a tutorial at ICML on (multi)calibration and its applications. You can find slides and an annotated bibliography on the website: calibration-tutorial.github.io as well as an interactive demo of online calibration algs.