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Bridging the Gap Between Homogeneous and Heterogeneous Asynchronous Optimization Is Surprisingly Difficult

Lower bounds show heterogeneous asynchronous optimization cannot match homogeneous rates under standard similarity assumptions; strong interpolation plus local PL condition closes the gap.

The paper examines whether pessimistic optimal time complexities for asynchronous distributed optimization with heterogeneous workers (different data distributions) can be overcome. It proves improvement is provably impossible under widely used first- and second-order similarity assumptions for any randomized algorithm, and that the weak interpolation assumption alone is also insufficient. Combining strong interpolation with the local Polyak-Lojasiewicz condition yields a new time complexity bound matching the best-known homogeneous dependence on worker computation times without requiring identical data distributions.

arXiv cs.AI / cs.LG / cs.CLSep 15, 17:24 UTC · 1d agoAI research

Unsolved Problem by Fields Medalist Breached by Two High School Students

Two high school students used Claude Opus 5 and GPT-5.6 Sol to help solve an open Lorentzian polynomials problem, posting a 75-page arXiv proof.

Aayush Bathija and Prince Rohatgi of Oak Park High School, mentored by UCLA postdoc Daniel Soskin, published the 75-page paper 'Bounded Ratios for Lorentzian Polynomials' (arXiv 2609.05341), solving an open problem in Fields Medalist June Huh's Lorentzian polynomial theory. The main structural theorem extends bounded coefficient-ratio characterization from quadratic to arbitrary-degree polynomials via discrete convexity conditions. The students used Claude Opus 5 and GPT-5.6 Sol for exploration and proof ideas but independently verified all arguments; the result follows an open letter from 25 Fields Medalists voicing concerns about AI's impact on mathematical rigor.

Hacker News · securitySep 14, 12:23 UTC · 2d agoAI research HN 22↑ · 19 comments

Why don't machine learning research agents overfit?

Amazon researchers explain why ML research agents avoid benchmark overfitting, attributing generalization to compressibility of successful strategies.

Amazon Science summarizes the paper "What fits (into few tokens) doesn't overfit: Compression and generalization in ML research agents," which investigates why benchmark hill-climbing loops, whether run by human communities or LLM research agents, do not produce rampant overfitting. The explanation formalizes Occam's razor via a counting argument: successful ML strategies are highly compressible, so short descriptions lack room to memorize benchmark data and must capture real structure. LLM-based agents, being resettable and controllable, allow this hypothesis to be tested empirically.

Hacker News · securitySep 14, 16:32 UTC · 2d agoAI research HN 21↑ · 3 comments