This paper made me smile a lot while working on it, so I want to share a bit about it arxiv.org/abs/2405.09676. We draw a parallel story to the Eckart-Young Theorem (from numerical analysis) in stochastic optimization/learning problems. (with Josh Cutler and Dima Drusvyatskiy)

Today, we share a breakthrough on the planar unit distance problem, a famous open question first posed by Paul Erdős in 1946. For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids. An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better. This marks the first time AI has autonomously solved a prominent open problem central to a field of mathematics.

New paper studies when spectral gradient methods (e.g., Muon) help in deep learning: 1. We identify a pervasive form of ill-conditioning in DL: post-activations matrices are low-stable rank. 2. We then explain why spectral methods can perform well despite this. Long thread

NEW PAPER ALERT 📢 Score-based diffusion models are powerful—but slow to sample. Could there be something better? Drop the scores, use proximals instead! We present Proximal Diffusion Models (ProxDM), a faster alternative both in theory* and practice. Here’s how it works 🧵(1/n)

🚨 New Textbook on Conformal Prediction 🚨 arxiv.org/abs/2411.11824 “The goal of this book is to teach the reader about the fundamental technical arguments that arise when researching conformal prediction and related questions in distribution-free inference. Many of these proof strategies, especially the more recent ones, are scattered among research papers, making it difficult for researchers to understand where to look, which results are important, and how exactly the proofs work. We hope to bridge this gap by curating what we believe to be some of the most important results in the literature and presenting their proofs in a unified language, with illustrations, and with an eye towards pedagogy.” We are looking for feedback — and this is only a draft, with Part 4 coming soon! Please reach out! With Rina Foygel Barber and @stats_stephen