Related papers: Solving a Research Problem in Mathematical Statist…
AI models like GPT-5 are an increasingly valuable tool for scientists, but many remain unaware of the capabilities of frontier AI. We present a collection of short case studies in which GPT-5 produced new, concrete steps in ongoing research…
Recent progress in large language models has made them increasingly capable research assistants in mathematics. Yet, as their reasoning abilities improve, evaluating their mathematical competence becomes increasingly challenging. The…
On August 20, 2025, GPT-5 was reported to have solved an open problem in convex optimization. Motivated by this episode, we conducted a controlled experiment in the Malliavin--Stein framework for central limit theorems. Our objective was to…
Recent announcements from frontier AI model labs have highlighted strong results on high-school and undergraduate math competitions. Yet it remains unclear whether large language models can solve new, simple conjectures in more advanced…
Can AI make progress on important, unsolved mathematical problems? Large language models are now capable of sophisticated mathematical and scientific reasoning, but whether they can perform novel research is still widely debated and…
Large language models (LLMs) have shown remarkable progress in coding and math problem-solving, but evaluation on advanced research-level problems in hard sciences remains scarce. To fill this gap, we present CMT-Benchmark, a dataset of 50…
Robust estimation is an important problem in statistics which aims at providing a reasonable estimator when the data-generating distribution lies within an appropriately defined ball around an uncontaminated distribution. Although minimax…
We describe a general technique that yields the first {\em Statistical Query lower bounds} for a range of fundamental high-dimensional learning problems involving Gaussian distributions. Our main results are for the problems of (1) learning…
Large language models (LLMs) have recently achieved remarkable success in generating rigorous mathematical proofs, with "AI for Math" emerging as a vibrant field of research (Ju et al., 2026). While these models have mastered…
We study nonparametric density estimation problems where error is measured in the Wasserstein distance, a metric on probability distributions popular in many areas of statistics and machine learning. We give the first minimax-optimal rates…
Algorithmic robust statistics has traditionally focused on the contamination model where a small fraction of the samples are arbitrarily corrupted. We consider a recent contamination model that combines two kinds of corruptions: (i) small…
As the mathematical capabilities of large language models (LLMs) improve, it becomes increasingly important to evaluate their performance on research-level tasks at the frontier of mathematical knowledge. However, existing benchmarks are…
Contaminations are a key concern in modern statistical learning, as small but systematic perturbations of all datapoints can substantially alter estimation results. Here, we study Wasserstein-$r$ contaminations ($r\ge 1$) in an $\ell_q$…
Machine learning-based automatic scoring faces challenges with unbalanced student responses across scoring categories. To address this, we introduce a novel text data augmentation framework leveraging GPT-4, a generative large language…
With the significant expansion of the context window in Large Language Models (LLMs), these models are theoretically capable of processing millions of tokens in a single pass. However, research indicates a significant gap between this…
Real-time flood forecasting is vital for effective emergency responses, but bridging the gap between complex numerical models and practical decision-making remains challenging. Decision-makers often rely on experts, while the public…
During 2024 and 2025 the discussion about the theorem-proving capabilities of large language models started reporting interesting success stories, mostly to do with difficult exercises (such as problems from the International Mathematical…
We propose a generative model that achieves minimax-optimal convergence rates for estimating probability distributions supported on unknown low-dimensional manifolds. Building on Fefferman's solution to the geometric Whitney problem, our…
We propose a hybrid resampling method to approximate finitely supported Wasserstein barycenters on large-scale datasets, which can be combined with any exact solver. Nonasymptotic bounds on the expected error of the objective value as well…
We give new results for problems in computational and statistical machine learning using tools from high-dimensional geometry and probability. We break up our treatment into two parts. In Part I, we focus on computational considerations in…