From the 1 of 5 linked papers with an AI index.
5 papers
Random sets are close to low-discrepancy sets
Gleb Smirnov, Roman Vershynin
The paper proves that a random sample from any probability distribution in ℝⁿ can be slightly adjusted to become a low‑discrepancy point set with star discrepancy roughly polylog(n…
Thinning to improve two-sample discrepancy
Gleb Smirnov, Roman Vershynin
The discrepancy between two independent samples \(X_1,\dots,X_n\) and \(Y_1,\dots,Y_n\) drawn from the same distribution on typically has order \(O(\sqrt{n})\) even…
On the Dimension-Free Concentration of Simple Tensors via Matrix Deviation
Pedro Abdalla, Roman Vershynin
We provide a simpler proof of a sharp concentration inequality for subgaussian simple tensors obtained recently by Al-Ghattas, Chen and Sanz-Alonso. Our approach uses a matrix devi…
Improving discrepancy by moving a few points
Gleb Smirnov, Roman Vershynin
We show how to improve the discrepancy of an iid sample by moving only a few points. Specifically, modifying \( O(m) \) sample points on average reduces the Kolmogorov-Smirnov dist…
LLM Watermarking Using Mixtures and Statistical-to-Computational Gaps
Pedro Abdalla, Roman Vershynin
Given a text, can we determine whether it was generated by a large language model (LLM) or by a human? A widely studied approach to this problem is watermarking. We propose an unde…