This paper introduces a novel algorithm for generating k Hamming weight binary words in linear time while minimizing random bit consumption.

This paper settles the complexity of three sketching problems in graphs and distributions.

The paper provides a tight, transparent, and closed-form analysis of the trade-off function for Differentially Private SGD using random shuffling, significantly improving upon previous methods and est…

The paper analyzes language generation and identification in the limit under bounded memory, showing that memory constraints significantly alter learnability, particularly affecting achievable density…

This paper measures the lower bound for the shortest program generating a sequence, proving a conservation law and providing a deterministic engine to recover generating programs for certain sequences…

The polynomial-time low-degree conjecture, which predicts that low-degree indistinguishability, a uniform null distribution, permutation invariance, and independent resampling imply polynomial-time ha…

This paper presents conditions for achieving optimal uniformity in Quasi-Monte Carlo estimators using Sobol' sequences and Artin-Schreier polynomials.

The paper establishes information-theoretic lower bounds for stochastic optimization using low-bit gradients by reducing the problem to compressed Gaussian mean estimation, yielding sharp bounds on co…

This paper studies the behavior and complexity of randomized algorithms that may terminate almost surely but run forever on exceptional random tapes. It provides bounds on the survival tail, Kolmogoro…

This paper proves an inverse-polynomial spectral-gap bound for the lazy swap chain on binary matrices with prescribed row and column sums, which is a standard sampler for fixed-margin null models.

This paper proposes two algorithms for approximating the number of four-cycles in graph edge streams, improving upon existing theoretical bounds and handling non-concentrated four-cycles in one-pass.

This paper studies the existence of polynomial measures of dependence between two random variables that satisfy the data processing inequality and vanish on independence. It proves that no such polyno…

This paper introduces a streaming model with catalytic memory and shows dramatic space savings for data stream algorithms, providing exact computation of frequency moments using multi-pass algorithms…