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 undetectable and elementary watermarking scheme in the closed setting. Also, in the harder open setting, where the adversary has access to most of the model, we propose an unremovable watermarking scheme.
Pedro Abdalla, Afonso S. Bandeira
Semidefinite programming is an important tool to tackle several problems in data science and signal processing, including clustering and community detection. However, semidefinite programs are often slow in practice, so speed up techniques such as sketching are often considered. In the context of community detection in the stochastic block model, Mixon and Xie \cite{mixon2020sketching} have recently proposed a sketching framework in which a semidefinite program is solved only on a subsampled subgraph of the network, giving rise to significant computational savings. In this short paper, we provide a positive answer to a conjecture of Mixon and Xie about the statistical limits of this technique for the stochastic block model with two balanced communities.