有限群的可混合性
计算机与社会
2025-01-30 v1 人工智能
机器学习
摘要
若有限群 中的元素可独立从两个选项中选择，其乘积能够在 上均匀分布，则称 为可混合的(mixable)。我们给出可混合性的条件与限制。我们证明 -群、对称群、简单交错群、若干矩阵群和孤立群，以及大多数有限 Coxeter 群均为可混合的。我们还给出此类群的混合长度的界限。
引用
@article{arxiv.2501.17805,
title = {International AI Safety Report},
author = {Yoshua Bengio and Sören Mindermann and Daniel Privitera and Tamay Besiroglu and Rishi Bommasani and Stephen Casper and Yejin Choi and Philip Fox and Ben Garfinkel and Danielle Goldfarb and Hoda Heidari and Anson Ho and Sayash Kapoor and Leila Khalatbari and Shayne Longpre and Sam Manning and Vasilios Mavroudis and Mantas Mazeika and Julian Michael and Jessica Newman and Kwan Yee Ng and Chinasa T. Okolo and Deborah Raji and Girish Sastry and Elizabeth Seger and Theodora Skeadas and Tobin South and Emma Strubell and Florian Tramèr and Lucia Velasco and Nicole Wheeler and Daron Acemoglu and Olubayo Adekanmbi and David Dalrymple and Thomas G. Dietterich and Edward W. Felten and Pascale Fung and Pierre-Olivier Gourinchas and Fredrik Heintz and Geoffrey Hinton and Nick Jennings and Andreas Krause and Susan Leavy and Percy Liang and Teresa Ludermir and Vidushi Marda and Helen Margetts and John McDermid and Jane Munga and Arvind Narayanan and Alondra Nelson and Clara Neppel and Alice Oh and Gopal Ramchurn and Stuart Russell and Marietje Schaake and Bernhard Schölkopf and Dawn Song and Alvaro Soto and Lee Tiedrich and Gaël Varoquaux and Andrew Yao and Ya-Qin Zhang and Fahad Albalawi and Marwan Alserkal and Olubunmi Ajala and Guillaume Avrin and Christian Busch and André Carlos Ponce de Leon Ferreira de Carvalho and Bronwyn Fox and Amandeep Singh Gill and Ahmet Halit Hatip and Juha Heikkilä and Gill Jolly and Ziv Katzir and Hiroaki Kitano and Antonio Krüger and Chris Johnson and Saif M. Khan and Kyoung Mu Lee and Dominic Vincent Ligot and Oleksii Molchanovskyi and Andrea Monti and Nusu Mwamanzi and Mona Nemer and Nuria Oliver and José Ramón López Portillo and Balaraman Ravindran and Raquel Pezoa Rivera and Hammam Riza and Crystal Rugege and Ciarán Seoighe and Jerry Sheehan and Haroon Sheikh and Denise Wong and Yi Zeng},
journal= {arXiv preprint arXiv:2501.17805},
year = {2025}
}