滤等价函数：列表长度通用外推的对称性账户
介观与纳米尺度物理
2025-09-05 v2 量子物理
摘要
对于超出已知输入/输出示例的函数应呈何种形式，这是一个普遍而富有挑战性的问题，因为任何匹配这些示例输出的函数原则上都可能是正确的外推器。我们认为，"好"的外推器应遵循某些规则，本文研究一种特别引人注目的规则遵循标准：函数即使在删除某些元素后仍应表现出可预测性。函数式编程中，标准的表达此类删除操作的方式是使用滤函数。因此，我们引入了一种新的语义函数类——滤等价函数。我们展示了该类包含有趣的例子，证明了一些基本定理，并将其与众所周知的映射等价函数类相关联。我们还提出了滤等价函数的几何论述，表明它们自然对应于某些单纯形结构。我们的亮点结果是混合算法，它通过首先研究函数在输入子列表上的行为来构造任何滤等价函数的输出，以实现完美的外推。
引用
@article{arxiv.2507.08795,
title = {Distinct Lifetimes for $X$ and $Z$ Loop Measurements in a Majorana Tetron Device},
author = {Morteza Aghaee and Zulfi Alam and Rikke Andersen and Mariusz Andrzejczuk and Andrey Antipov and Mikhail Astafev and Lukas Avilovas and Ahmad Azizimanesh and Eric Banek and Bela Bauer and Jonathan Becker and Umesh Kumar Bhaskar and Andrea G. Boa and Srini Boddapati and Nichlaus Bohac and Jouri D. S. Bommer and Jan Borovsky and Léo Bourdet and Samuel Boutin and Lucas Casparis and Srivatsa Chakravarthi and Hamidreza Chalabi and Benjamin J. Chapman and Nikolaos Chatzaras and Tzu-Chiao Chien and Jason Cho and Patrick Codd and William Cole and Paul W. Cooper and Fabiano Corsetti and Ajuan Cui and Tareq El Dandachi and Celine Dinesen and Andreas Ekefjärd and Saeed Fallahi and Luca Galletti and Geoffrey C. Gardner and Gonzalo Leon Gonzalez and Deshan Govender and Flavio Griggio and Ruben Grigoryan and Sebastian Grijalva and Sergei Gronin and Jan Gukelberger and Marzie Hamdast and A. Ben Hamida and Esben Bork Hansen and Caroline Tynell Hansen and Sebastian Heedt and Samantha Ho and Laurens Holgaard and Kevin van Hoogdalem and John Hornibrook and Henrik Ingerslev and Lovro Ivancevic and Sherwan Jamo and Max Jantos and Thomas Jensen and Jaspreet Singh Jhoja and Jeffrey C Jones and Vidul Joshi and Konstantin V. Kalashnikov and Ray Kallaher and Rachpon Kalra and Farhad Karimi and Torsten Karzig and Seth Kimes and Evelyn King and Maren Elisabeth Kloster and Christina Knapp and Jonne V. Koski and Pasi Kostamo and Tom Laeven and Jeffrey Lai and Gijs de Lange and Thorvald W. Larsen and Kyunghoon Lee and Kongyi Li and Guangze Li and Shuang Liang and Tyler Lindemann and Matthew Looij and Marijn Lucas and Roman Lutchyn and Morten Hannibal Madsen and Nasiari Madulid and Michael J. Manfra and Laveena Manjunath and Signe Markussen and Esteban Martinez and Marco Mattila and J. R. Mattinson and R. P. G. McNeil and Alba Pérez Millan and Ryan V. Mishmash and Sarang Mittal and Christian Møllgaard and M. W. A. de Moor and Eduardo Puchol Morejon and Trevor Morgan and George Moussa and B. P. Nabar and Anirudh Narla and Chetan Nayak and Jens Hedegaard Nielsen and William Hvidtfelt Padkær Nielsen and Frédéric Nolet and Michael J. Nystrom and Eoin O'Farrell and Thomas A. Ohki and Keita Otani and Camille Papon and Karl D Petersson and Luca Petit and Dima Pikulin and Mohana Rajpalke and Alejandro Alcaraz Ramirez and David Razmadze and Yuan Ren and Ivan Sadovskyy and Lauri Sainiemi and Juan Carlos Estrada Saldaña and Irene Sanlorenzo and Tatiane Pereira dos Santos and Simon Schaal and John Schack and Emma R. Schmidgall and Christina Sfetsou and Cristina Sfiligoj and Sarat Sinha and Patrick Sohr and Thomas L. Sørensen and Kasper Spiegelhauer and Tomaš Stankević and Lieuwe J. Stek and Patrick Strøm-Hansen and Henri J. Suominen and Judith Suter and Samuel M. L. Teicher and Raj Tholapi and Mason Thomas and D. W. Tom and Emily Toomey and Joshua Tracy and Michelle Turley and Matthew D. Turner and Shivendra Upadhyay and Ivan Urban and Dmitrii V. Viazmitinov and Anna Wulff Viazmitinova and Beatriz Viegas and Dominik J. Vogel and John Watson and Alex Webster and Joseph Weston and Timothy Williamson and Georg W. Winkler and David J. van Woerkom and Brian Paquelet Wuetz and Chung-Kai Yang and Shang-Jyun and Yu and Emrah Yucelen and Jesús Herranz Zamorano and Roland Zeisel and Guoji Zheng and A. M. Zimmerman},
journal= {arXiv preprint arXiv:2507.08795},
year = {2025}
}
备注
Extended discussion of switching dynamics and multiple time scales in App. A. Added App. C on alternative scenarios. Corrected Figs. 2(i) & A4. Explained the method for extracting multiple time scales from long time traces in App. A