标题： 数据放大理论上的限制 显示英文标题

标题： An information theoretic limit to data amplification

摘要： 近年来，生成式人工智能已被用于创建支持科学分析的数据。 例如，生成对抗网络（GANs）已使用蒙特卡罗模拟的输入进行训练，然后用于生成相同问题的数据。 这具有显著减少计算时间的优点。 GAN 的 N 个训练事件可以生成 GN 个事件，增益因子 G 大于 1。 这似乎违反了不能免费获得信息的原则。 这不是放大数据的唯一方式，因此该过程将被称为数据放大，它使用信息论概念进行研究。 研究表明，可以在保持数据信息内容不变的情况下实现大于 1 的增益。 这导致了一个仅依赖于生成和训练事件数量的数学界限。 本研究确定了确保这一界限的潜在概率分布和重建概率分布的条件。 特别是，放大数据中变量的分辨率不会因该过程而改善，但样本量的增加仍可提高统计显著性。 该界限通过计算机模拟以及文献中 GAN 生成数据的分析得到证实。 显示英文摘要

摘要： In recent years generative artificial intelligence has been used to create data to support science analysis. For example, Generative Adversarial Networks (GANs) have been trained using Monte Carlo simulated input and then used to generate data for the same problem. This has the advantage that a GAN creates data in a significantly reduced computing time. N training events for a GAN can result in GN generated events with the gain factor, G, being more than one. This appears to violate the principle that one cannot get information for free. This is not the only way to amplify data so this process will be referred to as data amplification which is studied using information theoretic concepts. It is shown that a gain of greater than one is possible whilst keeping the information content of the data unchanged. This leads to a mathematical bound which only depends on the number of generated and training events. This study determines conditions on both the underlying and reconstructed probability distributions to ensure this bound. In particular, the resolution of variables in amplified data is not improved by the process but the increase in sample size can still improve statistical significance. The bound is confirmed using computer simulation and analysis of GAN generated data from the literature.