A rapidly growing area of research is the use of machine learning approaches such as autoencoders for dimensionality reduction of data and models in scientific applications. We show that the canonical formulation of autoencoders suffers from several deficiencies that can hinder their performance. Using a meta-learning approach, we reformulate the autoencoder problem as a bi-level optimization procedure that explicitly solves the dimensionality reduction task. We prove that the new formulation corrects the identified deficiencies with canonical autoencoders, provide a practical way to solve it, and showcase the strength of this formulation with a simple numerical illustration.
翻译:一个迅速增长的研究领域是使用自动校正器等机器学习方法来减少数据和模型在科学应用中的维度。我们证明,自动校正器的金字塔配方存在若干缺陷,可能妨碍其性能。我们采用元化学习方法,重新将自动校正器问题改造成一个双级优化程序,明确解决了减少维度的任务。我们证明,新配方纠正了用卡通自动校正器查明的缺陷,提供了解决这一问题的实用方法,并用简单的数字插图展示了这种配方的强度。