We present Spectral Inference Networks, a framework for learning
eigenfunctions of linear operators by stochastic optimization. Spectral
Inference Networks generalize Slow Feature Analysis to generic symmetric
operators, and are closely related to Variational Monte Carlo methods from
computational physics. As such, they can be a powerful tool for unsupervised
representation learning from video or graph-structured data. We cast training
Spectral Inference Networks as a bilevel optimization problem, which allows for
online learning of multiple eigenfunctions. We show results of training
Spectral Inference Networks on problems in quantum mechanics and feature
learning for videos on synthetic datasets. Our results demonstrate that
Spectral Inference Networks accurately recover eigenfunctions of linear
operators and can discover interpretable representations from video in a fully
unsupervised manner.

本文提出了一种称为 Spectral Inference Networks 的框架，通过随机优化来学习线性算子的特征函数，可以成为从视频或基于图的数据中进行无监督表示学习的强有力工具。我们将训练 Spectral Inference Networks 视为一个双层优化问题，并展示了它在量子力学和合成数据集上的应用，在完全无监督的情况下从视频中准确恢复线性算子的特征函数并发现可解释的表示。