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.

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光谱推理网络：统一深度学习和光谱学习

我们提出了光谱推理网络，这是一种通过随机优化学习线性算子特征函数的框架。光谱推理网络将慢特征分析推广到通用对称算子，并且与计算物理学中的变分蒙特卡罗方法密切相关。因此，它们可以成为从视频或图结构数据进行无监督表示学习的强大工具。我们将训练频谱推理网络作为一个双层优化问题，允许多个特征函数的在线学习。我们展示了针对量子力学问题和合成数据集视频特征学习训练光谱推理网络的结果。