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In this paper, we study the representation of neural networks from the viewof kernels. We first define the Neural Fisher Kernel (NFK), which is the FisherKernel applied to neural networks. We show that NFK can be computed for bothsupervised and unsupervised learning models, which can serve as a unified toolfor representation extraction. Furthermore, we show that practical NFKs exhibitlow-rank structures. We then propose an efficient algorithm that computes a lowrank approximation of NFK, which scales to large datasets and networks. We showthat the low-rank approximation of NFKs derived from unsupervised generativemodels and supervised learning models gives rise to high-quality compactrepresentations of data, achieving competitive results on a variety of machinelearning tasks.

Learning Representation from Neural Fisher Kernel with Low-rank Approximation