Learning Representation from Neural Fisher Kernel with Low-rank Approximation

• URL: http://arxiv.org/abs/2202.01944v1
• Date: Fri, 4 Feb 2022 02:28:02 GMT
• Title: Learning Representation from Neural Fisher Kernel with Low-rank Approximation
• Authors: Ruixiang Zhang, Shuangfei Zhai, Etai Littwin, Josh Susskind
• Abstract summary: We first define the Neural Fisher Kernel (NFK), which is the Fisher Kernel applied to neural networks. We show that NFK can be computed for both supervised and unsupervised learning models. We then propose an efficient algorithm that computes a low rank approximation of NFK, which scales to large datasets and networks.
• Score: 16.14794818755318
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we study the representation of neural networks from the view of kernels. We first define the Neural Fisher Kernel (NFK), which is the Fisher Kernel applied to neural networks. We show that NFK can be computed for both supervised and unsupervised learning models, which can serve as a unified tool for representation extraction. Furthermore, we show that practical NFKs exhibit low-rank structures. We then propose an efficient algorithm that computes a low rank approximation of NFK, which scales to large datasets and networks. We show that the low-rank approximation of NFKs derived from unsupervised generative models and supervised learning models gives rise to high-quality compact representations of data, achieving competitive results on a variety of machine learning tasks.

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