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Compression techniques for deep neural network models are becoming veryimportant for the efficient execution of high-performance deep learning systemson edge-computing devices. The concept of model compression is also importantfor analyzing the generalization error of deep learning, known as thecompression-based error bound. However, there is still huge gap between apractically effective compression method and its rigorous background ofstatistical learning theory. To resolve this issue, we develop a newtheoretical framework for model compression and propose a new pruning methodcalled {\it spectral pruning} based on this framework. We define the ``degreesof freedom'' to quantify the intrinsic dimensionality of a model by using theeigenvalue distribution of the covariance matrix across the internal nodes andshow that the compression ability is essentially controlled by this quantity.Moreover, we present a sharp generalization error bound of the compressed modeland characterize the bias--variance tradeoff induced by the compressionprocedure. We apply our method to several datasets to justify our theoreticalanalyses and show the superiority of the the proposed method.

Spectral Pruning: Compressing Deep Neural Networks via Spectral Analysis and its Generalization Error