Layer-wise analysis of deep networks with Gaussian kernels

Part of Advances in Neural Information Processing Systems 23 (NIPS 2010)

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Grégoire Montavon, Klaus-Robert Müller, Mikio Braun


Deep networks can potentially express a learning problem more efficiently than local learning machines. While deep networks outperform local learning machines on some problems, it is still unclear how their nice representation emerges from their complex structure. We present an analysis based on Gaussian kernels that measures how the representation of the learning problem evolves layer after layer as the deep network builds higher-level abstract representations of the input. We use this analysis to show empirically that deep networks build progressively better representations of the learning problem and that the best representations are obtained when the deep network discriminates only in the last layers.