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Convexified Convolutional Neural Networks
Yuchen Zhang · Percy Liang · Martin Wainwright

Mon Aug 07 01:30 AM -- 05:00 AM (PDT) @ Gallery #101

We describe the class of convexified convolutional neural networks (CCNNs), which capture the parameter sharing of convolutional neural networks in a convex manner. By representing the nonlinear convolutional filters as vectors in a reproducing kernel Hilbert space, the CNN parameters can be represented as a low-rank matrix, which can be relaxed to obtain a convex optimization problem. For learning two-layer convolutional neural networks, we prove that the generalization error obtained by a convexified CNN converges to that of the best possible CNN. For learning deeper networks, we train CCNNs in a layer-wise manner. Empirically, CCNNs achieve competitive or better performance than CNNs trained by backpropagation, SVMs, fully-connected neural networks, stacked denoising auto-encoders, and other baseline methods.

Author Information

Yuchen Zhang (Stanford)
Percy Liang (Stanford University)
Martin Wainwright (University of California at Berkeley)

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