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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)
Related Events (a corresponding poster, oral, or spotlight)
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2017 Talk: Convexified Convolutional Neural Networks »
Mon Aug 7th 05:48 -- 06:06 AM Room C4.8
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