Direct Parameterization of Lipschitz-Bounded Deep Networks
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This paper introduces a new parameterization of deep neural networks (both fully-connected and convolutional) with guaranteed Lipschitz bounds, i.e. limited sensitivity to perturbations. The Lipschitz guarantees are equivalent to the tightest-known bounds based on certification via a semidefinite program (SDP), which does not scale to large models. In contrast to the SDP approach, we provide a “direct” parameterization, i.e. a smooth mapping from ℝ^N onto the set of weights of Lipschitz-bounded networks. This enables training via standard gradient methods, without any computationally intensive projections or barrier terms. The new parameterization can equivalently be thought of as either a new layer type (the sandwich layer), or a novel parameterization of standard feedforward networks with parameter sharing between neighbouring layers. We illustrate the method with some applications in image classification (MNIST and CIFAR-10).
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