Sparse random feature networks with in-degree d are equivalent to order-d additive models, and a distribution of in-degrees yields a mixture of additive kernels.
Kernel-based Translations of Convolutional Networks
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abstract
Convolutional Neural Networks, as most artificial neural networks, are commonly viewed as methods different in essence from kernel-based methods. We provide a systematic translation of Convolutional Neural Networks (ConvNets) into their kernel-based counterparts, Convolutional Kernel Networks (CKNs), and demonstrate that this perception is unfounded both formally and empirically. We show that, given a Convolutional Neural Network, we can design a corresponding Convolutional Kernel Network, easily trainable using a new stochastic gradient algorithm based on an accurate gradient computation, that performs on par with its Convolutional Neural Network counterpart. We present experimental results supporting our claims on landmark ConvNet architectures comparing each ConvNet to its CKN counterpart over several parameter settings.
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Additive function approximation in the brain
Sparse random feature networks with in-degree d are equivalent to order-d additive models, and a distribution of in-degrees yields a mixture of additive kernels.