On his Twitter feed, Atlas mentioned three preprints: the first allows the building of deeper construction out of kernels (shallow methods). The next one shows how some deep nets can be considered as some sorts of ensemble of shallower nets. Finally, the last one makes the case that dropout and stochastic depth are somehow equivalent to averaging over shallower networks.
In this paper, we propose a new image representation based on a multilayer kernel machine that performs end-to-end learning. Unlike traditional kernel methods, where the kernel is handcrafted or adapted to data in an unsupervised manner, we learn how to shape the kernel for a supervised prediction problem. We proceed by generalizing convolutional kernel networks, which originally provide unsupervised image representations, and we derive backpropagation rules to optimize model parameters. As a result, we obtain a new type of convolutional neural network with the following properties: (i) at each layer, learning filters is equivalent to optimizing a linear subspace in a reproducing kernel Hilbert space (RKHS), where we project data, (ii) the network may be learned with supervision or without, (iii) the model comes with a natural regularization function (the norm in the RKHS). We show that our method achieves reasonably competitive performance on some standard "deep learning" image classification datasets such as CIFAR-10 and SVHN, and also state-of-the-art results for image super-resolution, demonstrating the applicability of our approach to a large variety of image-related tasks.
Residual Networks are Exponential Ensembles of Relatively Shallow Networks by Andreas Veit, Michael Wilber, Serge Belongie
In this work, we introduce a novel interpretation of residual networks showing they are exponential ensembles. This observation is supported by a large-scale lesion study that demonstrates they behave just like ensembles at test time. Subsequently, we perform an analysis showing these ensembles mostly consist of networks that are each relatively shallow. For example, contrary to our expectations, most of the gradient in a residual network with 110 layers comes from an ensemble of very short networks, i.e., only 10-34 layers deep. This suggests that in addition to describing neural networks in terms of width and depth, there is a third dimension: multiplicity, the size of the implicit ensemble. Ultimately, residual networks do not resolve the vanishing gradient problem by preserving gradient flow throughout the entire depth of the network - rather, they avoid the problem simply by ensembling many short networks together. This insight reveals that depth is still an open research question and invites the exploration of the related notion of multiplicity.
Swapout: Learning an ensemble of deep architectures by Saurabh Singh, Derek Hoiem, David Forsyth
We describe Swapout, a new stochastic training method, that outperforms ResNets of identical network structure yielding impressive results on CIFAR-10 and CIFAR-100. Swapout samples from a rich set of architectures including dropout, stochastic depth and residual architectures as special cases. When viewed as a regularization method swapout not only inhibits co-adaptation of units in a layer, similar to dropout, but also across network layers. We conjecture that swapout achieves strong regularization by implicitly tying the parameters across layers. When viewed as an ensemble training method, it samples a much richer set of architectures than existing methods such as dropout or stochastic depth. We propose a parameterization that reveals connections to exiting architectures and suggests a much richer set of architectures to be explored. We show that our formulation suggests an efficient training method and validate our conclusions on CIFAR-10 and CIFAR-100 matching state of the art accuracy. Remarkably, our 32 layer wider model performs similar to a 1001 layer ResNet model.
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