Neural Information Processing Systems http://nips.cc/

Convolutional neural networks have achieved extraordinary results in many computer vision and pattern recognition applications; however, their adoption in the computer graphics and geometry processing communities is limited due to the non-Euclidean structure of their data. In this paper, we propose Anisotropic Convolutional Neural Network (ACNN), a generalization of classical CNNs to non-Euclidean domains, where classical convolutions are replaced by projections over a set of oriented anisotropic diffusion kernels. We use ACNNs to effectively learn intrinsic dense correspondences between deformable shapes, a fundamental problem in geometry processing, arising in a wide variety of applications. We tested ACNNs performance in challenging settings, achieving state-of-the-art results on recent correspondence benchmarks.

This paper introduces Non-Autonomous Input-Output Stable Network (NAIS-Net), a very deep architecture where each stacked processing block is derived from a time-invariant non-autonomous dynamical system. Non-autonomy is implemented by skip connections from the block input to each of the unrolled processing stages and allows stability to be enforced so that blocks can be unrolled adaptively to a pattern-dependent processing depth. NAIS-Net induces non-trivial, Lipschitz input-output maps, even for an infinite unroll length. We prove that the network is globally asymptotically stable so that for every initial condition there is exactly one input-dependent equilibrium assuming tanh units, and multiple stable equilibria for ReL units. An efficient implementation that enforces the stability under derived conditions for both fully-connected and convolutional layers is also presented. Experimental results show how NAIS-Net exhibits stability in practice, yielding a significant reduction in generalization gap compared to ResNets.