Related papers: Kernelized Capsule Networks
It has long been known that a single-layer fully-connected neural network with an i.i.d. prior over its parameters is equivalent to a Gaussian process (GP), in the limit of infinite network width. This correspondence enables exact Bayesian…
We present a theoretically grounded Gaussian process framework that leverages neural feature maps to construct expressive kernels. We show that the learned feature map can be interpreted as an optimal low-rank approximation to a Gram matrix…
Neural networks are a promising tool for characterizing intermediate-scale quantum devices from limited amounts of measurement data. A challenging problem in this area is to learn the action of an unknown quantum process on an ensemble of…
In this paper, we propose a novel technique for generating images in the 3D domain from images with high degree of geometrical transformations. By coalescing two popular concurrent methods that have seen rapid ascension to the machine…
Bayesian methods in machine learning, such as Gaussian processes, have great advantages com-pared to other techniques. In particular, they provide estimates of the uncertainty associated with a prediction. Extending the Bayesian approach to…
Most existing neural networks for learning graphs address permutation invariance by conceiving of the network as a message passing scheme, where each node sums the feature vectors coming from its neighbors. We argue that this imposes a…
In many real-world applications we are interested in approximating costly functions that are analytically unknown, e.g. complex computer codes. An emulator provides a fast approximation of such functions relying on a limited number of…
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…
Graph models are relevant in many fields, such as distributed computing, intelligent tutoring systems or social network analysis. In many cases, such models need to take changes in the graph structure into account, i.e. a varying number of…
We investigate iterated compositions of weighted sums of Gaussian kernels and provide an interpretation of the construction that shows some similarities with the architectures of deep neural networks. On the theoretical side, we show that…
Despite recent advances in automated machine learning, model selection is still a complex and computationally intensive process. For Gaussian processes (GPs), selecting the kernel is a crucial task, often done manually by the expert.…
Learning invariant representations has been the long-standing approach to self-supervised learning. However, recently progress has been made in preserving equivariant properties in representations, yet do so with highly prescribed…
In this work, we investigate the following: 1) how the routing affects the CapsNet model fitting; 2) how the representation using capsules helps discover global structures in data distribution, and; 3) how the learned data representation…
Neural networks and Gaussian processes are complementary in their strengths and weaknesses. Having a better understanding of their relationship comes with the promise to make each method benefit from the strengths of the other. In this…
We present a novel scheme to accurately predict atomic forces as vector quantities, rather than sets of scalar components, by Gaussian Process (GP) Regression. This is based on matrix-valued kernel functions, on which we impose the…
Learning precise surrogate models of complex computer simulations and physical machines often require long-lasting or expensive experiments. Furthermore, the modeled physical dependencies exhibit nonlinear and nonstationary behavior.…
We introduce a new class of nonstationary kernels, which we derive as covariance functions of a novel family of stochastic processes we refer to as string Gaussian processes (string GPs). We construct string GPs to allow for multiple types…
Gaussian processes (GPs) are powerful but computationally expensive machine learning models, requiring an estimate of the kernel covariance matrix for every prediction. In large and complex domains, such as graphs, sets, or images, the…
The wide adoption of Convolutional Neural Networks (CNNs) in applications where decision-making under uncertainty is fundamental, has brought a great deal of attention to the ability of these models to accurately quantify the uncertainty in…
Capsule Networks have shown encouraging results on \textit{defacto} benchmark computer vision datasets such as MNIST, CIFAR and smallNORB. Although, they are yet to be tested on tasks where (1) the entities detected inherently have more…