Related papers: Geometry of Deep Convolutional Networks
Graph-structured data arise in many scenarios. A fundamental problem is to quantify the similarities of graphs for tasks such as classification. R-convolution graph kernels are positive-semidefinite functions that decompose graphs into…
In comparison to classical shallow representation learning techniques, deep neural networks have achieved superior performance in nearly every application benchmark. But despite their clear empirical advantages, it is still not well…
Neural networks can be thought of as applying a transformation to an input dataset. The way in which they change the topology of such a dataset often holds practical significance for many tasks, particularly those demanding non-homeomorphic…
This paper introduces a new Convolutional Neural Network (ConvNet) architecture inspired by a class of partial differential equations (PDEs) called quasi-linear hyperbolic systems. With comparable performance on the image classification…
This paper investigates the foundations of deep learning through insight of geometry, algebra and differential calculus. At is core, artificial intelligence relies on assumption that data and its intrinsic structure can be embedded into…
To what extent is the success of deep visualization due to the training? Could we do deep visualization using untrained, random weight networks? To address this issue, we explore new and powerful generative models for three popular deep…
The design of periodic nanostructures allows to tailor the transport of photons, phonons, and matter waves for specific applications. Recent years have seen a further expansion of this field by engineering topological properties. However,…
We present an analysis of different techniques for selecting the connection be- tween layers of deep neural networks. Traditional deep neural networks use ran- dom connection tables between layers to keep the number of connections small and…
Deep neural networks are widely used in various domains. However, the nature of computations at each layer of the deep networks is far from being well understood. Increasing the interpretability of deep neural networks is thus important.…
Deep learning based on deep neural networks has been very successful in many practical applications, but it lacks enough theoretical understanding due to the network architectures and structures. In this paper we establish some analysis for…
Graph convolutional networks are a popular class of deep neural network algorithms which have shown success in a number of relational learning tasks. Despite their success, graph convolutional networks exhibit a number of peculiar features,…
Deep Neural Networks (DNNs) are generated by sequentially performing linear and non-linear processes. Using a combination of linear and non-linear procedures is critical for generating a sufficiently deep feature space. The majority of…
Establishing accurate morphological measurements of galaxies in a reasonable amount of time for future big-data surveys such as EUCLID, the Large Synoptic Survey Telescope or the Wide Field Infrared Survey Telescope is a challenge. Because…
We investigate the performance of fully convolutional networks to simulate the motion and interaction of surface waves in open and closed complex geometries. We focus on a U-Net architecture and analyse how well it generalises to geometric…
In this paper, we revisit the problem of 3D human modeling from two orthogonal silhouettes of individuals (i.e., front and side views). Different from our prior work, a supervised learning approach based on convolutional neural network…
Why and how that deep learning works well on different tasks remains a mystery from a theoretical perspective. In this paper we draw a geometric picture of the deep learning system by finding its analogies with two existing geometric…
In this paper we show the similarities and differences of two deep neural networks by comparing the manifolds composed of activation vectors in each fully connected layer of them. The main contribution of this paper includes 1) a new data…
We survey the mathematical foundations of geometric deep learning, focusing on group equivariant and gauge equivariant neural networks. We develop gauge equivariant convolutional neural networks on arbitrary manifolds $\mathcal{M}$ using…
We show that the output of a (residual) convolutional neural network (CNN) with an appropriate prior over the weights and biases is a Gaussian process (GP) in the limit of infinitely many convolutional filters, extending similar results for…
For a simple model of shallow and wide neural networks, we show that the epigraph of its input-output map as a function of the network parameters approximates epigraph of a. convex function in a precise sense. This leads to a plausible…