Related papers: Algebraic Convolutional Filters on Lie Group Algeb…

Network data can be conveniently modeled as a graph signal, where data values are assigned to nodes of a graph that describes the underlying network topology. Successful learning from network data is built upon methods that effectively…

Edges are a basic and fundamental feature in image processing, that are used directly or indirectly in huge amount of applications. Inspired by the expansion of image resolution and processing power dilated convolution techniques appeared.…

Convolutional neural networks are constructed with massive operations with different types and are highly computationally intensive. Among these operations, multiplication operation is higher in computational complexity and usually requires…

Identifying symmetries in data sets is generally difficult, but knowledge about them is crucial for efficient data handling. Here we present a method how neural networks can be used to identify symmetries. We make extensive use of the…

Do convolutional networks really need a fixed feed-forward structure? What if, after identifying the high-level concept of an image, a network could move directly to a layer that can distinguish fine-grained differences? Currently, a…

Multilayer graphs are commonly used for representing different relations between entities and handling heterogeneous data processing tasks. New challenges arise in multilayer graph clustering for assigning clusters to a common multilayer…

In this paper we consider a problem of searching a space of predictive models for a given training data set. We propose an iterative procedure for deriving a sequence of improving models and a corresponding sequence of sets of non-linear…

Steerable CNN imposes the prior knowledge of transformation invariance or equivariance in the network architecture to enhance the the network robustness on geometry transformation of data and reduce overfitting. It has been an intuitive and…

The paper presents the complete classification of Automorphic Lie Algebras based on $\mathfrak{sl}_n (\mathbb{C})$, where the symmetry group $G$ is finite and the orbit is any of the exceptional $G$-orbits in $\overline{\mathbb{C}}$. A key…

We present a loss function for neural networks that encompasses an idea of trivial versus non-trivial predictions, such that the network jointly determines its own prediction goals and learns to satisfy them. This permits the network to…

This paper proposes a novel regularization approach to bias Convolutional Neural Networks (CNNs) toward utilizing edge and line features in their hidden layers. Rather than learning arbitrary kernels, we constrain the convolution layers to…

Convolutional sparse representations are a form of sparse representation with a dictionary that has a structure that is equivalent to convolution with a set of linear filters. While effective algorithms have recently been developed for the…

Deep convolutional neural networks have proven to be well suited for image classification applications. However, if there is distortion in the image, the classification accuracy can be significantly degraded, even with state-of-the-art…

This paper proposes an equivariant neural network that takes data in any semi-simple Lie algebra as input. The corresponding group acts on the Lie algebra as adjoint operations, making our proposed network adjoint-equivariant. Our framework…

We generalize the scattering transform to graphs and consequently construct a convolutional neural network on graphs. We show that under certain conditions, any feature generated by such a network is approximately invariant to permutations…

Modeling generative process of growing graphs has wide applications in social networks and recommendation systems, where cold start problem leads to new nodes isolated from existing graph. Despite the emerging literature in learning graph…

We study the family of functions that are represented by a linear convolutional neural network (LCN). These functions form a semi-algebraic subset of the set of linear maps from input space to output space. In contrast, the families of…

We introduce a family of adaptive estimators on graphs, based on penalizing the $\ell_1$ norm of discrete graph differences. This generalizes the idea of trend filtering [Kim et al. (2009), Tibshirani (2014)], used for univariate…

Over the last couple of years, deep learning and especially convolutional neural networks have become one of the work horses of computer vision. One limiting factor for the applicability of supervised deep learning to more areas is the need…

A positive integer is expressed as a sum of squares of positive integers in a unique way applying a special technique. The expression, thus obtained is resolved into two factors using the concept of the Clifford algebra. This technique is…