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Employing equivariance in neural networks leads to greater parameter efficiency and improved generalization performance through the encoding of domain knowledge in the architecture; however, the majority of existing approaches require an a…

The performance of multi-task learning in Convolutional Neural Networks (CNNs) hinges on the design of feature sharing between tasks within the architecture. The number of possible sharing patterns are combinatorial in the depth of the…

A rigorous formulation of the dynamics of a signal processing scheme aimed at dense signal scanning without any loss in accuracy is introduced and analyzed. Related methods proposed in the recent past lack a satisfactory analysis of whether…

We start out by demonstrating that an elementary learning task, corresponding to the training of a single linear neuron in a convolutional neural network, can be solved for feature spaces of very high dimensionality. In a second step,…

Symmetries built into a neural network have appeared to be very beneficial for a wide range of tasks as it saves the data to learn them. We depart from the position that when symmetries are not built into a model a priori, it is…

\textbf{G}raph \textbf{C}onvolutional \textbf{N}etwork (\textbf{GCN}) is widely used in graph data learning tasks such as recommendation. However, when facing a large graph, the graph convolution is very computationally expensive thus is…

Convolutional neural networks (CNNs) based solutions have achieved state-of-the-art performances for many computer vision tasks, including classification and super-resolution of images. Usually the success of these methods comes with a cost…

We introduce Group equivariant Convolutional Neural Networks (G-CNNs), a natural generalization of convolutional neural networks that reduces sample complexity by exploiting symmetries. G-CNNs use G-convolutions, a new type of layer that…

A fruitful approach for solving signal deconvolution problems consists of resorting to a frame-based convex variational formulation. In this context, parallel proximal algorithms and related alternating direction methods of multipliers have…

Symmetry is a key feature observed in nature (from flowers and leaves, to butterflies and birds) and in human-made objects (from paintings and sculptures, to manufactured objects and architectural design). Rotational, translational, and…

Real bipartite networks combine degree-constrained random mixing with structured, locality-like rules. We introduce a statistical filter that benchmarks node-level bipartite clustering against degree-preserving randomizations to classify…

Representation learning seeks meaningful sensory representations without supervision and can model aspects of human development. Although many neural networks empirically learn useful features, a principled account of what makes a…

We propose a simple and generic layer formulation that extends the properties of convolutional layers to any domain that can be described by a graph. Namely, we use the support of its adjacency matrix to design learnable weight sharing…

In the current era of neural networks and big data, higher dimensional data is processed for automation of different application areas. Graphs represent a complex data organization in which dependencies between more than one object or…

Following the traditional paradigm of convolutional neural networks (CNNs), modern CNNs manage to keep pace with more recent, for example transformer-based, models by not only increasing model depth and width but also the kernel size. This…

Graph kernels have been successfully applied to many graph classification problems. Typically, a kernel is first designed, and then an SVM classifier is trained based on the features defined implicitly by this kernel. This two-stage…

This paper introduces Lie groups in degenerate geometric (Clifford) algebras that preserve four fundamental subspaces determined by the grade involution and reversion under the adjoint and twisted adjoint representations. We prove that…

Convolutional neural networks (CNNs) have demonstrated their capability to solve different kind of problems in a very huge number of applications. However, CNNs are limited for their computational and storage requirements. These limitations…

Recent work (Cohen & Welling, 2016) has shown that generalizations of convolutions, based on group theory, provide powerful inductive biases for learning. In these generalizations, filters are not only translated but can also be rotated,…

We report on the construction of a deep convolutional neural network that can reproduce the sensitivity of a matched-filtering search for binary black hole gravitational-wave signals. The standard method for the detection of well modeled…