Related papers: Geometry of Linear Convolutional Networks
Over the last few years, we have witnessed the availability of an increasing data generated from non-Euclidean domains, which are usually represented as graphs with complex relationships, and Graph Neural Networks (GNN) have gained a high…
Convolutional Neural Networks (CNNs) have become the state-of-the-art in supervised learning vision tasks. Their convolutional filters are of paramount importance for they allow to learn patterns while disregarding their locations in input…
Graph Neural Networks (GNNs) are information processing architectures for signals supported on graphs. They are presented here as generalizations of convolutional neural networks (CNNs) in which individual layers contain banks of graph…
Despite the phenomenal success of deep neural networks in a broad range of learning tasks, there is a lack of theory to understand the way they work. In particular, Convolutional Neural Networks (CNNs) are known to perform much better than…
Graph Convolutional Network (GCN) is an emerging technique that performs learning and reasoning on graph data. It operates feature learning on the graph structure, through aggregating the features of the neighbor nodes to obtain the…
Graph Convolutional Neural Networks (GCNNs) are generalizations of CNNs to graph-structured data, in which convolution is guided by the graph topology. In many cases where graphs are unavailable, existing methods manually construct graphs…
The graph structure is a commonly used data storage mode, and it turns out that the low-dimensional embedded representation of nodes in the graph is extremely useful in various typical tasks, such as node classification, link prediction ,…
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…
We propose a novel class of neural network-like parametrized functions, i.e., general transformation neural networks (GTNNs), for high-dimensional approximation. Conventional deep neural networks sometimes perform less accurately on…
Although Deep Convolutional Neural Networks (CNNs) have liberated their power in various computer vision tasks, the most important components of CNN, convolutional layers and fully connected layers, are still limited to linear…
Equivariant neural networks are neural networks with symmetry. Motivated by the theory of group representations, we decompose the layers of an equivariant neural network into simple representations. The nonlinear activation functions lead…
A machine learning (ML) feature network is a graph that connects ML features in learning tasks based on their similarity. This network representation allows us to view feature vectors as functions on the network. By leveraging function…
Within the world of machine learning there exists a wide range of different methods with respective advantages and applications. This paper seeks to present and discuss one such method, namely Convolutional Neural Networks (CNNs). CNNs are…
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…
Graphs have been widely adopted to denote structural connections between entities. The relations are in many cases heterogeneous, but entangled together and denoted merely as a single edge between a pair of nodes. For example, in a social…
Hypergraphs are a powerful abstraction for representing higher-order interactions between entities of interest. To exploit these relationships in making downstream predictions, a variety of hypergraph neural network architectures have…
Convolutional neural networks have been successfully applied to various NLP tasks. However, it is not obvious whether they model different linguistic patterns such as negation, intensification, and clause compositionality to help the…
Graph Neural Networks (GNN) can capture the geometric properties of neural representations in EEG data. Here we utilise those to study how reinforcement-based motor learning affects neural activity patterns during motor planning, leveraging…
In this position paper, we promote the study of function spaces parameterized by machine learning models through the lens of algebraic geometry. To this end, we focus on algebraic models, such as neural networks with polynomial activations,…
Polygonal meshes provide an efficient representation for 3D shapes. They explicitly capture both shape surface and topology, and leverage non-uniformity to represent large flat regions as well as sharp, intricate features. This…