Related papers: Topological Neural Networks over the Air

This work introduces the Topological CNN (TCNN), which encompasses several topologically defined convolutional methods. Manifolds with important relationships to the natural image space are used to parameterize image filters which are used…

The Artificial Neural Networks (ANNs) have been originally designed to function like a biological neural network, but does an ANN really work in the same way as a biological neural network? As we know, the human brain holds information in…

Deep Neural Networks (DNN) and especially Convolutional Neural Networks (CNN) are a de-facto standard for the analysis of large volumes of signals and images. Yet, their development and underlying principles have been largely performed in…

Graph Nerual Networks (GNNs) are effective models in graph embedding. It extracts shallow features and neighborhood information by aggregating neighbor information to learn the embedding representation of different nodes. However, the local…

A promising approach to improve climate-model simulations is to replace traditional subgrid parameterizations based on simplified physical models by machine learning algorithms that are data-driven. However, neural networks (NNs) often lead…

We propose Sparse Neural Network architectures that are based on random or structured bipartite graph topologies. Sparse architectures provide compression of the models learned and speed-ups of computations, they can also surpass their…

Tensorizing a neural network involves reshaping some or all of its dense weight matrices into higher-order tensors and approximating them using low-rank tensor network decompositions. This technique has shown promise as a model compression…

The natural world is full of complex systems characterized by intricate relations between their components: from social interactions between individuals in a social network to electrostatic interactions between atoms in a protein.…

Deep learning methods have demonstrated outstanding performances on classification and regression tasks on homogeneous data types (e.g., image, audio, and text data). However, tabular data still pose a challenge, with classic machine…

We present Linear Diffusion Networks (LDNs), a novel architecture that reinterprets sequential data processing as a unified diffusion process. Our model integrates adaptive diffusion modules with localized nonlinear updates and a…

Interpreting graph neural networks (GNNs) is difficult because message passing mixes signals and internal channels rarely align with human concepts. We study superposition, the sharing of directions by multiple features, directly in the…

Programming language processing (similar to natural language processing) is a hot research topic in the field of software engineering; it has also aroused growing interest in the artificial intelligence community. However, different from a…

While convolutional neural networks (CNNs) have recently made great strides in supervised classification of data structured on a grid (e.g. images composed of pixel grids), in several interesting datasets, the relations between features can…

A topological neural network (TNN), which takes data from a Tychonoff topological space instead of the usual finite dimensional space, is introduced. As a consequence, a distributional neural network (DNN) that takes Borel measures as data…

Graph convolutional neural networks (GCNs) generalize tradition convolutional neural networks (CNNs) from low-dimensional regular graphs (e.g., image) to high dimensional irregular graphs (e.g., text documents on word embeddings). Due to…

Convolutional Neural Networks (CNNs) have recently led to incredible breakthroughs on a variety of pattern recognition problems. Banks of finite impulse response filters are learned on a hierarchy of layers, each contributing more abstract…

Graph neural networks excel at modeling pairwise interactions, but they cannot flexibly accommodate higher-order interactions and features. Topological deep learning (TDL) has emerged recently as a promising tool for addressing this issue.…

Although neural networks are capable of reaching astonishing performances on a wide variety of contexts, properly training networks on complicated tasks requires expertise and can be expensive from a computational perspective. In industrial…

Topological deep learning is a rapidly growing field that pertains to the development of deep learning models for data supported on topological domains such as simplicial complexes, cell complexes, and hypergraphs, which generalize many…

Graph classification is an important learning task for graph-structured data. Graph neural networks (GNNs) have recently gained growing attention in graph learning and have shown significant improvements in many important graph problems.…