Related papers: Sparse Dowker Nerves
Radar-based perception has gained increasing attention in autonomous driving, yet the inherent sparsity of radars poses challenges. Radar raw data often contains excessive noise, whereas radar point clouds retain only limited information.…
We introduce a unified framework for group equivariant networks on homogeneous spaces derived from a Fourier perspective. We consider tensor-valued feature fields, before and after a convolutional layer. We present a unified derivation of…
In recent years, deep learning-based point cloud normal estimation has made great progress. However, existing methods mainly rely on the PCPNet dataset, leading to overfitting. In addition, the correlation between point clouds with…
In principle, sparse neural networks should be significantly more efficient than traditional dense networks. Neurons in the brain exhibit two types of sparsity; they are sparsely interconnected and sparsely active. These two types of…
Recently, there have been increasing demands to construct compact deep architectures to remove unnecessary redundancy and to improve the inference speed. While many recent works focus on reducing the redundancy by eliminating unneeded…
Machine learning problems involving sparse datasets may benefit from the use of convolutional neural networks if the numbers of samples and features are very large. Such datasets are increasingly more frequently encountered in a variety of…
With the development of range sensors such as LIDAR and time-of-flight cameras, 3D point cloud scans have become ubiquitous in computer vision applications, the most prominent ones being gesture recognition and autonomous driving.…
In this paper, we propose 3D point-capsule networks, an auto-encoder designed to process sparse 3D point clouds while preserving spatial arrangements of the input data. 3D capsule networks arise as a direct consequence of our novel unified…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
The Laplacian operator transforms the image into its Laplacian field, which usually is sparse and satisfies a stable distribution. On the other hand, an image can be uniquely reconstructed from its Laplacian field via solving a Poisson…
The goal of this paper is to introduce pooling strategies for simplicial convolutional neural networks. Inspired by graph pooling methods, we introduce a general formulation for a simplicial pooling layer that performs: i) local aggregation…
Sparse neural networks attract increasing interest as they exhibit comparable performance to their dense counterparts while being computationally efficient. Pruning the dense neural networks is among the most widely used methods to obtain a…
While end-to-end training of Deep Neural Networks (DNNs) yields state of the art performance in an increasing array of applications, it does not provide insight into, or control over, the features being extracted. We report here on a…
This work examines the problem of exact data interpolation via sparse (neuron count), infinitely wide, single hidden layer neural networks with leaky rectified linear unit activations. Using the atomic norm framework of [Chandrasekaran et…
More competent learning models are demanded for data processing due to increasingly greater amounts of data available in applications. Data that we encounter often have certain embedded sparsity structures. That is, if they are represented…
High-dimensional sparse data present computational and statistical challenges for supervised learning. We propose compact linear sketches for reducing the dimensionality of the input, followed by a single layer neural network. We show that…
Sparse incidence tensors can represent a variety of structured data. For example, we may represent attributed graphs using their node-node, node-edge, or edge-edge incidence matrices. In higher dimensions, incidence tensors can represent…
We prove a generalization of the Kolmogorov-Barzdin theorem for maps from simplicial complexes into Euclidean space. Along the way we introduce the notion of sparse maps and discuss maps from simplicial complexes with controlled 1-waist.
Motivated by distributed machine learning settings such as Federated Learning, we consider the problem of fitting a statistical model across a distributed collection of heterogeneous data sets whose similarity structure is encoded by a…
Sparse regression on a library of candidate features has developed as the prime method to discover the partial differential equation underlying a spatio-temporal data-set. These features consist of higher order derivatives, limiting model…