Related papers: Sparse Dowker Nerves
The alpha complex efficiently computes persistent homology of a point cloud $X$ in Euclidean space when the dimension $d$ is low. Given a subset $A$ of $X$, relative persistent homology can be computed as the persistent homology of the…
We derive exact equations for the spectral density of sparse networks with an arbitrary distribution of the number of single edges and triangles per node. These equations enable a systematic investigation of the effect of clustering on the…
We present a parallelizable algorithm for computing the persistent homology of a filtered chain complex. Our approach differs from the commonly used reduction algorithm by first computing persistence pairs within local chunks, then…
In model-based-clustering mixture models are used to group data points into clusters. A useful concept introduced for Gaussian mixtures by Malsiner Walli et al (2016) are sparse finite mixtures, where the prior distribution on the weight…
Given the ever-increasing size of modern neural networks, the significance of sparse architectures has surged due to their accelerated inference speeds and minimal memory demands. When it comes to global pruning techniques, Iterative…
We propose a neural network for 3D point cloud processing that exploits `spherical' convolution kernels and octree partitioning of space. The proposed metric-based spherical kernels systematically quantize point neighborhoods to identify…
Recently, neural network architectures have been developed to accommodate when the data has the structure of a graph or, more generally, a hypergraph. While useful, graph structures can be potentially limiting. Hypergraph structures in…
The use of Gaussian process models is typically limited to datasets with a few tens of thousands of observations due to their complexity and memory footprint. The two most commonly used methods to overcome this limitation are 1) the…
Deep neural networks (DNNs) have emerged as key enablers of machine learning. Applying larger DNNs to more diverse applications is an important challenge. The computations performed during DNN training and inference are dominated by…
Sparse coding can learn good robust representation to noise and model more higher-order representation for image classification. However, the inference algorithm is computationally expensive even though the supervised signals are used to…
Sparse expert models are a thirty-year old concept re-emerging as a popular architecture in deep learning. This class of architecture encompasses Mixture-of-Experts, Switch Transformers, Routing Networks, BASE layers, and others, all with…
From the moment Neural Networks dominated the scene for image processing, the computational complexity needed to solve the targeted tasks skyrocketed: against such an unsustainable trend, many strategies have been developed, ambitiously…
Sparse neural networks are often hypothesized to be more interpretable than dense models, motivated by findings that weight sparsity can produce compact circuits in language models. However, it remains unclear whether structural sparsity…
Computation of the simplicial complexes of a large point cloud often relies on extracting a sample, to reduce the associated computational burden. The study considers sampling critical points of a Morse function associated to a point cloud,…
We show how fitting sparse linear models over learned deep feature representations can lead to more debuggable neural networks. These networks remain highly accurate while also being more amenable to human interpretation, as we demonstrate…
Deep neural networks with lots of parameters are typically used for large-scale computer vision tasks such as image classification. This is a result of using dense matrix multiplications and convolutions. However, sparse computations are…
Identifying the structural priors that enable Deep Neural Networks (DNNs) to overcome the curse of dimensionality is a fundamental challenge in machine learning theory. Existing literature suggests that effective high-dimensional learning…
Recent years have seen an increasing popularity of learning the sparse \emph{changes} in Markov Networks. Changes in the structure of Markov Networks reflect alternations of interactions between random variables under different regimes and…
The Discrete Morse Theory of Forman appeared to be useful for providing filtration-preserving reductions of complexes in the study of persistent homology. So far, the algorithms computing discrete Morse matchings have only been used for…
In this paper, we investigate the Rademacher complexity of deep sparse neural networks, where each neuron receives a small number of inputs. We prove generalization bounds for multilayered sparse ReLU neural networks, including…