Related papers: Sparse Dowker Nerves
We propose a new approach for metric learning by framing it as learning a sparse combination of locally discriminative metrics that are inexpensive to generate from the training data. This flexible framework allows us to naturally derive…
We address the basic question in discrete Morse theory of combining discrete gradient fields that are partially defined on subsets of the given complex. This is a well-posed question when the discrete gradient field $V$ is generated using a…
This paper proposes and illustrates a general framework to integrate the areas of vision research and complex networks. Each image pixel is associated to a network node and the Euclidean distance between the visual properties (e.g.…
Balancing predictive power and interpretability has long been a challenging research area, particularly in powerful yet complex models like neural networks, where nonlinearity obstructs direct interpretation. This paper introduces a novel…
Modern artificial intelligence has revolutionized our ability to extract rich and versatile data representations across scientific disciplines. Yet, the statistical properties of these representations remain poorly controlled, causing…
Inspired by Kalikow-type decompositions, we introduce a new stochastic model of infinite neuronal networks, for which we establish sharp oracle inequalities for Lasso methods and restricted eigenvalue properties for the associated Gram…
Most adversarial attacks on point clouds perturb a large number of points, causing widespread geometric changes and limiting applicability in real-world scenarios. While recent works explore sparse attacks by modifying only a few points,…
That neural networks may be pruned to high sparsities and retain high accuracy is well established. Recent research efforts focus on pruning immediately after initialization so as to allow the computational savings afforded by sparsity to…
Sparse deep learning aims to address the challenge of huge storage consumption by deep neural networks, and to recover the sparse structure of target functions. Although tremendous empirical successes have been achieved, most sparse deep…
Sparse neural networks have received increasing interest due to their small size compared to dense networks. Nevertheless, most existing works on neural network theory have focused on dense neural networks, and the understanding of sparse…
Image convolutions have been a cornerstone of a great number of deep learning advances in computer vision. The research community is yet to settle on an equivalent operator for sparse, unstructured continuous data like point clouds and…
Utilizing uniformly distributed sparse annotations, weakly supervised learning alleviates the heavy reliance on fine-grained annotations in point cloud semantic segmentation tasks. However, few works discuss the inhomogeneity of sparse…
We show that hypernetworks can be regarded as posets which, in their turn, have a natural interpretation as simplicial complexes and, as such, are endowed with an intrinsic notion of curvature, namely the Forman Ricci curvature, that…
Despite strong empirical performance for image classification, deep neural networks are often regarded as ``black boxes'' and they are difficult to interpret. On the other hand, sparse convolutional models, which assume that a signal can be…
We study a class of dynamical networks modeled by linear and time-invariant systems which are described by state-space realizations. For these networks, we investigate the relations between various types of factorizations which preserve the…
In this paper, we introduce new density-sensitive bifiltrations for data using the framework of Dowker complexes. Previously, Dowker complexes were studied to address directional or bivariate data whereas density-sensitive bifiltrations on…
This paper presents a Sparse Hierarchical Fourier Interaction Networks, an architectural building block that unifies three complementary principles of frequency domain modeling: A hierarchical patch wise Fourier transform that affords…
Simplicial complexes can be viewed as high dimensional generalizations of graphs that explicitly encode multi-way ordered relations between vertices at different resolutions, all at once. This concept is central towards detection of higher…
We introduce "weakly chained spaces", which need not be locally connected or path connected, but for which one has a reasonable notion of generalized fundamental group and associated generalized universal cover. We show that in the compact…
When modeling network data using a latent position model, it is typical to assume that the nodes' positions are independently and identically distributed. However, this assumption implies the average node degree grows linearly with the…