Related papers: Convexity Certificates from Hessians

A homomorphism from a graph G to a graph H is a function from the vertices of G to the vertices of H that preserves edges. A homomorphism is surjective if it uses all of the vertices of H and it is a compaction if it uses all of the…

In this paper, we study the problem of certifying whether a graph is bipartite (i.e. $2$-colorable) with a locally checkable proof (LCP) that is able to hide a $2$-coloring from the verifier. More precisely, we say an LCP for $2$-coloring…

This paper presents the 'hyper-sinh', a variation of the m-arcsinh activation function suitable for Deep Learning (DL)-based algorithms for supervised learning, such as Convolutional Neural Networks (CNN). hyper-sinh, developed in the open…

We study the problem of variable selection in convex nonparametric regression. Under the assumption that the true regression function is convex and sparse, we develop a screening procedure to select a subset of variables that contains the…

We develop and analyze a variant of Nesterov's accelerated gradient descent (AGD) for minimization of smooth non-convex functions. We prove that one of two cases occurs: either our AGD variant converges quickly, as if the function was…

The study of convex functions - in particular, of their optimization (really minimization) is one of the most important fields of applied mathematics. Convexity seems to be one of those incredibly well-chosen hypotheses which is just…

Counting small cohesive subgraphs in a graph is a fundamental operation with numerous applications in graph analysis. Previous studies on cohesive subgraph counting are mainly based on the clique model, which aim to count the number of…

Hyperspectral image (HSI) classification involves assigning unique labels to each pixel to identify various land cover categories. While deep classifiers have achieved high predictive accuracy in this field, they lack the ability to…

Prompted by an example related to the tensor algebra, we introduce and investigate a stronger version of the notion of separable functor that we call heavily separable. We test this notion on several functors traditionally connected to the…

Symbolic regression aims to find a function that best explains the relationship between independent variables and the objective value based on a given set of sample data. Genetic programming (GP) is usually considered as an appropriate…

Dijkstra observed that verifying correctness of a program is difficult and conjectured that derivation of a program hand-in-hand with its proof of correctness was the answer. We illustrate this goal-oriented approach by applying it to the…

Deep learning methods have proved highly effective for classification and image recognition problems. In this paper, we ask whether this success can be transferred to hypothesis testing: if a neural network can distinguish, for example, an…

The \textsc{Degree Realization} problem with respect to a graph family $\mathcal{F}$ is defined as follows. The input is a sequence $d$ of $n$ positive integers, and the goal is to decide whether there exists a graph $G \in \mathcal{F}$…

We propose Convexity-Driven Projection (CDP), a boundary-free linear method for dimensionality reduction of point clouds that targets preserving detour-induced local non-convexity. CDP builds a $k$-NN graph, identifies admissible pairs…

Mathematical models are sometime given as functions of independent input variables and equations or inequations connecting the input variables. A probabilistic characterization of such models results in treating them as functions with…

Conformal prediction is widely adopted in uncertainty quantification, due to its post-hoc, distribution-free, and model-agnostic properties. In the realm of modern deep learning, researchers have proposed Feature Conformal Prediction (FCP),…

In many real-world network datasets such as co-authorship, co-citation, email communication, etc., relationships are complex and go beyond pairwise. Hypergraphs provide a flexible and natural modeling tool to model such complex…

Verifying that input-output relationships of a neural network conform to prescribed operational specifications is a key enabler towards deploying these networks in safety-critical applications. Semidefinite programming (SDP)-based…

Given a real-valued function defined on the Heisenberg group, we provide a definition of abstract convexity and Fenchel transform that takes into account the sub-Riemannian structure of the group. In our main result, we prove that, likewise…

Models like support vector machines or Gaussian process regression often require positive semi-definite kernels. These kernels may be based on distance functions. While definiteness is proven for common distances and kernels, a proof for a…