arXiv Machine Learning
Aug 18
The canonical facets of multi-separator polytopes
arXiv:2608. 16861v1 Announce Type: cross Abstract: We initiate a polyhedral study of the graph multi-separator problem proposed by Irmai et al.
Pyramidal Width Can Increase Under Vertex Insertion
arXiv:2607. 29555v1 Announce Type: new Abstract: Lacoste-Julien and Jaggi conjectured in 2015 that the pyramidal width of a polytope cannot increase when a vertex is added, provided that every old point remains a vertex.
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arXiv AI
Jul 1
Improved Upper Bounds for Slicing the Hypercube
arXiv:2602. 16807v2 Announce Type: replace Abstract: A collection of hyperplanes $\mathcal{H}$ slices all edges of the $n$-dimensional hypercube $Q_n$ with vertex set $\{-1,1\}^n$ if, for every edge $e$ in the hypercube, there exists a hyperplane in $\mathcal{H}$ intersecting $e$ in its interior.
arXiv Machine Learning
Jun 30
Chamber geometry and specification numbers of Boolean threshold functions
arXiv:2606. 29477v1 Announce Type: cross Abstract: The specification number $\sigma_n(f)$ of a Boolean threshold function $f$ on $n$ variables is the least number of points whose $f$-values determine $f$ uniquely among all threshold functions.
arXiv AI
Sep 15
Edge-addition monotonicity of positive p-energy fails for every p >= 1
arXiv:2609.13476v1 Announce Type: cross Abstract: At a 2021 AIM workshop, Guo conjectured that the positive square energy s+ = E+_2 should inherit the familiar edge-addition monotonicity of the spect...
arXiv Machine Learning
Jul 7
A simplex-based measure of symmetry
arXiv:2607. 03815v1 Announce Type: cross Abstract: For compact convex sets $L,K \subset \mathbb{R}^n$, denote by $\lambda_K(L)$ the smallest size of a homothet of $K$ that contains $L$.
arXiv AI
Aug 11
Exact Zarankiewicz Values On Two Finite Frontier Slices
arXiv:2608. 08154v1 Announce Type: cross Abstract: The Zarankiewicz number Z(m,n,s,t) is the maximum number of edges in a bipartite graph with parts of orders m and n containing no copy of Ks,t.
arXiv Machine Learning
1d ago
Geometry-Dependent Bounds for Online Non-Monotone DR-Submodular Maximization
arXiv:2610. 00545v1 Announce Type: new Abstract: We study adversarial online maximization of nonnegative, non-monotone DR-submodular functions over compact convex down-closed sets.
arXiv Machine Learning
Aug 18
High-Dimensional Nonparametric Change-Point Detection via Low-Rank Degree-Three Density Projection
arXiv:2608. 15466v1 Announce Type: new Abstract: Distributional changes can be invisible to means and covariances yet appear in skewness, asymmetric interactions, or other third-order structure.
arXiv AI
Sep 16
On the Expressive Power of Implicit Line-Graph Higher-Order Weisfeiler--Leman
arXiv:2609.16412v1 Announce Type: cross Abstract: Whitney's theorem allows isomorphism testing for connected simple graphs, apart from $K_3$ and $K_{1,3}$, to be formulated as distinguishing their li...
arXiv AI
Aug 13
A Forced-Structure Reduction and Verifiable Bounds for Conway's 99-Graph
arXiv:2608. 11211v1 Announce Type: new Abstract: Conway's 99-graph problem asks whether a strongly regular graph with parameters $\mathrm{srg}(99,14,1,2)$ exists.
arXiv Machine Learning
Jul 27
Shallower ReLU Network Representations via Exact Linear Algebra
arXiv:2607. 21651v1 Announce Type: new Abstract: We prove that the maximum of $n$ real numbers is exactly representable by a ReLU network with two hidden layers for every $n\le 10$.
arXiv Machine Learning
Sep 2
A penalised Saito functional for heuristic search of free line arrangements
arXiv:2604. 02995v3 Announce Type: replace-cross Abstract: We introduce the penalised Saito functional $\mathfrak S_{\lambda,\beta}(\mathcal{A};d_1,d_2)$ for a reduced arrangement $\mathcal{A}$ of $n$ lines and a prescribed pair $d_1+d_2=n-1$.