arXiv Machine Learning
1d ago
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 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
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
6d ago
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 AI
Jun 10
Moonshine: An Autonomous Mathematical Research Agent Centered on Conjecture Generation
arXiv:2606. 10806v1 Announce Type: new Abstract: Moonshine is an autonomous agent whose central objective is to generate mathematical conjectures.
arXiv AI
Jul 28
Formalizing Flag Algebras in Lean
arXiv:2607. 23500v1 Announce Type: cross Abstract: Razborov's flag algebra method is a powerful tool for proving asymptotic inequalities in extremal graph theory, often reducing the task to finding a finite certificate by semidefinite programming.
arXiv Machine Learning
23h ago
Fourth-Moment Geometry of Rademacher Sums
arXiv:2608. 17802v1 Announce Type: new Abstract: Let $\varepsilon_1,\ldots,\varepsilon_n$ be independent Rademacher signs and let $a=(a_1,\ldots,a_n)\in\R^n$ satisfy the normalization below.
arXiv AI
Aug 6
On Hamming-Lipschitz Type Stability of the Subdominant (Minmax) Ultrametric: Theory and Simple Proofs
arXiv:2608. 04014v1 Announce Type: cross Abstract: The subdominant (minmax) ultrametric is a canonical tree-structured summary of a dissimilarity matrix, arising equivalently as the ultrametric induced by single-linkage clustering.