arXiv:2607. 10194v1 Announce Type: cross Abstract: We present IsalHG, a method for representing the structure of any finite, connected hypergraph of bounded hyperedge arity as a string over a compact instruction alphabet $\Sigma_{\mathrm{HG}}$.
arXiv:2605. 21510v2 Announce Type: replace-cross Abstract: Reference-based graph compression encodes each vertex's neighbor list as differences from a nearby encoded list.
arXiv:2608. 08118v1 Announce Type: new Abstract: There are several methods for searching for graphs with prescribed properties, such as SAT solvers and specialized generators.
arXiv:2608. 11716v1 Announce Type: new Abstract: Chain of Thought (CoT) lifts the expressive ceiling of bounded-depth Transformers, with characterizations tying the number of CoT steps to circuit complexity classes.
arXiv:2606. 18520v1 Announce Type: cross Abstract: Computing geometric representations of data is a cornerstone of modern machine learning, typically achieved by training dual encoders which map queries and documents into a shared embedding space.
Chain of Thought (CoT) lifts the expressive ceiling of bounded-depth Transformers, with characterizations tying the number of CoT steps to circuit complexity classes. What remains largely missing are concrete instantiations with explicit, depth-bounded constructions, and the traversal procedures such characterizations presuppose.
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: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.
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: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:2608. 10420v1 Announce Type: new Abstract: Reasoning shortcuts are solutions of a neurosymbolic system's rules that produce correct predictions through unintended concepts.
arXiv:2607. 23361v1 Announce Type: cross Abstract: Language generation in the limit is an elegant model introduced by Kleinberg and Mullainathan [KM24] to formally study language generation by an algorithm that learns solely based on example strings.
arXiv:2606. 24421v1 Announce Type: new Abstract: Spectral filtering recently delivered substantial pruning for \emph{static} subgraph matching: Laplacian interlacing rejects candidates whose neighborhoods cannot host the query.