arXiv:2604. 08485v2 Announce Type: replace-cross Abstract: The purpose of this paper is two-fold.
Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Computation and Language.
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 $d_1+d_2=n-1$.
The article reports a machine‑checked Lean 4 formalization of Dong and Yang’s classification of optimal finite‑length $(n,4)$ binary block codes for binary symmetric channels. The authors used an AI tool to feed the paper’s proofs into Lean, verified the main theorem statements and accepted axioms, and documented corrections, simplifications, and discrepancies found during the formalization. The Lean code is publicly available on GitHub.
arXiv:2609. 20231v1 Announce Type: cross Abstract: Let \(\cthreshold(n)\) be the largest integer \(q\) such that every loopless digraph on \(n\) vertices with at most \(q\) arcs is isomorphic to a spanning subdigraph of a self-complementary digraph of order \(n\).
arXiv:2409. 15600v3 Announce Type: replace Abstract: A representation of a molecule or material should be invariant to the symmetries of physics, unique, continuous, efficient and general.
The paper investigates the polynomial coefficients of lightning self‑attention, treating them as coordinates of an algebraic variety. In the single‑token case it identifies the coefficient variety as a rank‑constrained Chow‑type variety and derives algebraic equations; for multiple tokens it shows that linear relations reduce the geometry to coefficients involving interactions between distinct tokens, characterized by a common linear factor and a low‑rank condition. The authors provide explicit families of determinantal, Veronese‑type, and Sylvester resultant‑based invariants, and in the rank‑one case give pencil and flattening equations that define the variety set‑theoretically, with small‑dimension computations confirming the theoretical generators.
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 $n\le 10$.