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HyperPatch: Sequential Knowledge Editing Under n-ary Structural Drift
Announce Type: new Abstract: Large Language Models (LLMs) rely on Knowledge Editing (KE) to maintain temporal validity, yet real-world knowledge is inherently n-ary. We demonstrate that in non-stationary environments, sequential updates to complex relations induce N-ary Structural Drift, a phenomenon where the binary reification of n-ary events into triples fractures relational atomicity. This precipitates Structure-Conditioned Knowledge Transfer Failure, a systematic mis-grounding of the...
The Size of the Intersection of $q$-ary Hamming Balls
Announce Type: cross Abstract: The interest in studying the size of the intersection of multiple $q$-ary Hamming balls has grown due to the recent advances in DNA-based data storage systems. We present an exact formula for the cardinality of the intersection of $s$ Hamming balls of varying radii over a $q$-ary alphabet. It is known that the distances between the center points of the Hamming balls are not enough, in general, to determine the size of the intersection.
Formal Foundations and Proof-Carrying Certificates for q-ary Covering Codes in Lean 4
Announce Type: new Abstract: Covering codes in finite Hamming spaces ask for small sets of words whose Hamming balls cover the whole space. This paper presents a Lean 4 formalization of the elementary theory of q-ary covering codes, centered on certificate predicates for upper bounds, lower bounds, and exact covering numbers $K_q(n,r)$. The formalization proves the q-ary Hamming-ball volume formula, the sphere-covering lower bound, elementary exact cases, product and relation rules, and...
Meta acquires robotics AI startup as it makes the push into humanoid machines
Meta acquires robotics AI startup as it makes the push into humanoid machines Meta has purchased Assured Robot Intelligence (ARI), a startup company that's building artificial intelligence for robots in order to "address critical challenges" in "high-value labor markets." The company is already working on robot hardware and AI in-house, but a spokesperson told Bloomberg that ARI "will bring a deep expertise in how [it] can design [its] models and frontier capabilities for robot control and...
On the Maximal Length of MDS Elliptic Codes
arXiv:2605.29439v2 Announce Type: replace Abstract: The determination of the maximal length of maximum distance separable (MDS) codes arising from elliptic curves is a central problem in coding theory. For an elliptic curve $E$ over $\mathbb{F}_q$, let $\operatorname{MEC}(k,q)$ denote the maximal length of a $q$-ary MDS elliptic code of dimension $k$. It was recently shown that $\operatorname{MEC}(k,q)\le\frac{q+1}{2}+\sqrt{q}$ for $q\ge289$ and $3\le k\le(q+1-2\sqrt{q})/10$, with equality...
Distributionally Robust Physical-Layer Security for Satellite Communication via Aerial Reconfigurable Intelligent Surface
arXiv:2605.31526v1 Announce Type: new Abstract: Satellite communications are envisioned as a key enabler for ubiquitous coverage in future 6G networks, yet the broadcast nature renders them vulnerable to eavesdropping, especially given the long-distance transmissions and associated high uncertainties. In this paper, we propose the physical layer security enhancement for multi-beam satellite communications with the assistance of an aerial reconfigurable intelligent surface (ARIS). Considering...
'Umpiring decisions go in their favour': Pakistan's Khushdil alleges bias towards India in cricket
Pakistan's all-rounder Khushdil Shah has claimed that India often benefits from favorable umpiring and match-related decisions during India-Pakistan encounters. Speaking on the ARY Podcast alongside teammate Abbas Afridi, Khushdil opened up about the unique pressure and emotions that surround India-Pakistan encounters. However, it was his remarks about alleged bias in key aspects of the game that quickly grabbed attention on social media.
Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits
arXiv:2602.03970v3 Announce Type: replace-cross Abstract: We study the statistical behavior of reasoning probes in a stylized model of iterative computation inspired by neural algorithmic reasoning. The underlying computation is given by a looped Boolean circuit whose graph is a perfect $\nu$-ary tree ($\nu\ge 2$), with outputs recursively fed back as inputs across computation rounds. A probe observes a sampled subset of internal nodes and seeks to infer the latent operation at each node,...
General Dynamics Will Spend $200 Million to Reboot Ammo Plant
A Ukrainian serviceman prepares 155mm artillery shells at a front line position in eastern Ukraine. Photographer: Aris Messinis/AFP/Getty Images
Weight distributions of two classes of linear codes with few weights derived from Weil sums
arXiv:2510.25578v2 Announce Type: replace Abstract: Linear codes with few weights have been a subject of study for many years, as they have applications in secret sharing, authentication codes, association schemes, and strongly regular graphs. In this article, two distinct classes of $p$-ary linear codes are constructed through the selection of two specific defining sets. Their weight distributions are completely determined for each case by detailed calculations on certain Weil sums.