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A universal complementarity identity for polarized double-slit interferometry
arXiv:2604.18760v2 Announce Type: replace-cross Abstract: An exact identity is established among four experimentally accessible quantities in polarized double-slit interferometry: the phase-reference-dependent in-phase and quadrature components $V_A$ and $V_N$ of fringe visibility, the path predictability $\mathcal{P}$, and the mixedness $\mathcal{I}$ of the reduced path state satisfy $V_A^2+V_N^2+\mathcal{P}^2+\mathcal{I}^2=1$. The identity is an algebraic consequence of positivity and...
DynMuon: A Dynamic Spectral Shaping View of Muon
arXiv:2605.17109v3 Announce Type: replace Abstract: In recent years, Muon has emerged as the dominant method for training large language models, and transformers more broadly. The essential difference, when compared to standard gradient descent methods, is to replace the usual update matrix $M=U\Sigma V^\top$ with its polar factor $UV^\top$. In this work, we consider a class of Muon-like updates, where we replace the update $M$ with $U\Sigma^p V^\top$ for some parameter $p$. We call this a...
P-Cast Precision in FP8 Attention: Sink-Induced Collapse and the Optimality of S=2^8
arXiv:2606.06521v1 Announce Type: new Abstract: FP8 (E4M3) acceleration for attention computation offers significant throughput gains, but the 3-bit mantissa introduces precision challenges when the softmax probability matrix P is cast to FP8 before the P*V matrix multiplication. We analyze two implementation choices that affect output precision under the Attention Sink phenomenon: (1) the KV block iteration order, and (2) the static scaling factor applied to P before casting.
Strong Polarization and Entropy
arXiv:2606.02567v1 Announce Type: cross Abstract: We show that for any set of $n$ unit vectors $v_1,\ldots,v_n$ in a real Hilbert space and positive numbers $p_1,\ldots,p_n$ satisfying $\sum_j p_j = 1$, there exists a unit vector $u$ such that \[ \sum_{j=1}^n \frac{p_j^2}{\langle v_j, u\rangle^2}\leq 1. This inequality is a weighted version of the strong polarization inequality. As immediate corollaries, it yields a polarization inequality for products of powers of linear functionals and a...
Decomposing tournaments into comparability graphs
Announce Type: cross Abstract: In this note, we introduce the \emph{partial order decomposition number} of a digraph $D$, denoted $pod(D)$, defined as the minimum integer $k$ such that $A(D)=A(P_1)\cup\cdots\cup A(P_k)$, where $P_1,\ldots,P_k$ are partial orders on $V(D)$. We prove that $\dic(D)\le \diomega(D)^{pod(D)}$ for every digraph $D$. In particular, every class of digraphs with bounded $pod$ is polynomially $\dic$-bounded. We apply this to tournaments, showing that if $\mathcal C$ is...
Building user-driven climate adaptation products
Abstract Climate adaptation products have traditionally been developed using a supply-driven model reliant on available climate information, leading to usability gaps1,2,3,4. To better meet user needs, the climate services field has recognized a need to shift towards a demand-driven model emphasizing co-production, that is, user-driven, scientifically informed products created through shared knowledge practices1,2,3,4,5. However, co-production can be challenging, especially for researchers...
On the sharp linear convergence rate of the circumcentered--reflection method on subspaces
arXiv:2606.07888v1 Announce Type: cross Abstract: For two subspaces $U,V\subseteq\RR^n$, the circumcentered--reflection method (CRM) of Behling, Bello-Cruz, and Santos~\cite{BBS2018} computes the projection onto $U\cap V$ using only the reflections across $U$ and $V$, with known linear-convergence rate $c_F$, the cosine of the Friedrichs angle. We prove that, when CRM is initialized in $V$, it contracts at the strictly smaller rate...
Depth-Dependent Indirect Prompt Injection in Tool-Calling ReAct Agents: Injection Depth, Payload Framing, and Turn-Budget Sensitivity
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Generative Drifting is Secretly Score Matching: a Spectral and Variational Perspective
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Not All Warm Starts Help: Benchmarking Primal-Dual Initializations for ACOPF Algorithms
arXiv:2606.08984v1 Announce Type: cross Abstract: Warm starts are widely used to accelerate AC optimal power flow (ACOPF) solves, but the impact of different initialization strategies has received limited systematic study, particularly for the primal-dual interior-point methods that dominate large-scale ACOPF algorithms. This paper benchmarks initialization strategies for ACOPF solved with the interior-point solver IPOPT on 19 PGLib-OPF instances (5 to 30,000 buses), testing all 15 non-empty...