arXiv preprints from January 1, 2026 through September 22, 2026 — 17:14:37 EST
Electro-optic frequency conversion and synthetic-frequency coupling are established functions in integrated photonic devices. Their role within a multiport switching fabric, however, depends on how simultaneous optical connections share spatial paths, frequency channels, and device controls. Here, we investigate how coherent coupling...
We identify a recurrent algebraic regularity in Transformer attention: a sparse subset of effective OV operators $T=OV^\top$ nearly closes under composition, $T^2\approxαT$. Across six pretrained endpoints spanning 2.8B--235B parameters, 3.98--8.00% of heads reach squared closure alignment $\mathcal{P}\geq0.9$, while no matched...
In this paper we study the motivic Chabauty--Kim method, which aims to determine the set of $S$-integral points of $\mathbb{P}^1\smallsetminus \{0,1,\infty\}$, over cyclotomic fields. We focus on the case $K=\mathbb{Q}(ζ_8)$ and $S=\left\{(1-ζ_8)\right\}$, where we obtain explicit polylogarithmic Kim functions up to depth $4$ and...
We investigate pattern formation in generic two-species reaction--diffusion systems with chemotaxis. We show that chemotaxis can give rise to a striking nonmonotonic dependence of pattern formation on its strength, opening the possibility of re-entrant transitions between patterned and homogeneous states controlled by chemotaxis. In...
Online adaptation can help edge time-series forecasting under distribution drift, but its measured benefit is sensitive to evaluation choices. We study six public multivariate streams, including building-sensor and smart-meter data, under a leakage-free streaming protocol. We identify two additional sources of comparison bias. First,...
The 21 cm hyperfine transition of neutral hydrogen provides one of the few direct probes of the early cosmic history. High-redshift detections of this signal could shine light on the poorly understood epochs of the Dark Ages and Cosmic Dawn, periods that remain among the least understood in the Universe's history. However, this signal...
Multinomial probit choice probabilities over n alternatives are Gaussian orthant integrals, computed by simulation for thirty years, one expensive integral per alternative. Inversion, which is to say determining item attractiveness consistent with a prescribed choice probability vector, is even more difficult and has been considered...
Reconstructing a damaged musical fragment is an inverse problem: the observed sequence contains partial information, while a raga encodes constraints limiting allowable completions. This paper formalizes a mathematical framework for this, proposing the Artificial Rosetta Stone (ARS). We separate three claims often conflated: a...
Uniform-state discrete diffusion models update all tokens in parallel while keeping every position revisable. Even when the commonly used top-$p$ rule leaves only one candidate at a position, that choice affects only the current reverse step and can be revised at the next sampling step. We ask what changes when selected hypotheses...
The central flow of Cohen et al. (2025) is an empirically accurate continuous-time model of gradient descent at the edge of stability in deep learning, However, its derivation is heuristic. We propose a perturbative regime in which the central flow is the limit of gradient descent: we assume that the loss decomposes as $f = g +...
Conditional independence tests (CITs) test for conditional dependence between two random objects $X$ and $Y$ given a third random object $Z$. Existing CITs have limited applicability to high-dimensional data, especially multimodal data like text. However, we show that such tests are of interest for large language model (LLM) outputs,...
Sampling from distributions conditioned on desired semantic properties is an emerging challenge in modern generative modeling. Metropolis-Hastings (MH) provides a principled route to conditional sampling, but requires access to exact pointwise target-density evaluations, which are not available in generative settings. Meanwhile,...
We consider semi-supervised classification from a partially classified sample arising from a two-component Weibull mixture. The feature is observed for all data, whereas some class labels are missing. The probability of a missing label is modelled as a function of classification uncertainty, giving a feature-dependent...
High-dimensional clustering is challenging when component distributions are both heavy-tailed and directionally asymmetric. We propose a deep skew-$t$ mixture model (DStMM), a hierarchical factor-analytic mixture based on the generalised-hyperbolic skew-$t$ normal mean--variance representation. A shared inverse-gamma mixing variable...
Fixed-width sequential stopping rules terminate a stochastic simulation once an estimated confidence interval reaches a prescribed width. Classical fixed-width theory typically relies on a strongly consistent estimator of the asymptotic variance. This makes the normalized stopping time asymptotically deterministic, allowing...
Post-hoc out-of-distribution detectors are fitted on a finite reference set, so every score they produce is an estimate. If we had chosen a different set, some verdicts would have moved. We measure that movement by resampling the reference set and recording the bootstrap standard deviation of the score, which we call verdict...
We introduce a closed-form, refit-free procedure for leave-one-cluster-out (LOCO) cross-validation in multilevel Gaussian Bayesian structural equation models (SEMs), together with predictive scoring of every nested submodel. Conditional independence of clusters given the parameters expresses the cluster-deleted posterior as a...
Matrix-variate data with missing entries arise frequently in applications where observations are naturally organized as two-dimensional arrays. Although the matrix normal distribution provides a parsimonious model through its Kronecker covariance structure, standard EM estimation can be computationally expensive because arbitrary...
Many sequential distribution shift detectors update a growing reference set with incoming observations. After a change, this update contaminates the reference set with post-change observations and can weaken subsequent evidence. Keeping the calibration sample fixed mitigates this contamination, but repeated reuse induces dependence...
Set-based genetic association tests provide a powerful framework for detecting genetic effects on complex traits by jointly analyzing multiple genetic variants. Although set-based methods have been developed for interval-censored survival outcomes, existing approaches primarily focus on a single survival phenotype and therefore do not...
Gibbs sampling and coordinate ascent variational inference (CAVI) are two basic coordinate-wise methods for statistical computation. Recent analyses under strong log-concavity establish convergence rates for versions of these algorithms that update one uniformly selected block at each step. We extend both results to arbitrary fixed,...
This paper develops a general convolutional neural network (CNN) framework for detecting heterogeneous event-driven dynamics in univariate time series windows. We show that the induced CNN class exactly represents classifiers based on range, maximum drawup, maximum drawdown and slope change, and uniformly approximates realised...
We propose a generalized Bayesian clustering with regression model for unaligned longitudinal binary outcomes, motivated by seizure diary data from the Human Epilepsy Project. Seizure diaries are sparse, irregularly observed, and vary enormously across patients. A single fully-specified generative model tends to be either misspecified...
Gaussian graphical models (GGMs) describe the dependence structure among jointly Gaussian random variables. However, the most common parameterisation of GGMs, the precision matrix, describes both the dependence and scale of the variables. This has been shown to lead to model selection methods that depend on the scale of the variables,...
This work shows that diffusion models learned with standard denoising loss can provide effective global MCMC proposals for complex high-dimensional target densities. The method is motivated by the observation that sequentially applying a forward and reverse diffusion process defines a Markov chain with a target stationary distribution...