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arXiv2026

On Inherent Privacy of Posterior Sampling: A Unified Rényi-Divergence Framework

Differential Privacy (DP) provides a rigorous framework for quantifying privacy guarantees. While most methods achieve DP by injecting calibrated random noise, the intrinsic randomness of certain procedures such as sampling can yield DP guarantees ``for free''. In this work, we develop a unified Rényi divergence framework to characterize the inherent DP guarantees of sampling from a Bayesian posterior distribution. We show that the privacy loss incurred by One-Posterior-Sampling (OPS) is governed by posterior exponential moments of the single-record log-likelihood ratio, and establish explicit DP guarantees under uniformly bounded, sub-Gaussian, or sub-exponential tail regimes. We apply the framework to representative Bayesian models, including categorical likelihoods with arbitrary priors, Gaussian-Gaussian conjugate pair, generalized linear models from the exponential family and linear regression with Gaussian likelihood, both with Gaussian priors on the regression coefficients. Our results elucidate sample size, model structure, neighboring relations in DP (bounded or unbounded), and how prior if applicable, jointly determine the inherent DP guarantees of OPS. Furthermore, our results recover the existing DP guarantees for OPS as special cases -- often with tighter privacy loss bounds -- and substantially broaden the class of Bayesian models for which the inherent DP guarantees of OPS can be rigorously characterized.

stat.ML↗

arXiv2026

The Density and Quantitative Upper Bound of Integers Not Expressible as the Sum of a Prime and a Zumkeller Number

A Zumkeller number is a positive integer whose set of positive divisors can be partitioned into two disjoint subsets of equal sums. In this paper, we investigate the additive properties of these numbers in conjunction with prime numbers. Specifically, we study the natural density of the exceptional set $\mathcal{E}$ consisting of all positive integers not expressible as the sum of a prime and a Zumkeller number. Let $α(x) = \#\{n \le x : n \in \mathcal{E}\}$ denote its counting function. We establish a quantitative upper bound for $α(x)$, demonstrating that $α(x) \ll x(\log \log x)^{-A}$, where $A = \log_2\left(\frac{2π^2}{2π^2-3}\right) \approx 0.2378$, thereby proving that the natural density of this exceptional set is $0$.

math.NT↗

arXiv2026

Radion/Dilaton portal freeze-in dark matter in extra-dimensional theories

We perform a comprehensive analysis of a radion/dilaton portal freeze-in dark matter in models of stabilized warped extra-dimensions. We show that the relic abundance of a generic dark matter particle (scalars, vectors, or fermions) is obtained via the conformal coupling of the radial mode in a consistent model stabilized warped extra- dimensions; our calculations show that in scenarios where the reheating temperature is much smaller than the radion mass, keV-TeV scale dark matter particles can saturate the relic density. We perform a comprehensive analysis of a radion/dilaton portal freeze-in dark matter in models of stabilized warped extra-dimensions. We show that the relic abundance of a generic dark matter particle (scalars, vectors, or fermions) is obtained via the conformal coupling of the radial mode in a consistent model stabilized warped extra- dimensions; our calculations show that in scenarios where the reheating temperature is much smaller than the radion mass, keV-TeV scale dark matter particles can saturate the relic density. Furthermore, we show that the model is subject to Lyman-alpha constraints in the keV-GeV range, providing a unique, model-independent probe of this sector. Our calculations extend previous attempts to calculate the freeze-in relic abundance in extra-dimensional portals by providing a consistent theoretical calculation of matrix elements, clearly laying out the underlying motivation and assumptions and providing a comprehensive account of the cosmological constraints on the model.

hep-ph↗

arXiv2026

Learning Across Temporal Graph Representation Silos

Temporal graph data are recorded in different representations, but whether these differences also determine the scope of learned knowledge reuse remains unclear. This study investigates whether predictive structure learned from relational histories can be reused between continuous-time dynamic graphs (CTDGs) and temporal knowledge graphs (TKGs). Bidirectional reuse emerges while retaining distinct input and prediction interfaces and independent vocabularies, and sources with the same representation are not always more useful. Controlled reorganizations of source histories show that the organization contributing to reuse varies across source-target conditions. We show that learned aspects of Relational Dynamics, the predictive structure present in relational histories, can be reused across conventional representation boundaries. Independently pretrained TKG and CTDG learners can also be fused at the score level to improve prediction on a third dataset without entity or relation-semantic alignment. Two proofs of concept in recommendation and security detection illustrate that external temporal sources without direct alignment can also become useful pretraining resources.

cs.LG↗

arXiv2026

Two-Way Coupled Dynamics of Quantized Vortex Bundle Formation in Spatially Periodic Normal-Fluid Turbulence

Using fully coupled two-way simulations combining the vortex filament model with the Navier--Stokes equations, we discover that quantized vortices in superfluid $^4$He are systematically rolled up into coherent bundles within normal-fluid vortex tubes. Although co-rotating quantized vortices do not aggregate spontaneously, mutual friction with the normal fluid actively drives their bundling, directly inheriting the spatial hierarchy of classical turbulence. Mutual friction excites high-wavenumber normal-fluid vortex tubes adjacent to quantized vortices, while the superfluid forms a nested structure of thick low-wavenumber outer tubes and fine high-wavenumber inner tubes around the vortex lines. A distinct time lag between superfluid kinetic energy and dissipation fuels the energy cascade, giving rise to Kolmogorov's $k^{-5/3}$ spectrum. Crucially, bundle lifetimes are governed by the ratio of the local coupling time scale $t_\mathrm{cl}$ to the Kolmogorov dissipation time scale $τ_η$ ($t_\mathrm{cl}/τ_η< 20$), leading to enhanced thermal stability at higher temperatures. These findings establish a unified mechanism for two-fluid multiscale vortex organization.

physics.flu-dyn↗

arXiv2026

Bridging the Topological Divide: Dual-Branch Graph Distillation with Semantic Priors for Robust Cold-Start Recommendation

Graph Collaborative Filtering models have achieved remarkable success in recommendation systems. However, they inherently suffer from a catastrophic representation collapse in strict cold-start scenarios due to the topological isolation of unobserved items. While integrating multi-modal semantic features offers a potential remedy, directly mapping isolated semantic attributes into a globally topology-driven collaborative space frequently precipitates representation degradation and optimization conflicts. To bridge this fundamental structural divide, we propose DualGCN, an innovative Dual-Branch Graph Knowledge Distillation Framework. Operating under a decoupled two-stage training paradigm, DualGCN first constructs a robust collaborative teacher network where item representations are anchored by a topology-smoothed semantic prior, effectively reshaping the latent manifold. Subsequently, a semantic student branch employs a residual mapping mechanism and a magnitude-agnostic cosine distillation objective to achieve high-fidelity cross-modal alignment without disrupting established collaborative signals. Furthermore, we introduce a dynamic norm reconstruction mechanism to rigorously calibrate the physical scales of novel and warm items during global retrieval. Extensive experiments across three real-world benchmark datasets demonstrate that DualGCN significantly outperforms state-of-the-art baselines in strict cold-start scenarios while comprehensively preserving recommendation accuracy for highly active items.

cs.IR↗

arXiv2026

Back on Track: Deployment-time Policy Improvement via World Model Planning

State-of-the-art visuomotor policies are increasingly capable of executing complex tasks, yet can fail during deployment in ways they cannot predict or recover from on their own. Improving their performance and robustness typically requires collecting more data, retraining, or modifying the policy architecture, all of which are time- and resource-intensive in practice. We instead propose an offline-trained monitoring-and-intervention framework that improves a policy during deployment using only black-box query access. From a limited set of labeled on-policy rollouts, we learn a policy-conditioned liveness value that measures the nominal policy's progress toward task completion; we additionally train a compact latent world model using these rollouts together with play data. At deployment, the liveness value continuously monitors execution. When it detects a loss of progress, a short-horizon planner searches the world model for corrective actions using the same value as its planning objective, after which control returns to the nominal policy. We evaluate our method on the LIBERO-Goal task suite and on a Franka Panda manipulator, using the vision-language-action model $π_{0.5}$ and a diffusion policy as nominal policies, and demonstrate significant improvements in task success rates, while supporting real-time control. Additional results and videos are available on the project website (https://policy-improvement-wm.pages.dev/).

cs.RO↗

arXiv2026

Maximizing Reaction via Spatial Localization: A PDE-Constrained Variational Approach

We study a PDE-constrained variational problem for the optimal spatial distribution of a catalytic material reacting with a substrate in a biological or materials system. With a given catalyst concentration, the substrate concentration is determined by a reaction-diffusion equation. The reaction functional for the catalyst concentrations is defined to be the total reaction output, which is the product of catalyst and substrate concentrations. Both the linear and Michaelis-Menten reaction kinetics are considered. We construct reaction-maximizing sequences through the localization of catalysts using barrier functions and show the non-existence of a global maximizer. We also derive the first and second variations of the reaction functional. By constructing a competing catalyst concentration, we show the non-existence of a local maximizer. Based on our analysis, we propose a regularized variational model and prove the existence of its global maximizer.

math.AP↗

arXiv2026

XferAgent: Cross-Agent Experience Transfer for Self-Improving LLM Agents

Large language model (LLM) agents can reuse experience from prior task executions to improve performance on subsequent tasks. Although existing methods enable cross-agent experience sharing, differences in agents' execution histories and task requirements make shared experiences difficult to reuse effectively. We propose XferAgent, a framework for cross-agent experience transfer that organizes reusable experience in local and shared experience graphs. XferAgent reconciles compatible contributions from heterogeneous agents while avoiding unreliable merges. For each new task, it selects shared experiences and integrates them with the target agent's local experience to support task execution. Experiments across diverse task domains show improvements over representative memory-based methods and effective experience transfer between heterogeneous agent frameworks. Cumulative task success also increases over successive task passes as agents update and reuse their experiences.

cs.MA↗

arXiv2026

Magnetic proximity beyond the interface: Layer-sequence-dependent exchange in WSe$_2$/CrI$_3$ heterostructures

Magnetic proximity effects in transition metal dichalcogenide (TMD)/2D-magnet heterostructures are often described in terms of the magnetization of the interfacial magnetic layer. Here, we show that this picture is sufficient to describe the neutral-exciton valley splitting of the TMD, but incomplete for its hole-doped electronic structure. We study a gate-tunable van der Waals heterostructure composed of monolayer WSe$_2$ in direct contact with trilayer CrI$_3$. By combining spatially and helicity-resolved reflection-contrast spectroscopy with magnetic circular dichroism, we identify two distinct magnetic domains in the trilayer CrI$_3$: one with purely antiferromagnetic interlayer coupling and one with a mixed antiferromagnetic (AFM)/ferromagnetic~(FM) coupling. In both domains, the sign of the neutral-exciton valley splitting of WSe$_2$ switches with the magnetization reversal of the adjacent CrI$_3$ layer. In contrast, helicity-resolved positive-trion spectroscopy of WSe$_2$ reveals a qualitatively different response. While the AFM domain shows a strongly helicity-selective trion resonance, the mixed AFM/FM domain exhibits trion resonances in both helicities. This behavior disappears when all CrI$_3$ layers are aligned in a parallel magnetization direction. Our results demonstrate that charged excitons are sensitive to the full layer-resolved magnetic sequence of the adjacent 2D-magnet, revealing magnetic proximity beyond the interface.

cond-mat.mtrl-sci↗

arXiv2026

Who's Behind the Text? Robust Model Authorship Attribution

As large language models (LLMs) are increasingly used to generate text, their misuse has become a growing societal problem, with implications for academic misconduct, model distillation, and cyberattacks. For these reasons, Model Authorship Attribution (MAA), which identifies the source model of a given text, is important for promoting the responsible use of LLMs and improving AI safety. In practice, attribution systems must remain reliable beyond the distributions observed during training. They may encounter texts from unseen domains and writing settings, as well as generations from future versions of model families that were not available when the system was trained. However, existing MAA methods often exhibit substantial performance degradation under such distribution shifts. To address this challenge, we propose Authorship Tracing via Likelihood-based Attribution of Sources (ATLAS), which formulates MAA through source-conditioned text modeling rather than direct source prediction. ATLAS learns how text from each source family is generated and attributes a given text by comparing its likelihood under each learned source condition. We aggregate this likelihood evidence at the token level with clipping so that no single token dominates the decision. We further introduce MAABench, a broad MAA benchmark for evaluating practical OOD settings such as domain and version. Our experiments show that ATLAS consistently outperforms existing baselines across MAABench and OpenTuringBench. In particular, when both the generation domain and the model version change on MAABench, ATLAS achieves 74.27% accuracy, 9.00pp higher than the strongest baseline. Beyond MAA, ATLAS can also help identify distillation source models by measuring which source model a target LLM most closely resembles. Our extended experiments show that ATLAS recovers the known teacher of every distilled model we evaluate.

cs.AI↗

arXiv2026

Full AFLs Closed under Nested Iterated $k$-Variate Substitution and Depth-k Storage Automata

Greibach and Ginsburg (1969) studied abstract families of languages or AFLs. A full AFL is a class of languages closed under the following operations: homomorphism, inverse homomorphism, intersection with regular languages, union, concatenation, and Kleene star. Greibach (1970) used a restricted substitution, called nested iterated substitution, to introduce the notion of super AFLs, which are full AFLs that are further closed under nested iterated substitution. The smallest super AFL was shown to be the class of all context-free languages. From this fact, we focus on Greibach's limited, univariable application of nested iterated substitution and further generalize it into k-variate. This introduces the notion of nested iterated $k$-variate substitution whose definition does not rely on "machines". Recently, a "two-tape" version of Hibbard's (1967) rewriting systems, which were later reformulated by Pighizzini and Pisoni (2014) as k-limited automata with "single" input/work tapes, has been studied under the name of depth-k storage automata. This work unearths a few characteristics of the languages recognized by those automata under a restriction known as frozen blank sensitivity in terms of full AFLs and nested iterated k-variate substitution. This will promote a further abstract treatment of those languages.

cs.FL↗

arXiv2026

A short open space curve of unit width

In this work, we propose a curve to be a minimum of length among rectifiable, continuous curves of unit width in three-dimensional Euclidean space. We show that a previously conjectured minimizer of that problem is not of unit width, give the numerical derivation of a candidate family of unit width curves, prove that it admits a strict local minimum within that candidate family and that this minimum is of unit width and length $3.905124162243593\ldots$. The curve consists of eight straight segments, two cone geodesics, and three circular helices. Its parameters are specified by a uniquely isolated solution of the joining and stationarity equations. To establish unit width in every direction, we combine analytic estimates with interval arithmetic on a finite covering of the remaining directions. We conjecture that the curve is globally minimizing. We supplement this work with the programs used to identify the candidates, replicate the computer-assisted parts of our proof, as well as a formalization of our proof in Lean.

math.MG↗

arXiv2026

Seven Limit Cycles in a Periodically Forced Three-Zone Equation

We construct a seven-cycle example for a periodically forced scalar equation with a continuous three-zone piecewise-linear nonlinearity. Symbolic integration and linear elimination reduce the four-flight matching conditions to two equations in the residence times. The competing exterior visits produce an additional turn of the critical response and lead to the rational parameters $(A,B,μ)=(9,3/2,181363/100000)$. At these parameters, finite Taylor estimates give three sign changes of the return displacement. Scalar order, analyticity along transverse itineraries, and half-period reflection then establish at least seven distinct isolated periodic orbits on the phase cylinder.

cs.SC↗

arXiv2026

Moral Combat: Exploiting Moral Foundations Theory to Jailbreak LLMs

Social psychology has long described how people can be persuaded to interpret a harmful act as moral. Recent research suggests that Large Language Models (LLMs) echo aspects of human psychology, from cognitive biases to social conformity. This raises a question with direct safety implications: can LLMs be moralized to bypass safety guardrails? We answer this question with a multi-agent framework grounded in Moral Foundations Theory (MFT). Given a harmful request that is initially refused, our agents diagnose which moral foundation (MF) the prompt is violating, identify a justifiable foundation under which the same request appears virtuous, rewrite the prompt accordingly, and reinforce it with generated precedents of comparable moral reframing. We evaluate our framework on harmful prompts from three well-known jailbreak datasets across five open-source and proprietary models. Our analysis reveals that models are highly susceptible to moralization, exhibiting high single-trial jailbreak rates with success increasing further under repeated attempts. We also find that safety benchmarks are imbalanced in the MFs they violate, concentrating on foundations toward which models already exhibit biases.

cs.CL↗

arXiv2026

Projected Wasserstein-Fisher-Rao Flows for Hawkes Background-Intensity Estimation

We consider the problem of estimating the background intensity of a Hawkes process when the triggering mechanism is known, treating the background as an unknown finite positive measure with a regular density. We propose a likelihood-based variational approach based on the Wasserstein-Fisher-Rao geometry. In this setting, the relevant first variations are naturally distribution-valued and therefore fall outside the classical gradient-flow formulation. We develop a distributional framework for the resulting dynamics and give them a finite-dimensional meaning through projections onto statistical manifolds. We identify the true background as the unique zero of a limiting generalized gradient and, under suitable stability, compactness, integrability and approximation conditions, establish a conditional consistency theorem for measurable estimators satisfying the empirical projected equations on events whose probabilities tend to one. Finally, we specialize the construction to Gaussian-mixture manifolds and obtain an explicit finite-dimensional scheme.

stat.ML↗

arXiv2026

JockeyBench: Evaluating LLM Agents on Horse-Racing Decision-Making

Repeated event forecasting requires extracting predictive signals from noisy evidence and evaluating their value across successive decisions. We introduce JockeyBench, a benchmark and evaluation protocol that studies this problem through historical Japanese horse racing. The protocol combines time-gated evidence, priced tools, paired frozen-program controls, and two workflows: executing an LLM-written predictor or acquiring evidence for a fresh per-race LLM forecast. Evaluation separates forecast quality, benchmark-specific net utility, and retrospective betting returns and risk under fixed decision rules. Across 28 model--scaffold configurations on 324 races, paired tests identify seven revision gains and two declines after multiple-testing correction. Yet every configuration has negative mean profit under capped-Kelly settlement. In a four-model comparison, the reusable-program workflow has higher mean betting profit and lower research fees, although both workflows lose on average. Further diagnostics reveal that mean probability bias reverses on selected bets and that profitable individual runs can depend on concentrated returns. These findings motivate evaluating predictive competence, adaptation, resource use, and decision value separately when assessing agents for repeated event forecasting.

cs.AI↗

arXiv2026

On the Isomorphism of Semicircular Algebras

Building on OpenAI's proof of isomorphism of free group factors, we give a self-contained proof of a corresponding result for $C^{*}$-algebras generated by free semicircular systems: the isomorphism class of a $C^{*}$-algebra generated by a semicircular $n$-tuple does not depend on $n\in\{2,3,\dots,+\infty\}$. Similarly, reduced free products of $n$ copies of the Jiang--Su algebra are isomorphic for different $n$ in this range. While reduced free group $C^{*}$-algebras of different ranks are not isomorphic (by a result of Pimsner--Voiculescu), we show that they have strong free absorption properties. At the heart of the proof is an automorphism approximation property for inclusions of $C^{*}$- and $W^{*}$-algebras; a relative version of that property was previously used to derive free complementation results.

math.OA↗