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arXiv2026

Assouad type dimensions of generalized affine fractal interpolation functions and their applications

In this article, we investigate the Assouad spectrum and Assouad dimension of graphs of fractal functions generated by generalized affine iterated function systems. We establish upper and lower bounds for the Assouad spectrum in terms of the scaling functions and the underlying partition of the generalized affine construction. If the scaling function is Lipschitz continuous and the partition is uniform, we obtain an explicit expression for the Assouad spectrum of the associated graph. These results provide a connection between the parameters defining the generalized affine fractal function and the local multiscale geometry of its graph. As applications, we consider two classic examples of generalized affine fractal functions, namely the Weierstrass and Takagi functions. For the classical Weierstrass function $W$, whose graph $Γ_W$ has the box dimension $2+\log_Nλ$, we obtain \[ \dim_A^θ(Γ_W) \leq \frac{2+\log_Nλ-θ}{1-θ}, \qquad θ\in \left(0,\log_N\frac{1}λ\right). \] and if $λ^2 N <1$, we get \[ \dim_A(Γ_W)\geq 1 +\log_N\left(\frac{1}λ\right). \] For the classical Takagi function $T$ with graph $Γ_T$, we show that \[ \dim_A^θ(Γ_T)=1, θ\in(0,1), \] and consequently its quasi-Assouad dimension is equal to $1.$ These results settle an open problem on dimension of graphs posed by Fraser.

math.DS↗

arXiv2026

Mitigating Representation Gaps in Amortized Bayesian Inference with Auxiliary Supervision

Casting Bayesian inference as a neural network optimization problem targeting an amortized posterior is attractive, as it extends to otherwise intractable statistical models and offers near instantaneous inference for new datasets after prepaying the training cost. Although theory guarantees faithfulness under ideal convergence, practical amortized inference still requires iterating over architectures and optimization choices and ultimately ``satisficing'' under finite simulation, compute, and time budgets. Even the best-performing solution may thus retain avoidable representation gaps that typically require problem-specific fixes. Here, we propose a generic alternative which improves training dynamics with auxiliary guidance losses applied to internal representations. Specifically, we show how such guidance leads to faster convergence when training data is abundant and to better performance when it is scarce. We formalize representation gaps as getting stuck in a local optimum at the information bottleneck between the parts of the network tasked with feature learning and those tasked with conditional distribution learning, and offer a generic diagnostic to separate summary failures from inference failures. Finally, we demonstrate that auxiliary supervision improves convergence speed and accuracy on a range of challenging real-world inference problems.

stat.ML↗

arXiv2026

Discrete Forcing: Infusing Discrete Guidance into Continuous Denoising for Few-Step Action Experts

Efficient action generation in vision-language-action (VLA) models requires capturing both coarse action structure and fine-grained details. Discrete action tokens provide compact structural representations but sacrifice precision, while continuous action tokens offer high precision but often require multiple denoising steps. We introduce Discrete Forcing, a flow-matching framework that combines these representations through an explicit coarse-to-fine generation process. It first predicts discrete action tokens to establish a coarse action structure, then uses them to guide continuous action refinement. The discrete and continuous components share a common diffusion transformer backbone with specialized branches, maintaining a parameter count comparable to a conventional single-branch model while requiring only one forward pass per branch. Extensive evaluations across multiple benchmarks demonstrate improved performance and faster inference over a parameter-matched continuous action expert, with consistent performance gains as model capacity increases. Real-world experiments further demonstrate improvements on high-precision and dynamic manipulation tasks.

cs.RO↗

arXiv2026

Lens Flare Removal and Reconstruction

The presence of lens flares in images can significantly reduce the quality of downstream application results for tasks such as 3D scene reconstruction. This is because lens flares are a property of the camera imaging system, and not a part of the underlying scene being modeled. There are previous methods that tackle the removal of small flares focused around a light source. However, existing methods struggle with large flares, such as those that fill the entire image. In this work, we compile a novel dataset for large-flare removal, combining publicly available real-world data with a procedural generation pipeline. We fine-tune a diffusion-based model on our dataset to remove complex, large lens flares. On the other hand, lens flares remain effective artistic tools, widely used in the media. While there are ways to simulate 2D flares, representing and reconstructing lens flares consistently across multiple views has not yet been explored. To achieve this, we introduce a flare representation model that leverages the symmetry of lens flares about the camera's principal point. We propose a computational pipeline to jointly optimize this flare model and a Gaussian splatting model (3DGS). This enables the decomposition of a 3D scene into lens flares and the scene itself, using our flare-removal model. Because the reconstructed flare is explicit and re-renderable, it can be edited and transferred to novel images and new 3D scenes. We evaluate removal on an established benchmark and a new one for large reflective flares, quantify the flare/scene decomposition directly, and show that the pipeline is robust to errors in automatic light-source localization.

cs.CV↗

arXiv2026

Optimal local recovery cannot alter critical orthogonality exponents in quantum spin environments

We prove a local amplitude-ratio bound for positive ground states and an explicit reverse comparison for fidelity under finite-region erasure. An exact lattice calculation for a connected critical Ising chain gives amplitude exponent $1/8$, preserved by arbitrary optimal control on any fixed spin set and, at the level of logarithmic exponents, on $o(\log N)$ spins. We derive the finite Cauchy product and its uniform strip asymptotics, and document exact two-spin optimization and an interferometric protocol for measuring the recovery. A separate finite-mediator theorem quantifies local compression and a decoder while retaining the rest of the environment exactly. We also give a ground-preparation Ramsey bound, counterexamples to stronger projected-state inferences, and independent full-Hamiltonian calculations.

quant-ph↗

arXiv2026

Supermassive charged gravitinos and the Lux-Zeplin event

The Lux-Zeplin collaboration recently reported one unusual event which was interpreted as first evidence for a WIMP (arXiv:2609.02823[hep-ex]). In this note we offer an alternative explanation of this event, following our earlier proposal that dark matter could consist of fractionally charged supermassive gravitinos. A main difference between the two interpretations is that one expects small cross sections and large flux rates for WIMPs, whereas it is the opposite for supermassive gravitinos, namely large (electromagnetic) cross sections and very low flux rates. The observed nuclear recoil energy of about 250 keV and the occurrence of one event in one year fit well with the estimates quoted in (K.A. Meissner, H.~Nicolai, Eur.Phys.J.C 84 (2024) 3, 269). A main characteristic of the new interpretation distinguishing it unequivocally from the WIMP hypothesis would be the sequential occurrence of two or more recoils within a few microseconds along the gravitino's straight trajectory, a prediction that remains to be checked. Such a measurement would also allow to overcome the `neutrino floor'. In this note we refine our previous estimates and propose some extra steps so as to enable the experiment to discriminate between the WIMP and gravitino hypotheses.

hep-ph↗

arXiv2026

Extending eBPF observability to Non-standard execution environments

eBPF observability of non-standard execution environments (NEEs) like TEEs or LibOSes is hindered by their unconventional exception-handling and memory-access mechanisms that limit standard Linux tooling. This work introduces two mechanisms that enable eBPF-based observability for NEEs: (1) kernel memory extensions for safely accessing NEE memory from eBPF programs, and (2) a lightweight flexible probe performance measurement unit (LWFP PMU) that provides flexible and generic probing, for NEEs, through the following LWFP: simple (SLWFP), enclave (ELWFP) and extended (ExLWFP) probes. We demonstrate the practicality of these extensions by developing tooling for tracing, stack sampling with Flame Graphs, dynamic instrumentation, timing analysis, and USDT support for Intel SGX enclaves and LibOSes. Performance measurements show that SLWFP probes achieve a latency of 394 ns, outperforming uprobes, which exhibit 25% higher latency, while ELWFP probes incur a latency ~2.8 microseconds, which is practical for enclave observability. The addition of SLWFP introduces negligible overhead to existing uprobe performance. Taken together, this work lays the foundation for closing the long-standing gap between NEE tooling and Linux observability tooling by enabling generic and reusable eBPF tooling for diverse NEE hardware and software architectures.

cs.OS↗

arXiv2026

WEIRDO: WEak resIdual Regularized DOob's h-transform diffusion alignment

We study the problem of estimating the guidance that steers the distribution learned by a diffusion generative model toward a tilted target $q_0 \propto w\,p_0$ at inference time. Relying on the stochastic optimal control approach, we observe that the exact drift correction is the gradient of the logarithm of Doob's $h$-function, and we study the problem of estimating it from a sample. In the present paper, we assume that the score of the pretrained model is available, that the tilting weight is bounded and positive, and that the reference distribution has a bounded support, no smoothness of the weight is required. Introducing a penalized least-squares risk in which the penalty is the residual of the space-time harmonicity equation satisfied by the $h$-function, measured in a dual Sobolev norm, we derive high-probability bounds on the squared error of the resulting guidance estimate. Since the penalty vanishes at the target, the estimator is free of regularization bias, and in favourable scenarios its rate of convergence is faster than the minimax rate of estimating first-order derivatives of a smooth regression function. Assuming that $w$ is bounded and positive with $\mathbb{E}_{p_0}[w^{-\mathrm{s}}] < \infty$ for some $\mathrm{s} \in (0,\infty]$, and that the reference data are compactly supported, we prove that the guidance is estimable in squared $L^2$ at rate $\varepsilon_n^{\mathrm{s}/(\mathrm{s}+4)}$, where $\varepsilon_n = n^{-2(β-1)/(2(β-1)+d)}.$ We also transfer the obtained bounds to the total variation distance between the marginals of the estimated and the exactly guided samplers, and illustrate the performance of the suggested approach with numerical experiments.

math.ST↗

arXiv2026

Tight Liquid Welfare Guarantees for Auctions with Budgets via LP Duality

We study the efficiency of auctions with budget-constrained bidders and derive tight price of anarchy (PoA) bounds for coarse correlated equilibria (CCE). To this end, we develop a general framework that reduces proving PoA guarantees to finding feasible solutions to the dual of a linear program. The LP is formulated over a small number of per-bidder equilibrium statistics, incorporates constraints implied by the auction setting and equilibrium behavior, and captures a novel smoothness notion tailored to budget-constrained environments; we provide a reduction from classical smoothness to this new notion. Our approach enables simple and tight PoA analyses across a broad range of auction formats. Using our framework, we obtain tight liquid welfare guarantees for simultaneous first-price, second-price, and all-pay auctions, simultaneous auctions with restricted uniform bidding interfaces, discriminatory and uniform price multi-unit auctions, and generalized first-price position auctions. Beyond budget-constrained settings, we derive new lower bounds for the budget-free uniform price auction and generalized second-price auction; in particular, our lower bound for the uniform price auction matches the upper bound of $3.146$ by de Keijzer et al. (2013).

cs.GT↗

arXiv2026

CATCH: A Controllable Analysis Testbed for Reward Hacking in Coding RL

During reinforcement learning with verifiable rewards (RLVR), large language models (LLMs) can exploit loopholes in their environments to obtain high rewards without improving the intended capabilities, i.e., reward hacking. Despite its risks to training efficiency and safety, monitoring and mitigating reward hacking during training remain challenging, which is limited by a lack of testbeds that reproduce hacking and reliably identify it. We introduce CATCH, a controllable testbed for studying reward hacking in coding RL. CATCH deliberately exposes environmental loopholes and provides execution-based gold labels by comparing success under a vulnerable evaluator with task correctness under an independent audit. It also can control the model's initial hacking tendency through supervised fine-tuning data mixtures and the difficulty of earning rewards through reward designing, enabling systematic comparisons of hacking dynamics and interventions. Experiments show that CATCH can produce diverse RL training trajectories with clear reward hacking, and analyses demonstrate that both initial models and reward difficulties shape the emergence of reward hacking. We further evaluate the effectiveness of different reward hacking detection and mitigation methods. A key finding is that a chain-of-thought monitor initially suppresses hacking, but this protection erodes as the policy model learn to mislead the monitor with code comments. This highlights the need to evaluate hacking mitigations throughout training with CATCH. The source code and resources are publicly released at https://github.com/THUAIS-Lab/CATCH.

cs.CL↗

arXiv2026

First-Principles Study of I$_2$ and CH$_3$I Adsorption on Transition Metal Decorated 2D-Material substrates : Insights from Electronic Structure and Reaction Kinetics

Radioactive iodine species, particularly I$_2$ and CH$_3$I, pose significant environmental and technological hazards owing to their high volatility, chemical stability, and relatively weak interaction with traditional substrate and sorption materials. In this work, we proposed a series of transition-metal (TM) (Fe, Ni, Cu, Zn) decorated boron-doped graphene (BDG) and 2D-MoTe2 substrates for efficient adsorptive capture and mitigation of such volatile Iodine species. Using systematic first-principles density functional theory (DFT) calculations, we elucidate the microscopic origin of the enhanced adsorption by analyzing the changes in the electronic structure upon adsorption. More importantly, we analyzed the thermodynamic and kinetic feasibility of adsorption on these newly designed substrates using Climbing-Image Nudged Elastic band (CI-NEB) calculations and found that TM decoration serves as an effective catalytic center, thereby making the reaction thermodynamically and kinetically feasible. Conversely, the reaction becomes thermodynamically and kinetically unfavorable on pristine substrates in the absence of a TM atom as a catalytic center. This work deepens our understanding of the electronic origin of the enhanced adsorption and reaction kinetics, and the predictions made will be useful for experimental realization.

cond-mat.mtrl-sci↗

arXiv2026

Boron vacancies in bulk h-BN created by high-energy He+ irradiation

While color centers in diamond and other three-dimensional crystals are nowadays key elements of several types of sensors, color centers in two-dimensional materials are rapidly developing and promise high-tech applications. One of the interesting centers in 2D materials is the negatively charged boron vacancy in hexagonal boron nitride (h-BN), which has already shown some potential for magnetometry, but the reliable creation of boron vacancies remains challenging. Here, we demonstrate the fabrication of negatively charged boron vacancy color centers in bulk h-BN via implantation of helium ions at ~1 MeV, as confirmed by characteristic photoluminescence and optically detected magnetic resonance. The resonance has a width of 180 MHz and exhibits the expected Zeeman shift of the resonance lines. The depth of the color center along the c-axis of the h-BN crystal was measured and compared with predictions from Stopping and Range of Ions in Matter modeling. The experimental value and the modeled prediction are consistent within the reported uncertainties, as their 1σ intervals overlap, although the experiment shows a greater depth and a wider distribution.

quant-ph↗

arXiv2026

Tilting mutation of gentle algebras and its combinatorial description

Tilting mutation provides a natural way to construct derived-equivalent algebras by replacing an indecomposable summand of a tilting object. In this paper, we study tilting mutation of gentle algebras via generalized $\mathrm{BB}$-tilting modules. For a gentle algebra $A=\mathbb{k} Q/\langle I\rangle$ and a vertex $k\in Q_0$, we first give a necessary and sufficient condition, expressed in terms of the arrows and relations incident with $k$, for the corresponding minimal left approximation of $P(k)$ to yield a tilting mutation. This criterion applies uniformly to vertices with or without loops. When the mutation exists, we determine the irreducible morphisms between the indecomposable summands of the mutated tilting module and use them to construct explicitly the Gabriel quiver and defining relations of its endomorphism algebra. In particular, we obtain a combinatorial mutation $(Q,I)\mapsto(Q',I')$ of gentle pairs such that $μ_k^+(A)\cong \mathbb{k} Q'/\langle I'\rangle,$ so the resulting algebra is again gentle and derived equivalent to $A$. Finally, we formulate the dual cotilting mutation and its combinatorial description via opposite gentle pairs.

math.RT↗

arXiv2026

A Reusable Semantic Web Framework for Evidence-Grounded Fundamental Rights Impact Assessments under the EU AI Act

The EU AI Act (Art. 27) requires deployers of high-risk AI systems to conduct Fundamental Rights Impact Assessments (FRIAs) before deployment, yet the evidence needed for credible assessments is fragmented across incompatible incident repositories, risk vocabularies, and legal texts. We present a reusable Semantic Web-based framework that consolidates this evidence for two high-risk public sector categories: employment and worker management (Annex III(4)) and access to essential public services (Annex III(5)(a)). A curated 150-record corpus is annotated along four axes using keyword, LLM, and hybrid methods and serialised as a SPARQL-queryable knowledge graph of 1,351 RDF triples. Five FRIA demonstration scenarios surface 103 records (68.7% coverage). Evaluation against a 69-record gold standard reveals that LLM-assisted classification of the employment domain achieves only $κ= 0.045$, a cautionary result for automated fairness-related evidence retrieval in this domain. All artefacts are released openly to support adoption by regulators, national authorities, and SMEs.

cs.CY↗

arXiv2026

On the chromatic number of pseudohemisphere hypergraphs

A pseudohemisphere hypergraph is a hypergraph $\mathcal{H}$ with an ordered set of vertices $V$ for which there exists an $ABA$-free hypergraph $\mathcal{F}$ on $V$ and a subset $X$ of $V$ such that the hyperedge set of $\mathcal{H}$ is a subset of $\{FΔX: F\in \mathcal{F}\cup \overline{\mathcal{F}}\}$. We prove that the chromatic number of pseudohemisphere hypergraphs is at most four.

math.CO↗

arXiv2026

Finite-slope p-adic L-functions for $\mathrm{GL}_{3}$

Let $Π$ be a regular algebraic cuspidal automorphic representation of $\mathrm{GL}_{3}(\mathbb{A}_{\mathbb{Q}})$ of weight $(a, 0, -a)$, and let $p$ be a prime. Generalising work of Loeffler--Williams in the nearly-ordinary case, we construct $p$-adic $L$-functions for each small slope regular $P_{1}$-refinement of $Π$ at $p$ consistent with the conjectures of Coates--Perrin-Riou and Panchishkin.

math.NT↗

arXiv2026

Reconsidering the Vacuum Energy of a Massive Scalar Field in a Spherical Cavity

We reconsider the vacuum (Casimir) energy of a massive scalar field obeying Dirichlet boundary conditions inside a spherical cavity. Using zeta-function regularization, we carefully recalculate the analytic part of the zeta function via the uniform asymptotic expansion of the modified Bessel functions. We correct a sign error present in an earlier calculation (PR D56 (1997) 4896) that affected the large-mass behavior. The renormalized vacuum energy is shown to vanish for large mass, as required on physical grounds. Numerical results reveal that the energy changes sign several times as a function of the cavity radius.

math-ph↗

arXiv2026

On the Relation Between the Boson Peak and the Vibrational Phases in Glasses

The boson peak is a vibrational feature commonly found in glassy and disordered systems described as the deviation from the scaling of the Debye model ($g({E}){\propto}{E}^2$). Despite much interest, the microscopic nature of the vibrations is only anecdotally discussed. Here we report how the boson peak appears in conjunction with a crossover from localized to extended but non-wave-like and coincide with a maximum in phase coherence and spatial periodicity. Our analyses provide new insights into the microscopic origin of the boson peak across a wide range of glasses.

cond-mat.dis-nn↗