Science & Mathematics

This paper derives an exact attenuation formula for multivariate cross-moments under differential privacy achieved through randomized response. From a proposed alternative formulation of randomization matrices compliant with differential privacy guarantees we show that, under attribute-level randomization and where the randomization of the whole distribution is characterized by Kronecker products, any cross-moment of the anonymized dataset involving distinct attributes is equal to the original cross-moment multiplied by attenuation parameters, themselves determined by the part of the overall privacy budget allocated to each attribute. This characterization enables explicit and transparent controls of multivariate relationships preservations in differential privacy through privacy budget allocation. A simple numerical illustration demonstrates that identical total budgets can yield substantially different covariance-preservation profiles. The results also make the multiplicative loss of higher-order interactions explicit and thus can support mechanism design guided by analytical priorities.

Answerability readouts predict whether a passage supplies an answer, but whether calibration can compensate for removing negative passages during training remains unclear. We present a controlled study of how training-negative construction affects calibrated prediction, ranking, and downstream answer retention. We compare native training, which retains negative passages, with empty training, which removes them, holding questions, labels, positive examples, and model weights fixed. Both are calibrated on the same labeled native examples. On SQuAD 2.0 and RepLiQA, native-trained logistic readouts at selected depths achieve lower Brier loss for Qwen2.5-7B-Instruct and Gemma-2-9B-it, with or without output scores. Native fusion also outperforms calibrated output alone. Post-hoc AUROC analysis shows better ranking under native training, beyond what threshold adjustment alone can explain. On the official SQuAD 2.0 development set, native readout policies improve F1 over empty policies but retain more answers to unanswerable questions. The advantage varies by estimator and depth, while RepLiQA's text shortcuts limit claims about contextual understanding. Unfinished generations prevent complete answer-level evaluation, although worst-case bounds preserve the native-empty F1 gains. Our findings show that training negatives affect ranking and downstream decisions even after common calibration, without establishing a universal advantage for native training.

Scientific machine learning provides a promising framework for solving complex problems in science and engineering. Notably, physics informed neural networks (PINNs) have shown considerable potential for solving differential equations and modelling engineering systems. Solving time fractional Navier Stokes equations (TFNSEs) on complex domains is challenging due to temporal nonlocality, nonlinear flow dynamics, geometric complexity, and incompressibility constraints. To address these challenges, we propose a geometry gated, divergence-free Gaussian radial basis function Kolmogorov Arnold network (GeoDiv KAN). The proposed architecture uses geometry dependent feature gating and a streamfunction formulation to preserve incompressibility by construction. GeoDiv KAN is evaluated for the time fractional incompressible Navier-Stokes equations on square, circular, and star-shaped domains. Numerical experiments show that GeoDiv KAN achieves higher predictive accuracy than PINN, PIKAN, RBF KAN, and DF RBFKAN across the considered benchmark problems. To establish practical relevance, GeoDiv KAN is applied to two data driven CFD cases: unsteady flow past a circular cylinder using the \href{https://doi.org/10.5281/zenodo.5039610}{Zenodo dataset} and turbulent RANS flow through a complex U bend using the \href{https://huggingface.co/datasets/JDecke/ubend-cfd}{U-bend dataset}.

Large language models (LLMs) are increasingly used to generate Verus contracts for Rust programs together with the proofs that establish them. Yet verifier acceptance, the common measure of success, shows only that the implementation satisfies the generated contract, so it leaves open whether the contract captures the intended behavior. Assessing specification generation therefore requires an evaluation methodology, not a single metric. We present VerusEval, a framework that evaluates generated contracts along six dimensions, including Verus-native checks for semantic triviality, validated input-output (I/O) suites, and contract equivalence, and that relates them so that the strength and blind spots of each become measurable. Evaluating 13,716 artifacts from four workflows, five LLMs, and two prompting settings on 762 tasks, we find that acceptance overstates quality: only 42.3\% of the accepted artifacts complete all three semantic checks without a flag, and across workflows and models, higher acceptance does not consistently come with more correct contracts. I/O evaluation rejects 23.6\% of the accepted artifacts, yet only 63.2\% of those that pass it are proved equivalent. Of the accepted artifacts flagged by contract comparison, 84.1\% have a rejected completeness obligation, and the direction of a failure prioritizes inspection of the generated contract or the reference; it does not by itself establish which artifact is defective. Screening and review further identify 36 candidate defects among 61 selected reference contracts, and repairing one of them makes 10 of its 11 failing artifacts equivalent. Based on these findings, we derive four actionable lessons for evaluation, generation, and benchmark maintenance.

When does one equation imply another? Stage 2 of the SAIR Mathematics Distillation Challenge required teams to submit solvers to answer this question for sets equipped with a binary operation. For these sets, associativity, commutativity, or any other algebraic property was not assumed. Each answer required a proof or counterexample that could be verified by Lean. Programs also had to respect fixed resource limits. We present Rózsa, a Python solver that searches for both kinds of evidence. It begins with simple tests and considers more extensive searches when those fail. To find a proof, it applies a given equation and derives any further equations as needed, keeping a record of each step. To find a counterexample, it searches for operations on finite sets. It also tests one fixed infinite model. The given equation must hold for every assignment, while the target equation must fail for at least one. In either case, Rózsa turns the evidence into a Lean certificate. The submitted solver solved 199/200 problems (99.5%) in the official main evaluation getting the 6th overall position. Additional tests show that the solver can prove many implications linked by long chains of known results, but has limited success with infinite counterexamples. We explain the search methods, how they fit together, and what the unsolved cases reveal about their limits.

Building upon our previous Ancilia framework, this work presents \emph{YUTELA}, an edge--server--cloud AIoT system for long-term, multi-site video anomaly detection. YUTELA replaces workstation-based on-site processing with NVIDIA Jetson Thor edge devices and redesigns the multi-camera pipeline through camera batching and redistribution, shared memory, reduced inter-stage data transfer, task integration, and TensorRT-accelerated inference. It maintains a separate anomaly model per camera, retrained on a centralized GPU server once enough recent pseudo-normal data are collected, with updated weights returned to the edge. With eight cameras, TensorRT increases throughput from 14.17 to 29.94 FPS under normal density, and the optimized edge node exceeds the throughput of the workstation-based Ancilia system in seven of nine workload settings, reaching up to 2.03 times its throughput at extreme density. This gain comes at the cost of higher latency under lighter loads with four or eight streams. YUTELA was then operated continuously for 170 hours at four public sites using 31 existing CCTV cameras. The deployment shows that runtime load is driven by scene activity and input frame rate rather than by camera count, and that retraining frequency varies by about three times across sites. The 101 automatically triggered training events occupied only about 6.6\% of a single GPU, indicating that one global node can support adaptation for tens of sites. Mean end-to-end alert latency ranged from 6.8 to 15.4~s depending on site traffic and anomaly type. These results show that YUTELA enables practical multi-camera edge processing with low-cost, camera-specific adaptation across heterogeneous sites.

Reinforcement learning for computer-use agents increasingly relies on proactive reward agents that interact with the post-execution GUI environment to verify what recorded screenshots cannot reveal. The reliability of such verification hinges on two coupled decisions: what to check and when to stop. Existing methods leave these decisions to prompted foundation models. However, neither scaling up the model nor providing few-shot examples reliably improves verification: prompted Judges ranging from 4B to GPT-5.4 all plateau at 68%-70% macro-average agreement. This is because the value of a check depends on the environment rather than the task alone, and becomes apparent only through execution. Learning from execution is itself constrained, as the Actor's terminal state cannot be faithfully replicated during training, allowing only one verification attempt per state. We introduce VeriCUA, a proactive reward agent that learns its verification strategy from these single attempts. A trainable Judge decides what to check and when to stop, while a frozen Probe executes the checks in the live environment. Online reinforcement learning optimizes the Judge for both verdict correctness and efficient Probe use, with returns normalized across terminal states. Trained only on OSWorld and evaluated without further training on MobileWorld and WebArena-Verified, VeriCUA achieves the highest reward agreement across all three benchmarks and lies on the agreement-cost Pareto frontier among proactive verifiers. It surpasses few-shot GPT-5.4 by 5.36 points with 47.6%-59.8% fewer Probe tokens, and even a 1B VeriCUA exceeds every prompted Judge. As the reward for Actor RL, it raises task success by 3.21 points overall and 5.40 points on held-out multi-application tasks. These results identify the verification strategy, not verifier scale, as the key to reliable GUI rewards.

Expand-and-sparsify ($\texttt{EaS}$) representations lift an input to a much higher dimension through a linear map and keep only the $k$ largest coordinates. Existing theory builds that map at random and needs the expanded dimension to grow exponentially in the input dimension, which puts the construction out of practical reach. We ask what is gained by learning the map by gradient descent instead, and how that gain depends on how wide the expansion is. We sweep $73$ OpenML classification tasks and $48$ regression tasks under a protocol that holds the datasets, expanded dimensions, sparsity levels and splits fixed across every method, and we summarise each comparison by a median over datasets and a Wilcoxon signed rank test. We report four findings. First, learning the expansion helps most when the expansion is narrowest, and its advantage over a random map decays to nothing by the widest expansions we run, so a learned $\texttt{EaS}$ layer can be made small. Second, with the map learned, a top-$k$ representation that keeps at most a tenth of its coordinates is indistinguishable from a dense $\texttt{ReLU}$ layer of the same expanded dimension at every expansion factor we test, while GELU and SiLU are not. Third, when the representation is forced to be binary the sparse code is the better of the two, and the reason is that binarization costs it nothing while it costs the dense layer accuracy. Fourth, how sparse the representation can be is governed by how wide it is: the sparsity level that is free rises as the expansion grows, so there is no fixed limit on how sparse it can be. The regression tasks reproduce the first finding and qualify the second and third.

While quantum technologies are rapidly evolving, near-term applications heavily rely on hybrid quantum-classical paradigms. Among these, the classical shadows framework has gained a lot of traction, not only for quantum information science, but also for the development and verification of quantum hardware. It allows to efficiently classically estimate many properties of quantum states from randomized measurements alone, a task that is otherwise intractable due to the destructive nature of measurements in quantum systems. There are, however, many properties of interest that are, due to their very problem formulation, not efficiently estimable. In this work, we identify a computational kernel occurring in estimators of polynomial functions, a class of problems that are in general computationally difficult to solve. We show that this structure allows a row-wise partition that, together with a custom SIMD vectorization, enables massive parallelization and can reduce the computational cost significantly. We show applicability and scalability of the approach on different tasks, and our results showcase that the approach allows high sequential throughput and close-to-ideal parallel scaling. The work thus provides a new way of identifying and exploiting structure in classical shadow estimators, resulting in practical advantages on inherently difficult problems.

Gradient-variation online learning has attracted increasing attention for its connections to game theory and optimization. It has been studied in both non-stationary online learning, which aims to minimize dynamic regret against time-varying comparator sequences, and universal online learning, which seeks to adapt to unknown loss curvature. Prior work obtained gradient-variation bounds using different techniques tailored to each setting. We propose a simple and unified method based on surrogate losses with a quadratic penalty on decision movement, yielding gradient-variation bounds in both settings. For non-stationary online learning, the method induces an optimistic-to-gradient-variation reduction, enabling a broad class of algorithms to match the rate established by Zhao et al. (2024). For universal online learning, it yields a simple algorithm that matches the optimal universal regret bounds of Yan et al. (2024) while relaxing the extended smoothness assumption. Finally, we apply our method to online games and improve on existing guarantees.

Large language models (LLMs) designed to interact with users are typically trained to respond appropriately to harmful or toxic content. However, ensuring appropriate responses becomes more challenging in diverse linguistic and cultural contexts, where safety risks may be expressed or interpreted differently. Building safe AI systems therefore requires detecting safety risks, understanding their nature, and responding appropriately, while accounting for linguistic and cultural variations that add complexity to each stage. In this work, we introduce AfriGuard, a culturally grounded multilingual dataset for studying harmful intent, safety-category understanding, and refusal behavior across 10 African languages and English. Our findings reveal that guardrail models underperform both open- and closed-source LLMs on safety-intent and safety-category classification, while models show limited understanding of appropriate safety behavior, scoring below 60% F1. We further find that models often fail to respond appropriately to unsafe prompts not because they explicitly refuse, but because they produce linguistically inadequate responses that result in incidental non-assistance rather than proper refusals. Finally, using AfriGuard, we develop efficient guardrail models that achieve performance competitive with models up to 30x larger, introduce refusal detectors that improve average performance by 43.9% over existing detectors, and demonstrate that supervised fine-tuning can substantially improve overall safety performance.

Generative deep learning methods such as Variational Autoencoders, Generative Adversarial Networks or Diffusion Models have achieved remarkable results in image synthesis. In particular, Diffusion Models have demonstrated superior image fidelity and sample diversity compared to other approaches on standard benchmarks, while also offering more flexible training dynamics as evidenced both in natural image domains and in medical applications. In medical imaging including Computed Tomography, Magnetic Resonance Imaging or Positron Emission Tomography, such models have various important use-cases including data augmentation, domain transfer, image reconstruction, inpainting, image augmentation and artifact correction. Further, generated images can be conditioned on patient characteristics, medical reports, segmentation masks or other images. Specific challenges arise due to the 3D volumetric nature of medical images, which translate to substantial demands in terms of memory, compute, and training data. This article provides a comparative overview of 3D Diffusion Models which have been developed for medical images, with a focus on current performance, limitations, and an outlook for future work.

The establishment of metrics and control of fundamental noise sources in quantum sensing is a long-standing goal in quantum science and technology. We report on the observation of polariton-mediated optical noise in a thermal Rydberg atom vapor and demonstrate its active control and suppression using a radio-frequency field in Rydberg electrometry. The noise exhibits structured amplification and reduction across the Rydberg electromagnetically induced transparency resonance. This reveals a nonlinear slow-light feedback mechanism in which the polariton medium stores and releases probe-field energy. We show that the reference radio-frequency field used in Rydberg heterodyne receivers can also tune the medium into an operating regime where high electromagnetic-field responsivity coincides with reduced optical noise. This operating-point control enables optimization of the electric-field sensitivity within the constraints imposed by Rydberg-polariton physics. These results establish polariton noise as a previously unrecognized intrinsic noise source in thermal Rydberg vapors and the corresponding control method as a crucial aspect of continued efforts to achieve fundamental sensitivity limits in Rydberg electrometry.

We study Gaussian kernel approximation and regularized logistic classification on a connected compact smooth embedded manifold $X\subset\mathbb R^d$ without boundary and of intrinsic dimension $\varrho$. Two main challenges are to derive a fast oracle inequality without assuming a bounded Bayes function and to construct Gaussian approximants that exploit both the intrinsic dimension and the target's regularity without saturation. We address the first challenge through a Bernstein-type inequality whose constant depends linearly on the supremum norm of the predictor. Combined with localized complexity estimates, this yields an oracle inequality over separable normed function spaces. To address the second challenge, we establish a uniform Sobolev operator expansion and cancel its lower-order bias terms using a signed combination of Gaussian kernel integral operators at different bandwidths. Real interpolation then gives an $L_2(X)$ approximation error of order $γ^α$ for functions in $B^α_{2,\infty}(X)$, where $γ$ is the bandwidth. By constructing the approximants directly on the manifold without ambient extension, we obtain a squared Gaussian RKHS norm bound of order $γ^{-\varrho}$. This construction thus overcomes second-order saturation while retaining norm control governed by the intrinsic dimension. When the marginal distribution has a density $g\in L_p(X)$, these results yield the logistic excess-risk rate $\bigl((\log n)^{\varrho+1}/n\bigr)^{4α(1-1/p)/(4α(1-1/p)+3\varrho)}$. We further show that clipping predictions yields the faster clipped logistic excess-risk rate $\bigl((\log n)^{\varrho+2}/n\bigr)^{2α(1-1/p)/(2α(1-1/p)+\varrho)}$. For bounded densities, its polynomial exponent matches that of the minimax optimal rate for squared-loss regression, and its corresponding excess misclassification risk also matches the minimax optimal rate.

Recent work suggests that standard synchrophasors are inadequate for capturing high-frequency data center oscillations, primarily due to filtering and windowing attenuation during phasor estimation. We prove that widely used periodogram and RMS energy detectors remain largely robust to it and confirm this by simulation.