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01.
arXiv (CS.LG) 2026-06-17

Multi-Source Cybersecurity Logs: An ATT&CK-Labeled Dataset and SLM Evaluation

arXiv:2606.18190v1 Announce Type: cross Abstract: Multi-stage cyberattacks span system, network, and browser logs. Detecting them requires correlating events across all three sources. Machine learning methods can learn these cross-source patterns, but they need labeled multi-source data. Existing public datasets fall short. Network-only datasets such as CICIDS and UNSW-NB15 miss host and browser activity. Host-focused datasets such as LMDG and CICAPT-IIoT lack browser telemetry. ATLAS includes all three sources but labels events only as malicious or benign, without MITRE Adversarial Tactics, Techniques, and Common Knowledge (ATT&CK) technique granularity. No public dataset combines all three sources with per-entry ATT&CK technique labels. We close the gap by building a multi-source log dataset of 870 sessions (70 attack, 800 benign) and approximately 2.3 million events. We captured system, network, and browser activity simultaneously on Windows endpoints. We labeled malicious events with ATT&CK technique IDs, covering 12 tactics and 53 techniques. We generated all attack data using real tools, including Remote Access Trojan (RAT), Command and Control (C2) tunnels, and cloud exfiltration. To demonstrate learnability, we fine-tuned three Small Language Models (SLMs) (Qwen2.5-1.5B, Llama-3.2-3B, Phi-4-Mini) using Low-Rank Adaptation (LoRA). We compared each against its base variant across ten metrics on two tasks: chunk classification and ATT&CK technique identification. Fine-tuning improved every model on every metric. Chunk classification accuracy rose from approximately 8% in the base variants to between 90% and 97% after fine-tuning. Technique identification remained challenging, with the best exact-match accuracy at 42%, although high partial-match scores show the models captured most of the underlying reasoning.

02.
arXiv (CS.LG) 2026-06-11

Evaluating and Combating the Impact of Concept Drift on the Performance of Machine Learning-Based Phishing Detection Systems

arXiv:2606.11471v1 Announce Type: cross Abstract: The expansion of the digital domain has resulted in a substantial increase in digital communication, with email emerging as one of the most prominent channels. The proliferation of email communication is apparent in both professional and personal contexts, thereby creating numerous vulnerabilities for malicious actors to exploit. Spam emails, a form of unsolicited correspondence often bearing malicious intent towards recipients, have been an ongoing challenge for email users since the inception of email technology, and this problem has been exacerbated by the growth of the digital landscape. Email spam filters are integral components of email clients, engineered to identify potentially harmful messages and alert users to their malicious content. Phishing, frequently the initial phase of malware-based attacks, is evolving rapidly, with malware becoming increasingly sophisticated over time. A widely adopted approach for detecting malicious activity within malware and spam domains is the application of machine learning. Our aim is to assess the impact of the evolution within the spam email domain on these machine learning-based detection systems and to explore strategies for mitigating associated performance degradation.

03.
arXiv (CS.CL) 2026-06-19

Uncertainty Decomposition for Clarification Seeking in LLM Agents

Recent position papers argue that the classical aleatoric/epistemic uncertainty framework is insufficient for interactive large language model (LLM) agents and call for underspecification-aware, decomposed, and communicable uncertainty representations that can unlock new agent capabilities such as proactive clarification seeking and shared mental-model building. Practical deployment constraints – black-box APIs, interactive latency budgets, and the absence of labeled trajectories – rule out logprob-based, multi-sampling, and training-based methods, leaving prompt-based estimation as the most viable family for surfacing such signals at deployment time. We answer this call with a simple prompt-based decomposition that separates action confidence from request uncertainty (u), enabling the agent to ask for clarification when the task specification is ambiguous. To evaluate it, we introduce two clarification-augmented benchmarks (WebShop-Clarification and ALFWorld-Clarification) in which 50% of tasks are deliberately underspecified, and systematically compare the proposed decomposition against ReAct+UE and Uncertainty-Aware Memory (UAM) across five LLM backbones (GPT-5.1, DeepSeek-v3.2-exp, GLM-4.7, Qwen3.5-35B, GPT-OSS-120B) on these variants together with the standard WebShop, ALFWorld, and REAL benchmarks for fault detection. Averaged across the five backbones, the proposed decomposition improves clarification F1 on ALFWorld-Clarification by 73% over ReAct+UE and by 36% over UAM, and leads clarification F1 on every backbone on WebShop-Clarification and on four of five backbones on ALFWorld-Clarification, indicating that the gains generalize beyond a single LLM.

04.
arXiv (CS.LG) 2026-06-19

Federated Bilevel Performative Prediction

arXiv:2606.19734v1 Announce Type: new Abstract: Federated bilevel optimization is widely used for nested learning problems across distributed clients, such as federated hyperparameter tuning and meta-learning under privacy and communication constraints. Most existing formulations assume fixed client data distributions, which can be violated by performativity, where deployed decisions reshape client behavior and data collection, inducing client-specific, decision-dependent distribution shift. We study federated bilevel performative prediction, where both upper-level (UL) and lower-level (LL) objectives are evaluated under client-dependent, decision-dependent distributions. We formalize the federated bilevel performatively stable (FBPS) point under a decoupled-risk perspective and provide sufficient conditions for its existence and uniqueness. We then develop two federated methods to compute the FBPS solution: FBi-RRM, which converges linearly under a contraction condition, and FBi-SGD, a communication-efficient stochastic method based on federated hypergradient estimation with convergence guarantees under diminishing step sizes when sensitivities are sufficiently small. Experiments on strategic regression and meta strategic classification validate the predicted stability thresholds and demonstrate improved meta-generalization over non-performative baselines, and CNN-based classification further demonstrates the practical effectiveness of the proposed methods in nonconvex neural network settings.

05.
arXiv (quant-ph) 2026-06-16

Inverted Dirac oscillator

arXiv:2606.15303v1 Announce Type: new Abstract: The Dirac oscillator is obtained from the Dirac Hamiltonian $H^{\mathrm{D}} = \left( c\vec{\alpha}\cdot \vec{p} + mc^{2}\beta \right)$ by modifying the momentum through a non-Hermitian substitution $\overrightarrow{p} \rightarrow \overrightarrow{p} \pm i\omega \beta \overrightarrow{q}$. Despite the non-Hermitian nature of this momentum operator, the full Hamiltonian remains Hermitian due to the presence of the Dirac matrix $\vec{\alpha}$. However, if one instead introduces a Hermitian modification of the form $\vec{p} \rightarrow \vec{p} \pm \omega \beta \overrightarrow{q}$, the resulting Hamiltonian is no longer Hermitian. In this case, the system corresponds to an inverted Dirac oscillator $H^{\mathrm{r}}$, where the potential becomes unbounded from below, the energy spectrum becomes continuous, and the eigenfunctions fail to be square-integrable, leading to normalization difficulties. We show that the Hamiltonian $H^{\mathrm{r}}$ is a pseudo-$\mathcal{PT}$-symmetric operator, and we introduce an unbounded, non-unitary transformation that establishes a connection between $H^{\mathrm{r}}$ and $H^{\mathrm{D}}$. The purpose of this work is to analyze this relativistic quantum system – known as the Dirac inverted oscillator – which, despite its various applications, admits an exact analytical solution

06.
arXiv (quant-ph) 2026-06-12

Approximate quantum error correction theory of non-isometric codes

arXiv:2606.13559v1 Announce Type: new Abstract: Non-isometric encoding arises in various important contexts in quantum error correction, most notably in the finite-energy, non-ideal codewords inevitable in experimental realizations of continuous-variable codes, and holographic quantum gravity. In this work, we present a general and systematic theory of non-isometric quantum error-correcting codes. In particular, we employ the approximate quantum error correction framework to quantitatively study the fundamental limitations imposed by non-isometric encodings on the accuracy of quantum error correction and implementation of logical operations. We apply our theory to analyze GKP and tiger codes under energy constraints, and discuss the implications to holography.

07.
arXiv (CS.CV) 2026-06-16

When RAG Hurts: Diagnosing and Mitigating Attention Distraction in Retrieval-Augmented LVLMs

While Retrieval-Augmented Generation (RAG) is one of the dominant paradigms for enhancing Large Vision-Language Models (LVLMs) on knowledge-based VQA tasks, recent work attributes RAG failures to insufficient attention towards the retrieved context, proposing to reduce the attention allocated to image tokens. In this work, we identify a distinct failure mode that previous study overlooked: Attention Distraction (AD). When the retrieved context is sufficient (highly relevant or including the correct answer), the retrieved text suppresses the visual attention globally, and the attention on image tokens shifts away from question-relevant regions. This leads to failures on questions the model could originally answer correctly without the retrieved text. To mitigate this issue, we propose MAD-RAG, a training-free intervention that decouples visual grounding from context integration through a dual-question formulation, combined with attention mixing to preserve image-conditioned evidence. Extensive experiments on OK-VQA, E-VQA, and InfoSeek demonstrate that MAD-RAG consistently outperforms existing baselines across different model families, yielding absolute gains of up to 4.76%, 9.20%, and 6.18% over the vanilla RAG baseline. Notably, MAD-RAG rectifies up to 74.68% of failure cases with negligible computational overhead.

08.
arXiv (CS.AI) 2026-06-16

Adaptive and Explicit safe: Triggering Latent Safety Awareness in Large Reasoning Models

arXiv:2606.16808v1 Announce Type: new Abstract: While Large Reasoning Models (LRMs) excel at complex tasks, they remain highly vulnerable to sophisticated jailbreaks and direct harmful queries. To address this vulnerability, prior works depend heavily on external manual data annotation for safety alignment. However, we observe that LRMs can inherently identify safety risks when being re-presented with original queries alongside their own reasoning trajectories – a capability we term Latent Safety Awareness. To leverage this safety awareness, we first employ Supervised Fine-Tuning (SFT) to explicitly induce safe tags to trigger safety analysis and guidance following the initial reasoning content for unsafe queries, while preserving standard responses for general queries to ensure adaptive triggering. Subsequently, we apply Direct Preference Optimization (DPO) to further enhance the correctness and stability of the safety analysis and guidance. Notably, responses required for both training stages are entirely generated by models being optimized. With (Safe Trigger) SFT and DPO, experimental results demonstrate significant safety enhancement. For example, the Attack Success Rate (ASR) of DeepSeek-R1-Distill-Llama-8B, on average, drops 24.65% and 36.72% on harmful and jailbreak benchmarks, respectively. Finally, our Safe Trigger method exerts almost no negative impact on general performance or user experience.

09.
arXiv (CS.AI) 2026-06-16

FORTIS: Benchmarking Over-Privilege in Agent Skills

arXiv:2605.09163v3 Announce Type: replace Abstract: Large language model agents increasingly operate through an intermediate skill layer that mediates between user intent and concrete task execution. This layer is widely treated as an organizational abstraction, but we argue it is also a privilege boundary that current models routinely exceed. We present FORTIS, a benchmark that evaluates over-privilege in agent skills across two stages: whether a model selects the minimally sufficient skill from a large overlapping library, and whether it executes that skill without expanding into broader tools or actions than the skill permits. Across ten frontier models and three domains, we find that over-privileged behavior is the norm rather than the exception. Models consistently reach for higher-privilege skills and tools than the task requires, failing at both stages at rates that remain high even for the strongest available models. Failure is especially severe under the ordinary conditions of real user interaction: incomplete specification, convenience framing, and proximity to skill boundaries. None of these requires adversarial construction. The results indicate that the skill layer, far from containing agent behavior, is itself a primary source of privilege escalation in current systems.

10.
arXiv (CS.CL) 2026-06-19

Source-Grounded Data Generation for Text-to-JSON Learning

From financial filings to clinical records, legacy industries rely heavily on long, unstructured documents to store high-value information. Reliably extracting this information into structured, machine-readable representations is a key prerequisite to making the contents accessible to automated systems. JSON is a natural target for such structured extraction, yet constructing reliable and scalable text-to-JSON training data remains challenging. To address this gap, we propose STAGE (Spreadsheet-grounded Text-to-JSON Artifact GEneration), a source-grounded data generation pipeline that constructs reports and JSON schema by using LLMs for scalable synthesis while validating ground-truth values against the underlying spreadsheet. Evaluations on STAGE-Eval, our source-grounded benchmark with an 851-example test set, show that STAGE produces stronger training data than existing approaches. This improves Qwen3-4B exact match from 31.37% to 74.27% and value accuracy from 45.46% to 90.69%.

12.
arXiv (CS.CV) 2026-06-11

DroneShield-AI: A Multi-Modal Sensor Fusion Framework for Real-Time Autonomous Drone Threat Detection, Behavioral Intent Classification, and Swarm Intelligence in Contested Airspace

Unmanned Aerial Vehicle (UAV) threats have emerged as a defining security challenge of the 21st century. This paper presents DroneShield-AI, a unified open framework integrating six processing layers: RF signal classification, acoustic motor-signature detection, YOLOv8-based visual detection, evidence-weighted sensor fusion, a Behavioral Intent Classification Engine (BICE), and a Graph Neural Network Swarm Intelligence Module (GNN-SIM). BICE introduces the first systematic six-class threat taxonomy for drone flight patterns, enabling predictive operator alerts with a 30-second advance-warning horizon. GNN-SIM is the first open framework for adversarial multi-drone formation analysis using Graph Attention Networks. Evaluated on three publicly available real-world datasets, the fused pipeline achieves 96.1% detection accuracy, 3.2% false alarm rate, AUC-ROC: 0.981, and 142ms end-to-end latency on commodity CPU-class hardware at approximately $500-$780 USD total system cost. All code, model weights, and simulation datasets are publicly released at submission.

13.
arXiv (CS.LG) 2026-06-11

Machine-learning-based multipoint optimization of fluidic injection parameters for improving nozzle performance

arXiv:2409.12707v2 Announce Type: replace-cross Abstract: Fluidic injection offers a promising solution to improve the performance of the overexpanded single expansion ramp nozzles (SERNs) during vehicle acceleration. However, determining the injection parameters that yield the best overall performance across multiple nozzle operating conditions remains a challenge. The gradient-based optimization method requires gradients of injection parameters at each design point, which can lead to high computational costs when using computational fluid dynamics (CFD) simulations. This paper uses a pretrained neural network to replace CFD during optimization, enabling quick calculation of the nozzle flow field at multiple design points. Considering the physical characteristics of the nozzle flow field, a prior-based prediction strategy is adopted to enhance the model's accuracy. In addition, the neural network's back-propagation algorithm computes gradients quickly by running the computation only once, thereby greatly reducing gradient computation time compared to the finite difference method. As a test case, the average nozzle thrust coefficient of an SERN at seven design points is optimized, resulting in a 1.14\% improvement. The time cost is greatly reduced compared with traditional optimization methods, even when the time required to establish the training database is included.

14.
arXiv (CS.AI) 2026-06-16

Post-Hoc Merging is Not Enough: Many-Shot Model Merging with Loss-Gap Balancing

arXiv:2606.16501v1 Announce Type: new Abstract: Model merging has become a practical post-training strategy for building a single multi-task large language model (LLM) by combining multiple task-specialized models. However, most existing approaches rely on post-hoc merging, in which task-specific models are merged only once after training. This one-shot aggregation often suffers from task interference, leading to information erasure across individual tasks. In this work, we show that replacing post-hoc merging with an iterative many-shot merging protocol is effective in improving multi-task performance. Building on this insight, we propose METIS, Mitigating Erasure from Task Interference for Stable many-shot merging. METIS is a loss-aware many-shot merging method that addresses information erasure in post-hoc merging through task-wise loss-gap weighting and consensus-based masking. Notably, METIS exhibits significant performance improvement on the worst-performing task, effectively mitigating information erasure. (Project page: https://imkyungjin.github.io/METIS/)

15.
arXiv (CS.CV) 2026-06-17

Disentangling Perception and Reasoning in Multimodal LLMs via Reward Design

Reinforcement learning with verifiable rewards has driven major gains in LLM reasoning, and it is intuitive to assume this recipe will transfer well to multimodal models. However, multimodal models do two things: first, perceive what is in an image, then reason about what it implies. Because these stages are graded jointly, it is hard to tell how much room reasoning alone has to grow. We study this on algorithmic visual puzzles, where both components are necessary and show that perception, not reasoning, is the binding constraint. Replacing images with simple textual descriptions raises performance by over 20 points on average for Claude models. We then evaluate six reward designs aimed at inducing visual grounding during reasoning without chain-of-thought supervision. Training Qwen-2.5-VL-7B with GRPO, reward design induces long, structured reasoning with self-reflection and visual references, yielding a 5.56-point gain over the base model. These gains are, however, uneven; no single reward improves all categories, and rewards with verifiable accuracy signals trade out-of-domain transfer for in-domain accuracy. These results point to perception-aware reward design as a path forward, so that signals correct perception at its source rather than the reasoning that inherits its errors.

16.
arXiv (CS.LG) 2026-06-16

Filtered Conformal Ellipsoids for Graph-Native Time Series

arXiv:2606.17014v1 Announce Type: new Abstract: Joint prediction sets for multivariate time series should control a single event while adapting to cross-coordinate dependence. We study filtered conformal ellipsoids: a frozen state-space filter emits a one-step predictive mean and covariance, and split-conformal calibration is applied to the resulting Mahalanobis scores. The filter is used to choose the ellipsoid shape; conformal calibration chooses the scalar radius, so the construction benefits from a learned predictive covariance without relying on Gaussian tail probabilities for coverage. The main difficulty is that filtered scores are dependent and learned recurrent filters need not contract in their raw hidden state; we therefore analyse contraction in an observable predictive-law quotient that identifies hidden states producing the same future sequence of emitted Gaussian laws. Under a stable Bayes Gaussian-projection filter, covariance bounds, and a finite-horizon observability Fisher condition, small excess Gaussian negative log-likelihood implies contraction of the learned emitted laws. Combined with a threshold-autocovariance envelope this yields a Chebyshev-type approximate coverage bound for filtered split-conformal prediction under dependence; a sharper Bernstein-type bound requires an additional geometric-mixing concentration assumption. Under Gaussian oracle realisability we also obtain a near-oracle log-volume comparison within the class of conditionally valid Gaussian ellipsoid rules. We instantiate the framework with a GCN-GRU filter with diagonal-plus-low-rank covariance. On moderate-size graph-native traffic benchmarks (METRLA-$20$ and PEMSBAY-$50$), the learned filter gives sharper at-target ellipsoids than static-covariance and non-filter baselines; at full-graph scale and on non-graph-native datasets, factor and copula baselines can be stronger.

17.
arXiv (CS.AI) 2026-06-19

Triangular Consistency as a Universal Constraint for Learning Optical Flow

arXiv:2606.19938v1 Announce Type: cross Abstract: We propose triangular consistency as a first-principled constraint for optical flow, which is agnostic to network architecture, supervision type, and dataset, and applies to both image-pair and multi-frame settings. This simple but powerful constraint is to compose two flows to induce a third flow and enforce consistency among the three. The composed flows may arise from (i) image pairs, yielding cycle consistency; (ii) multiple video frames, producing longer-range motion through temporal chaining; or (iii) image pairs combined with controlled synthetic transformations, which becomes data augmentation. This triangular consistency introduces negligible computational overhead and requires no additional annotations. Since it is derived directly from the geometry of optical flow, it does not rely on model-specific assumptions and serves as a ``universal'' plug-and-play component for optical flow training. Experiments show consistent improvement across supervised, unsupervised, and transfer learning settings.

18.
arXiv (CS.AI) 2026-06-16

MASCOT-Android: A Curated Dataset and Automated Collection Pipeline for Android Malware Source Code Specimens

arXiv:2606.16072v1 Announce Type: cross Abstract: Compared with binaries and decompiled code, malware source code more directly reflects the attackers' original intent. However, the scarcity of source code and the high cost of manual review make such datasets difficult to build and maintain. We propose MASCOT-Android, a curated dataset of Android malware source code and an automated collection framework for scalable malware source code discovery on GitHub. A key finding of our work is that repository-level documentation alone provides a strong signal for malware source code collection. Our model extracts character-level TF-IDF features from 8,772 malware and 25,747 benign README documents and trains a LinearSVC classifier to distinguish malware repositories. This README-only model achieves an accuracy of 96.28\% and an FPR of 1.06\% in local evaluation. In addition, the model outputs confidence scores, allowing users to adjust the decision threshold to balance FPR and coverage, which is practical in real-world malware source code collection.

19.
arXiv (quant-ph) 2026-06-17

Twin-beam advantage in quantum LiDAR under correlated noise

arXiv:2606.17908v1 Announce Type: new Abstract: Quantum light promises improved precision in optical remote sensing, but its practical advantage depends critically on whether nonclassical resources remain useful under realistic noise and experimentally accessible detection. This question becomes especially relevant for LiDAR systems, where a quantum advantage has been demonstrated for target detection and joint range-velocity estimation, but mostly under idealized conditions or simple noise models, such as optical loss and thermal background. A key open point is whether entanglement provides an operational advantage when the dominant disturbance is not independent noise, but structured interference across sensing modes. Here, we address this question by studying the joint estimation of target range and velocity with bright two-mode Gaussian probes and homodyne detection, comparing coherent, separable squeezed, and twin-beam states at a fixed resource budget. Our results reveal a hierarchy of quantum resources set by the noise structure: separable squeezing provides a robust advantage over coherent illumination under loss and thermal background, whereas twin-beam probes become superior under correlated jamming when the receiver is adaptively optimized. These results establish correlated noise as the operational regime in which entanglement provides a robustness advantage beyond local squeezing, opening a receiver-aware route to quantum-enhanced LiDAR in realistic and potentially adversarial environments.

20.
arXiv (CS.LG) 2026-06-18

On the Stability of Nonlinear Dynamics in GD and SGD: Beyond Quadratic Potentials

arXiv:2602.14789v2 Announce Type: replace Abstract: The dynamical stability of the iterates during training plays a key role in determining the minima obtained by optimization algorithms. For example, stable solutions of gradient descent (GD) correspond to flat minima, which have been associated with favorable features. While prior work often relies on linearization to determine stability, it remains unclear whether linearized dynamics faithfully capture the full nonlinear behavior. Recent work has shown that GD may stably oscillate near a linearly unstable minimum and still converge once the step size decays, indicating that linear analysis can be misleading. In this work, we explicitly study the effect of nonlinear terms. Specifically, we derive an exact criterion for stable oscillations of GD near minima in the multivariate setting. Our condition depends on high-order derivatives, generalizing existing results. Extending the analysis to stochastic gradient descent (SGD), we show that nonlinear dynamics can diverge in expectation even if a single batch is unstable. This implies that stability can be dictated by a single batch that oscillates unstably, rather than an average effect, as linear analysis suggests. Finally, we prove that if all batches are linearly stable, the nonlinear dynamics of SGD are stable in expectation.

21.
arXiv (math.PR) 2026-06-11

Sample Path Properties of the Fractional Wiener–Weierstrass Bridge II

arXiv:2606.11994v1 Announce Type: new Abstract: Fractional Wiener–Weierstrass bridges are a class of Gaussian processes obtained by replacing trigonometric functions in the construction of classical Weierstrass functions by fractional Brownian bridges. A number of their sample path properties were derived in Schied–Zhang (2024,2026). The analysis in these papers left several open questions, most of which are addressed here. Specifically, we prove that, in the regime in which the Weierstrass mechanism dominates the underlying fractional Brownian bridge, the limiting $b$-adic variation coefficient has an absolutely continuous distribution and is therefore genuinely random. At the critical point between the two roughness regimes, we establish the power-variation formula and the critical $\Phi$-variation limit conjectured in Schied–Zhang (2024). Finally, we derive the Hausdorff dimension for the graphs of the sample paths by proving a conjecture from Schied–Zhang (2026) for the missing high-Hurst case.

22.
arXiv (CS.CL) 2026-06-12

It Takes One to Bias Them All: Breaking Bad with One-Shot GRPO

Warning: This paper contains several toxic and offensive statements. Modern large language models (LLMs) are typically aligned through large-scale post-training to ensure fair and reliable behavior. In this work, we investigate how easily such guardrails can be broken by Group Relative Policy Optimization (GRPO). We show that one-shot GRPO training on a single biased example is sufficient to induce systematic bias, with stereotype-driven reasoning generalizing across attributes, categories, and benchmarks. We further find that models differ in their susceptibility based on the initial likelihood of producing biased outputs. Our results reveal a critical vulnerability in post-training: alignment can be overridden by a single example.

23.
arXiv (math.PR) 2026-06-11

The $K$-th nearest neighbor random walk on a Poisson point process gets trapped

arXiv:2606.11271v1 Announce Type: new Abstract: The $K$-th nearest neighbor random walk $(X_n)_{n \geq 0}$ on a homogeneous Poisson point process $\chi$ on $\R^d$ ($d\geq 1$), starts at the origin and at each step picks its next Poisson point among its closest neighbors according to i.i.d. labels having the same distribution as $K$. Our main result (Theorem 1) states that the number of Poisson points visited by $(X_n)_{n \geq 0}$ admits an exponential decay whenever the random variable $K$ has a bounded support (BS). In particular, the $K$-th nearest neighbor random walk visits finitely many Poisson points if and only if $K$ satisfies Assumption (BS). To prove it, we introduce the key notion of pioneer point which allows us to deal with the region of $\R^d$ already explored by $(X_n)_{n \geq 0}$. Still under Assumption (BS), we also prove an exponential decay for the Euclidean length of the trajectory performed by $(X_n)_{n \geq 0}$ (Theorem 2). Finally, and quite surprisingly, we exhibit an example of label distribution with bounded support for which the $K$-th nearest neighbor random walk discovers new Poisson points after a number of steps whose tail distribution is at least polynomial (Theorem 3).

24.
arXiv (quant-ph) 2026-06-17

Closest Accessible Symmetry reduction: a tool for Hamiltonian interpolation analysis

arXiv:2606.18161v1 Announce Type: new Abstract: We introduce a framework for analysing the spectrum of Hamiltonian interpolations without heavily relying on discretising the interpolation parameter. The method is based on the concept of accessible symmetries: a problem-class-dependent family of certifiable reflections that induce bipartitions of the Hilbert space. At each step, the interpolation Hamiltonian is projected onto the sectors of the accessible symmetry that is closest to being satisfied, yielding a hierarchy of weakly coupled pseudo-eigenspaces together with explicit residual couplings between them. We show that this representation captures qualitative signatures of quantum phase transitions, provides estimates of their location, and offers insights into their nature. The quality of the approximation is controlled by the compatibility between the accessible symmetry family and the problem instance. Although motivated in spirit by adiabatic quantum computation, our approach applies more broadly to the study of Hamiltonian phase diagrams, providing a new perspective on the spectral reorganisation of many-body quantum systems.

25.
arXiv (CS.LG) 2026-06-18

UST-GNN: A Unified Spatial–Topological Graph Neural Network Framework for Urban Analytics–Demonstrated through a Case Study on Urban Health Prediction

arXiv:2504.04739v3 Announce Type: replace Abstract: Understanding how social, demographic, environmental, and spatial factors jointly shape urban outcomes is essential for sustainable urban development and evidence-based policy. Traditional statistical approaches often struggle to capture complex non-linear relationships, while many machine learning methods overlook the joint roles of spatial autocorrelation and network topology in urban systems. Recent advances in GeoAI have addressed these challenges only partially, often treating spatial effects, graph structure, evaluation, and interpretability separately. We present UST-GNN, a unified spatial–topological graph neural network framework that integrates neighbourhood connectivity, heterogeneous urban features, and positional/locational embeddings into a single representation. Using the MedSAT dataset, which contains over 150 environmental and socio-demographic variables and six prescription outcomes across 4,835 neighbourhoods in Greater London, UST-GNN outperforms strong statistical, geographically enhanced, and graph Machine Learning baselines, improving out-of-sample $R^2$ by 8.4–13.2\% under strict spatial cross-validation. We further introduce a lightweight principal-component module to interpret learned node embeddings geographically and relate them to policy-relevant covariates. The resulting analyses recover established patterns, offer new perspectives on debated associations, and reveal novel predictors warranting further causal investigation. Together, these findings demonstrate the value of graph-based spatial machine learning for urban health analytics, environmental inequality assessment, and evidence-based urban policy. Beyond predictive gains, UST-GNN provides a unified GeoAI analytical pipeline that can be embedded into urban digital twin workflows for scenario testing, monitoring, and data-informed decision-making for healthier, more sustainable cities.