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01.
arXiv (quant-ph) 2026-06-16

Interaction and non-Hermiticity controlled transmission in extended Su-Schrieffer-Heeger models

arXiv:2606.15245v1 Announce Type: cross Abstract: We study the transport characteristics of an extended version of the Su-Schrieffer-Heeger (SSH) model with next-nearest-neighbor (NNN) interactions and non-Hermitian onsite energies. We observed that transport in such a system is significantly modified by the NNN interaction and the non-Hermitian terms. The transmission coefficient exhibits oscillatory behavior as the strength of the NNN interaction varies in a fixed-length chain. Moreover, the transmission coefficient also shows oscillation with system size for a fixed strength of the NNN interaction. We find that novel oscillatory behavior of the transmission coefficient, arising form the NNN interaction, is a unique feature of such a model and has not been reported previously. The presence of the non-Hermitian terms also enhances/reduces the transmission coefficient depending on the values of the other system parameters like intra-, inter- and NNN hopping. It appears from our study that both the NNN interaction and the non-Hermiticity introduce significant changes in the transport properties of the extended SSH chain, which are not observed in the standard Hermitian nearest-neighbour variant of the SSH model.

02.
arXiv (quant-ph) 2026-06-19

Attosecond Path Qubits in High-Harmonic Generation: Classical Dephasing and Trace-Out Decoherence

arXiv:2606.20372v1 Announce Type: cross Abstract: High-harmonic generation (HHG) is governed by interference between electron trajectories. We propose that the dominant short and long trajectories define an experimentally addressable two-level subsystem: an attosecond path qubit (APQ). We formulate a trajectory-resolved density matrix to identify two distinct coherence-loss mechanisms: classical dephasing from ensemble averaging and quantum decoherence arising from the trace-out of unobserved degrees of freedom. By investigating shot-to-shot fluctuations and unresolved transverse momentum, we demonstrate that while dephasing suppresses coherence through averaging, the ``trace-out'' channel produces mixed states even for fixed driving parameters. We explore how these mechanisms modify APQ purity and show that mode selection and conditioning provide operational routes to isolate them. These results establish a reduced-state framework for diagnosing coherence loss in HHG and for engineering trajectory-based quantum states in attosecond interferometry.

03.
arXiv (CS.LG) 2026-06-17

HeteRo-Select: Informativeness as the Participation Driver in Heterogeneous Federated Learning

arXiv:2508.06692v2 Announce Type: replace Abstract: Federated learning systems typically allocate gradient compression by link speed. This is sensible when bandwidth and data informativeness align. However, under non-IID data, these signals often decorrelate or invert. A bandwidth-driven allocator then risks compressing the most informative gradients hardest. We propose HeteRo-Select, a framework that replaces bandwidth with a per-client informativeness score as the primary driver of compression. The score jointly governs three decisions per round: client selection, compression ratio, and server aggregation weight, with bandwidth retained only as a hard ceiling. Score-proportional selection provably reduces the effective heterogeneity of the chosen subset; score-proportional compression provably lowers aggregate top-$k$ error at fixed traffic. Under the exact FedCG simulation protocol, HeteRo-Select delivers a $1.78\times$ speedup and an $18.2\%$ reduction in traffic on CIFAR-10. The same configuration, unchanged, scales from a $7{,}850$-parameter logistic regression to an $11.27$M-parameter ResNet-18, hitting the accuracy target on three of four benchmarks. When bandwidth and informativeness are deliberately anti-correlated, the method still achieves the target accuracy with less traffic than the normal-bandwidth run.

04.
arXiv (CS.LG) 2026-06-12

Limits of spectral learning under noise

arXiv:2606.13067v1 Announce Type: new Abstract: Learning functional relationships from noisy data is a central problem in scientific inference. Spectral methods approximate unknown functions by expanding them in a basis and estimating the corresponding coefficients from data, but the stability of these coefficients under noise remains poorly understood. Here we study supervised regression with additive label noise using sparse spectral representations across multiple bases and dimensions. We show that noise induces a predictable drift in the learned coefficient vector whose magnitude depends on the effective number of active spectral modes. After whitening the empirical feature geometry, we derive a closed-form expression for the overlap between noisy and noiseless coefficient vectors, revealing a universal degradation curve governed by a single intrinsic noise scale. Numerical experiments across Fourier, Legendre, Bessel, and Haar bases confirm the theoretical prediction. The results demonstrate that spectral learning exhibits a fundamental noise threshold beyond which coefficient estimates become unstable, placing intrinsic limits on recovering functional structure from noisy data.

05.
arXiv (CS.CV) 2026-06-11

AerialClaw: An Open-Source Framework for LLM-Driven Autonomous Aerial Agents

Unmanned aerial vehicles (UAVs) are increasingly used in inspection, search and rescue, environmental monitoring, and emergency response. However, most UAV applications still rely on pre-defined command sequences or task-specific pipelines, where developers manually connect perception, planning, flight control, simulation, logging, and safety modules. This limits the flexibility, reproducibility, and extensibility of autonomous aerial systems. This paper presents AerialClaw, an open-source software framework that enables UAVs to operate as decision-making aerial agents rather than merely command-following platforms. Given a natural-language mission, AerialClaw allows an LLM-based agent to understand the task, maintain context, invoke executable aerial skills, observe perception and runtime feedback, and iteratively update its decisions in a closed loop. The framework adopts a modular brain-skill-runtime architecture, combining hard skills for atomic UAV operations, Markdown-based soft skills for reusable task strategies, document-driven agent state and capability boundaries, memory-driven reflection, safety-oriented runtime validation, and platform-agnostic execution adapters. AerialClaw supports lightweight mock execution, PX4 SITL with Gazebo, and AirSim-based simulation, together with a web console, pluggable model backends, example missions, simulation assets, and staged deployment scripts. By combining standardized aerial skills, document-driven agent state, memory, and closed-loop LLM decision-making, AerialClaw provides a reproducible and extensible open-source framework for building UAV systems that can interpret missions, make decisions, execute skills, and adapt their behavior from feedback.

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

Topological Codes Based on Space Groups

arXiv:2606.20548v1 Announce Type: new Abstract: Topological codes form one of the most important classes of stabilizer codes. Most existing algebraic constructions and analyses of topological codes assume translation invariance. Here we show that topological codes can arise in more general settings by incorporating point group operations. The central construction is a class of Calderbank-Shor-Steane (CSS) codes called space-group codes, whose check operators are built from group-algebra templates over space groups that combine translations with point-group operations. We develop methods for analyzing topological properties of space-group codes using ring-modules and their invariant theory. At first glance, space-group codes might appear to complicate practical implementation; however, we find that they can exhibit greater locality than previous codes based purely on translations. Our framework thus extends the landscape of topological codes and opens up a broader design space for the co-design of topological codes with quantum computing platforms.

07.
arXiv (CS.LG) 2026-06-12

EPM-JEPA: Operator-Side Experience Modulation in JEPA-Family World Models

Authors:

arXiv:2606.12979v1 Announce Type: new Abstract: JEPA-family world models use a static predictor whose weights do not adapt when test-time dynamics diverge from training. We compare two mechanisms for incorporating accumulated experience into a JEPA predictor under distribution shift: operand-side injection, where a compressed experience representation is added as a residual to the predictor's hidden state (EI-JEPA), and operator-side modulation, where the same representation generates low-rank weight deltas via LoRA applied to the predictor's weights (EPM-JEPA). On a pre-registered comparison (Moving MNIST, gravity shift), EPM-JEPA (D_shift^{n=50} = 0.7848 +/- 0.0078, three seeds) differs from EI-JEPA (0.8238) by delta = 4.74% - Outcome C: a null result - by our stated criterion, a valid outcome. As a secondary, non-pre-registered observation, EPM-JEPA improves 1.90% over a no-memory baseline (0.8000), consistently across seeds, while EI-JEPA underperforms the baseline, indicating the benefit is specific to weight-level modulation. Our primary contribution is a mechanism analysis: the D_shift^{n=50} trajectory reflects three independent dynamical processes - buffer cycling, EMA target drift, and an intrinsic LoRA settling transient of +0.021 - rather than convergence to equilibrium. These findings motivate PEM-JEPA, a physics-grounded successor addressing this dynamical-peak limitation.

08.
medRxiv (Medicine) 2026-06-15

Supporting people to access social security payments through the Special Rules for End of Life: a qualitative study of the perspectives of patients, carers and health care professionals

Background: People living with terminal illness face a double financial burden from additional costs and loss of earning for themselves and their carers. Social security benefits are intended to help alleviate some of this financial pressure, and in the UK and other countries people are eligible for fast-tracked access to financial support via the Special Rules for End of Life. One in 3 people who are eligible miss out on this support, yet there is limited evidence on the reasons for this take-up deficit. Objectives: The aim of this study is to understand the barriers and facilitators to claiming benefits for terminally ill people from the perspectives of patients, carers, and health care professionals. Methods: This is a qualitative study combining i) focus groups with healthcare professionals recruited via professional networks and social media, and ii) interviews with patients and carers recruited in hospital and hospice settings. We analysed the data using Practical Thematic Analysis Results: Fifty-five multidisciplinary healthcare professionals participated in 11 focus groups, and we interviewed 10 patients and carers. We constructed five descriptive themes to summarise the data: Navigating priorities and uncertainty; positive impacts alongside a sense of shame and stigma; talking about money, difficulties and dividends; everybodys, yet nobodys, responsibility; and sticking points in the system. Conclusion: The themes reveal several challenges that may contribute to people not taking up this financial support. However, discussions about access to benefits were also seen as a core part of holistic care, a positive way to offer support and a gateway to other discussions about end-of-life care preferences and decisions. Recommendations for policy and practice include evaluating the adoption of a diagnostic rather than a prognostic eligibility criteria, integrating discussions about benefits into existing processes such as advance care planning, and improving education and support for clinicians.

09.
arXiv (CS.LG) 2026-06-17

OmniPlan: An Adaptive Framework for Timely and Near-Optimal Network Planning Optimization

arXiv:2606.18105v1 Announce Type: cross Abstract: Network planning optimization is a fundamental problem across diverse domains, including transportation systems, communication networks, and power grids. It requires simultaneous optimization of multiple competing objectives under complex constraints. Existing network planning optimization frameworks rely on mixed integer programming (MIP) solvers, heuristics, and deep reinforcement learning (DRL) models to compute planning decisions. However, they lack effective adaptability to diverse and dynamic user intents, thus leading to the trade-off between execution time and optimality. In this paper, we propose OmniPlan, an adaptive framework that achieves both timeliness and near-optimality in network planning optimization. To achieve the adaptability lacking in existing solutions, OmniPlan employs a large language model (LLM)-based interpreter to convert heterogeneous natural-language intents into a unified and quantifiable user-preference vector. Then it employs a mixture-of-experts architecture that integrates MIP solvers, heuristics, and DRL models as specialized experts, where OmniPlan adapts to diverse intents by dynamically selecting timely and near-optimal experts. Finally, it incorporates a DRL-based expert configuration module that fine-tunes optimization objective weights to align planning decisions with user-specific preferences. We evaluate OmniPlan with a representative real-world workload, i.e., distributed machine learning (ML), where we leverage OmniPlan to offload a wide spectrum of ML inference tasks, e.g., decision trees, SVM, naive Bayes, XGBoost, and random forests, onto a network of hardware devices. Our experiments on a real-world testbed indicate that OmniPlan achieves near-optimal and low-execution-time offloading for real-world ML inference tasks, reducing latency by up to 97.8\% and network device resource consumption by up to 11.5\%.

10.
arXiv (math.PR) 2026-06-16

Transposition Approach to Optimal Control of McKean-Vlasov SPDEs

arXiv:2603.06245v2 Announce Type: replace Abstract: In this paper, we investigate an optimal control problem for McKean-Vlasov stochastic partial differential equations, in which the coefficients depend on the law of the state process. For systems with nonconvex control sets, we establish a Pontryagin-type stochastic maximum principle that provides necessary optimality conditions for admissible controls. The analysis is based on the classical spike variation method together with the introduction of an adjoint backward stochastic partial differential equation involving Lions derivatives with respect to probability measures. Our results extend the stochastic maximum principle for McKean-Vlasov controlled stochastic differential equations to the infinite-dimensional SPDE setting.

11.
arXiv (CS.AI) 2026-06-19

Cost-Optimal LLM Routing with Limited User Feedback under User Satisfaction Guarantees

arXiv:2606.19376v1 Announce Type: cross Abstract: Inference costs for large language model (LLM) applications are rapidly growing, driven by surging demand and rising infrastructure cost. Users expect high-quality responses, and in commercial settings this is formally codified in Service Level Agreements (SLAs), creating a fundamental tension between cost and quality. Recent progress on cost-aware LLM request routing has shown potential to resolve this tension, but existing approaches rely on complete feedback signals, offline training, extensive per-workload tuning, and most lack SLA guarantees or inference-time adaptivity. We introduce SLARouter, an online routing algorithm that learns a cost-optimal policy from the sparse, one-sided user feedback available in production systems. SLARouter provides theoretical guarantees for both cost optimality and strict SLA compliance. Experiments across a wide range of LLM benchmarks show that SLARouter satisfies SLA constraints without the need for per-benchmark tuning, reducing operating cost by up to 2.2x over existing baselines.

12.
arXiv (CS.CL) 2026-06-19

Med-R2: Perception and Reflection-driven Complex Reasoning for Medical Report Generation

Automated medical report generation (MRG) is increasingly used to reduce the burden of manual reporting and for decision support. Large vision-language models (LVLMs) hold great promise for automated MRG due to their fine-grained image-text alignment and advanced text-generation capabilities. Currently, state-of-the-art MRGs primarily focus on adapting pre-trained LVLMs with direct supervised fine-tuning (SFT), a fine-tuning strategy with medical image-report pairs. However, several factors limit the performance of these LVLMs. Firstly, direct SFT enables LVLMs to generate medical reports directly without an intermediate thinking process of pathological feature perception and diagnostic reasoning. This causes a potential failure to perceive pathological features and thus leads to misdiagnosis. Secondly, direct SFT lacks the incorporation of radiology-specific knowledge guidance, causing LVLMs to misinterpret perceived pathological features and make incorrect diagnoses. To address these gaps, we propose a novel fine-tuning strategy named Med-R2. We introduce a perception-driven long reasoning process that precedes report generation and incorporates radiology-specific knowledge as guidance. Additionally, to alleviate potential perceptual errors in complex reasoning, a reflection mechanism is introduced to refine the perception of pathological features and the generated report. Our experiments demonstrate that Med-R2 effectively enhances the capability of pathological features perception and diagnosis accuracy for MRG via fine-tuned LVLMs.

13.
arXiv (CS.CV) 2026-06-16

Contrastive Learning for Seismic Horizon Tracking with Domain-Specific Priors

Unsupervised 3D seismic horizon tracking faces a key limitation: signal-based propagators provide accurate trace-level alignment but often fail near faults, whereas texture-driven deep models are more robust to discontinuities, typically at the cost of labeled data requirements and reduced trace-level precision. We propose a self-supervised fusion of both paradigms in which signal-derived local horizon correspondences act as domain-specific priors to train a texture-based deep learning model. Specifically, we estimate reliable trace-to-trace flows from reflector slopes and use them to form positive pairs in a contrastive objective, while restricting training to high-confidence neighborhoods, optionally augmented with a fault mask. The objective is not to infer ambiguous correspondences close to discontinuities, but to preserve horizon identity across them. As a result, the network learns voxel-wise embeddings that preserve local signal continuity while enabling horizon propagation beyond discontinuities through similarity search. Experiments on the public F3 dataset and a faulted synthetic dataset achieve lower mean absolute error (MAE) than unsupervised baselines and competitive performance against a semi-supervised method using a single labeled slice.

14.
bioRxiv (Bioinfo) 2026-06-10

SPARQ-MI leverages end-to-end spatial single-cell analysis of the tumor microenvironment

Detailed spatial analysis of the tumor micro-environment (TME) through multiplexed fluorescence imaging requires quantitative image-processing and data-analysis methods. While data-preprocessing down to segmentation of individual cells is captured by available methods, statistical analysis of single-cell features is compromised by the uneven noise distribution especially in complex tissues such as the TME, as well as by labor-intensive manual cell-type annotation and region segmentation. Here, we present SPARQ-MI (Spatial Phenotyping, Architecture Reconstruction and Quantification from Multiplexed Imaging) for streamlined spatial single-cell analysis, along with a tissue microarray PhenoCycler data-set with 37 fluorescent channels from melanoma patients under immunotherapy. We demonstrate that SPARQ-MI enables robust reconstruction of the cellular and spatial composition in this and other tissue types. Our analysis reveals associations of the cell-state and spatial location of CD8 T cells with response to immunotherapy. Overall, SPARQ-MI allows for quantitative analysis of complex fluorescence histology samples under minimal user input, and accounting for spatially uneven coverage of antibody signals, setting the stage for quantitative analysis of clinical samples.

15.
arXiv (CS.CL) 2026-06-11

Fanar-Sadiq: A Multi-Agent Architecture for Grounded Islamic QA

Large language models (LLMs) can answer religious knowledge queries fluently, yet they often hallucinate and misattribute sources, which is especially consequential in Islamic settings where users expect grounding in canonical texts (Qur'an and Hadith) and jurisprudential (fiqh) nuance. Retrieval-augmented generation (RAG) improves grounding, however, a single retrieve-then-generate pipeline is insufficient for diverse Islamic queries, including verbatim scripture, citation-grounded guidance, and rule-constrained computations such as zakat and inheritance. To address these challenges, we present Fanar-Sadiq, a bilingual Arabic-English Islamic QA system built on a multi-agent, tool-augmented architecture. It is a core component of the Fanar AI platform. Fanar-Sadiq routes Islamic queries to specialized modules within an agentic tool architecture. It supports intent-aware routing, retrieval-grounded fiqh answers with normalized citations and verification traces, exact verse lookup with quotation validation, and deterministic Sunni zakat and inheritance calculators with madhhab-sensitive branching. We evaluate the end-to-end system on public Islamic QA benchmarks and show strong effectiveness and efficiency. It is publicly accessible through an API and Web application and has received over 1.9M accesses in less than a year (https://api.fanar.qa/docs).

16.
arXiv (CS.CV) 2026-06-15

RAMEN: Resolution-Adjustable Multimodal Encoder for Earth Observation

Earth observation (EO) data spans a wide range of spatial, spectral, and temporal resolutions, from high-resolution optical imagery to low resolution multispectral products or radar time series. While recent foundation models have improved multimodal integration for learning meaningful representations, they often expect fixed input resolutions or are based on sensor-specific encoders limiting generalization across heterogeneous EO modalities. To overcome these limitations we introduce RAMEN, a resolution-adjustable multimodal encoder that learns a shared visual representation across EO data in a fully sensor-agnostic manner. RAMEN treats the modality and spatial and temporal resolutions as key input data features, enabling coherent analysis across modalities within a unified latent space. Its main methodological contribution is to define spatial resolution as a controllable output parameter, giving users direct control over the desired level of detail at inference and allowing explicit trade-offs between spatial precision and computational cost. We train a single, unified transformer encoder reconstructing masked multimodal EO data drawn from diverse sources, ensuring generalization across sensors and resolutions. Once pretrained, RAMEN transfers effectively to both known and unseen sensor configurations and outperforms larger state-of-the-art models on the community-standard PANGAEA benchmark, containing various multi-sensor and multi-resolution downstream tasks. Our code and pretrained model are available at https://github.com/nicolashoudre/RAMEN.

17.
arXiv (CS.CV) 2026-06-18

PorTEXTO: A European Portuguese Benchmark for Visual Text Extraction

European Portuguese (pt-PT) is largely absent from OCR benchmarks, which skew toward high-resource languages. The few benchmarks that cover pt-PT focus on historical artifacts and literature. This work addresses modern OCR applications, introducing PorTEXTO, the first benchmark for contemporary and culturally relevant pt-PT visual text extraction. To ascertain quality, we employ an annotation pipeline combining transcriptions from a frontier LVLM with exhaustive review by native speakers. We observe a sharp performance drop from synthetic to real world samples in most models, and find that, currently, specialized multilingual data is a better driver for pt-PT performance than model size or resolution budget, motivating the release of open pt-PT OCR resources.

18.
arXiv (CS.CV) 2026-06-17

Gaussian Light Field Splatting: A Physical Prior-Driven Vision Transformer for Unsupervised Low-Light Image Enhancement

Existing unsupervised low-light image enhancement methods often encounter local exposure imbalance and color distortion under complex non-uniform illumination. In addition, most Vision Transformers lack an explicit mechanism for modeling the physical priors of illumination degradation. To address these limitations, we propose GLFS, a Gaussian light field splatting-based Vision Transformer that integrates continuous physical illumination modeling from Gaussian splatting into the Transformer architecture. In GLFS, scene illumination is represented by a superposition of anisotropic Gaussian basis functions. Physics-guided biases are introduced into self-attention to adaptively infer a spatial gain field, enabling accurate and uniform restoration under complex illumination. To reduce color bias and structural degradation during enhancement, a color-vector angular loss and a luminance-edge loss are further developed. These losses enforce hue consistency and improve the structural fidelity of local details. Extensive ablation studies and quantitative evaluations show that GLFS provides clear advantages in illumination correction and detail preservation. It achieves state-of-the-art performance and offers a new representation paradigm for low-light image enhancement.

19.
arXiv (CS.CL) 2026-06-12

M\"OVE: A Holistic LLM Benchmark for the German Public Sector

We present M\"OVE (Modelle für die \"Offentliche Verwaltung Evaluieren), a holistic benchmark for evaluating large language models (LLMs) in the context of the German public sector. While LLMs are increasingly adopted in public administration, model selection remains largely ad hoc, and existing benchmarks offer limited guidance: they are predominantly English-centric, US-centric in content, and focus exclusively on task performance. M\"OVE addresses these gaps by evaluating 39 models across two complementary dimensions. Performance criteria cover summarization, question answering, and topic extraction. Governance criteria assess hallucination tendencies, energy consumption, provider transparency, and alignment with German constitutional values and knowledge about positions by German political parties. In total, we utilize ten German-language datasets, including gold- and silverstandard datasets that we constructed to reflect public-administration domains. We employ a multi-metric evaluation strategy combining classical NLP metrics, embedding-based methods, and LLM-as-a-judge approaches. Our results show that no single model dominates across all criteria: top performers differ between tasks, and model size alone is a poor predictor of quality. We further evaluate the benchmark itself, analyzing its statistical precision, LLM judge reliability, the impact of our private datasets on model rankings, the sensitivity of our results to prompt formulation, and the validity of our energy consumption estimates. M\"OVE is designed as a living benchmark under active development; results are publicly available at https://moeve.bundesdruckerei.de/.

20.
arXiv (quant-ph) 2026-06-12

Toward quantum-noise-limited interferometric measurements of optical nonlinearity in vacuum

arXiv:2602.10896v2 Announce Type: replace-cross Abstract: Quantum Electrodynamics predicts that the vacuum must behave as a nonlinear optical medium: the vacuum optical index should increase when it is stressed by intense electromagnetic fields. The DeLLight (Deflection of Light by Light) project aims to measure it by using intense and ultra-short laser pulses. The experiment uses a Sagnac interferometer to amplify the tiny deflection signal of a low-intensity probe pulse crossing the vacuum refractive-index gradient produced by an external high-intensity pump pulse. The measurement of the amplified signal by a CCD camera requires a high spatial resolution, which is limited by the ultimate quantum noise of the CCD. However, interferometric phase noise induced by the mechanical vibrations of the interferometer is also amplified and degrades spatial resolution. To overcome this, we propose a new method named High-Frequency Phase Noise Suppression (HFPNS), based on the addition of a delayed replica (5 ns) of the probe pulse. The delayed pulse, which is not affected by the pump but is subject to the same vibration noise, enables offline subtraction of correlated phase noise. In this work, we present an experimental proof-of-concept on a prototype interferometer operating with a limited amplification factor ($\mathcal{A}\simeq25$), about 10 times smaller than the required value of the final experiment. We have succeeded in reducing phase noise by a factor of 40, resulting in a residual noise level 2.3 times higher than the expected quantum noise. The residual noise is linked to delay-line instabilities and incident beam pointing fluctuations present during these tests. This result validates HFPNS as a robust method for future quantum-noise-limited interferometric measurements of vacuum optical nonlinearity, though additional stabilization and higher interferometric amplification are still needed.

21.
arXiv (CS.LG) 2026-06-16

Scalable Graph Condensation with Evolving Capabilities

arXiv:2502.17614v3 Announce Type: replace Abstract: The rapid growth of graph data creates significant scalability challenges as most graph algorithms scale quadratically with size. To mitigate these issues, Graph Condensation (GC) methods have been proposed to learn a small graph from a larger one, accelerating downstream tasks. However, existing approaches critically assume a static training set, which conflicts with the inherently dynamic and evolving nature of real-world graph data. This work introduces a novel framework for continual graph condensation, enabling efficient updates to the distilled graph that handle data streams without requiring costly retraining. This limitation leads to inefficiencies when condensing growing training sets. In this paper, we introduce GECC (\underline{G}raph \underline{E}volving \underline{C}lustering \underline{C}ondensation), a scalable graph condensation method designed to handle large-scale and evolving graph data. GECC employs a traceable and efficient approach by performing class-wise clustering on aggregated features. Furthermore, it can inherit previous condensation results as clustering centroids when the condensed graph expands, thereby attaining an evolving capability. This methodology is supported by robust theoretical foundations and demonstrates superior empirical performance. Comprehensive experiments including real world scenario show that GECC achieves better performance than most state-of-the-art graph condensation methods while delivering an around 1000$\times$ speedup on large datasets.

22.
arXiv (CS.CV) 2026-06-18

Learning Patient-Specific Disease Dynamics with Latent Flow Matching for Longitudinal Imaging Generation

Understanding disease progression is a central clinical challenge with direct implications for early diagnosis and personalized treatment. While recent generative approaches have attempted to model progression, key mismatches remain: disease dynamics are inherently continuous and monotonic, yet latent representations are often scattered, lacking semantic structure, and diffusion-based models disrupt continuity with random denoising process. In this work, we propose to treat the disease dynamic as a velocity field and leverage Flow Matching (FM) to align the temporal evolution of patient data. Unlike prior methods, it captures the intrinsic dynamic of disease, making the progression more interpretable. However, a key challenge remains: in latent space, Auto-Encoders (AEs) do not guarantee alignment across patients or correlation with clinical-severity indicators (e.g., age and disease conditions). To address this, we propose to learn patient-specific latent alignment, which enforces patient trajectories to lie along a specific axis, with magnitude increasing monotonically with disease severity. This leads to a consistent and semantically meaningful latent space. Together, we present $\Delta$-LFM, a framework for modeling patient-specific latent progression with flow matching. Across three longitudinal MRI benchmarks, $\Delta$-LFM demonstrates strong empirical performance and, more importantly, offers a new framework for interpreting and visualizing disease dynamics.

23.
arXiv (CS.AI) 2026-06-17

First Proof Second Batch

arXiv:2606.18119v1 Announce Type: new Abstract: To assess the ability of current AI systems to correctly solve research-level mathematics problems, we tested several AI systems on a set of ten problems in a broad range of mathematical fields; these problems arose naturally in the research process of the contributors. This document includes the problems, our methodology, and the results of our testing. We provide links to supplementary documents including the human solutions, the AI-generated solutions, and the referee reports and logs for the AI-generated solutions. The ten problems were contributed by the following mathematicians: (1) Dariusz Kaloci\'nski and Theodore A. Slaman, (2) Richard Schwartz, (3) Aleksa Milojevic and Benny Sudakov, (4) Larry Guth, (5) Oleg Butkovsky, Jonathan Mattingly, and Lorenzo Zambotti, (6) Joshua Evan Greene and Duncan McCoy, (7) Sucharit Sarkar, (8) Sam Payne and Jidong (Jayden) Wang, (9) Sylvie Corteel and John Lentfer, (10) Srivatsav Kunnawalkam Elayavalli.

24.
arXiv (CS.AI) 2026-06-18

Scalable Batch Bayesian Optimization Via Subspace Acquisition Functions

arXiv:2411.16206v3 Announce Type: replace-cross Abstract: Extending Bayesian optimization to batch evaluation can enable the designer to make the most use of parallel computing technology. However, most of current batch approaches do not scale well with the batch size. That is, their optimization efficiencies often deteriorate as the batch size increases. To address this issue, we propose a simple and efficient approach to extend Bayesian optimization to large-scale batch evaluation in this work. Different from existing batch approaches, the idea of the new approach is to draw a batch of axis-aligned subspaces of the original problem and select one point from each subspace using existing acquisition functions. Numerical experiments show that our proposed approach speedups the convergence significantly when compared with the sequential Bayesian optimization algorithm, and performs very competitively when compared with ten batch Bayesian optimization algorithms. The implementation of our proposed approach is available at https://github.com/zhandawei/SubSpace_Acquisition_Functions.

25.
arXiv (math.PR) 2026-06-19

Towards practical PDMP sampling: Metropolis adjustments, locally adaptive step-sizes, and NUTS-based time lengths

arXiv:2503.11479v2 Announce Type: replace-cross Abstract: Piecewise-Deterministic Markov Processes (PDMPs) hold significant promise for sampling from complex probability distributions. However, their practical implementation is hindered by the need to compute model-specific bounds. Conversely, while Hamiltonian Monte Carlo (HMC) offers a generally efficient approach to sampling, its inability to adaptively tune step sizes impedes its performance when sampling complex distributions like funnels. To address these limitations, we introduce three innovative concepts: (a) a Metropolis-adjusted approximation for PDMP simulation that eliminates the need for explicit bounds without compromising the invariant measure, (b) an adaptive step size mechanism compatible with the Metropolis correction, and (c) a No U-Turn Sampler (NUTS)-inspired scheme for dynamically selecting path lengths in PDMPs. These three ideas can be seamlessly integrated into a single, `doubly-adaptive' PDMP sampler with favourable robustness and efficiency properties.