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01.
arXiv (CS.CV) 2026-06-12

Proto-LeakNet: Towards Signal-Leak Aware Attribution in Synthetic Human Face Imagery

The growing sophistication of synthetic image and deepfake generation models has turned source attribution and authenticity verification into a critical challenge for modern computer vision systems. Recent studies suggest that diffusion pipelines unintentionally imprint persistent statistical traces, known as signal-leaks, within their outputs, particularly in latent representations. Building on this observation, we propose Proto-LeakNet, a signal-leak-aware and interpretable attribution framework that integrates Closed-set classification with a density-based Open-set evaluation on the learned embeddings, enabling analysis of unseen generators without retraining. Acting in the latent domain of diffusion models, our method re-simulates partial forward diffusion to expose residual generator-specific cues. A temporal attention encoder aggregates multi-step latent features, while a feature-weighted prototype head structures the embedding space and enables transparent attribution. Trained solely on closed data and achieving a Macro AUC of 98.13\%, Proto-LeakNet learns a latent geometry that remains robust under post-processing, surpassing state-of-the-art methods, and achieves strong separability both between real images and known generators, and between known and unseen ones. The codebase is available at the following link: https://github.com/claudiunderthehood/Proto-LeakNet .

02.
arXiv (CS.AI) 2026-06-16

A Learning Method with Gap-Aware Generation for Heterogeneous DAG Scheduling

arXiv:2603.23249v2 Announce Type: replace-cross Abstract: Efficient scheduling of directed acyclic graphs (DAGs) is a core problem in large-scale data-intensive computing systems, where query plans, data-processing workloads, and computation graphs consist of dependent tasks competing for limited heterogeneous resource pools. In practice, achieving high-performance execution requires schedulers to adapt across environments with varying resource pools and task types, while generating schedules under tight runtime budgets. We propose WeCAN, an end-to-end reinforcement learning framework for heterogeneous DAG scheduling that addresses task-pool compatibility coefficients and generation-induced optimality gaps. It adopts a two-stage single-pass design: a single forward pass produces task-pool scores and global parameters, followed by a generation map that constructs schedules without repeated network calls. Its weighted cross-attention encoder models task-pool interactions gated by compatibility coefficients, and is size-agnostic to environment fluctuations. Moreover, widely used list-scheduling maps can incur generation-induced optimality gaps from restricted reachability. We introduce an order-space analysis that characterizes the reachable set of generation maps via feasible schedule orders, explains the mechanism behind generation-induced gaps, and yields sufficient conditions for gap elimination. Guided by these conditions, we design a skip-extended realization with an analytically parameterized decreasing skip rule, which enlarges the reachable order set while preserving single-pass efficiency. Experiments on real-world TPC-H query DAGs, resource-intensive workload datasets, and ML-compiler computation graphs demonstrate improved makespan over strong baselines, with inference time comparable to classical heuristics and faster than multi-round neural schedulers.

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

PrototypeNAS: Rapid Design of Deep Neural Networks for Microcontroller Units

arXiv:2603.15106v2 Announce Type: replace Abstract: Enabling efficient deep neural network (DNN) inference on edge devices with different hardware constraints is a challenging task that typically requires DNN architectures to be specialized for each device separately. To avoid the huge manual effort, one can use neural architecture search (NAS). However, many existing NAS methods are resource-intensive and time-consuming because they require the training of many different DNNs from scratch. Furthermore, they do not take the resource constraints of the target system into account. To address these shortcomings, we propose PrototypeNAS, a zero-shot NAS method to accelerate and automate the selection, compression, and specialization of DNNs to different target microcontroller units (MCUs). We propose a novel three-step search method that decouples DNN design and specialization from DNN training for a given target platform. First, we present a novel search space that not only cuts out smaller DNNs from a single large architecture, but instead combines the structural optimization of multiple architecture types, as well as optimization of their pruning and quantization configurations. Second, we explore the use of an ensemble of zero-shot proxies during optimization instead of a single one. Third, we propose the use of Hypervolume subset selection to distill DNN architectures from the Pareto front of the multi-objective optimization that represent the most meaningful tradeoffs between accuracy and FLOPs. We evaluate the effectiveness of PrototypeNAS on 12 different datasets in three different tasks: image classification, time series classification, and object detection. Our results demonstrate that PrototypeNAS is able to identify DNN models within minutes that are small enough to be deployed on off-the-shelf MCUs and still achieve accuracies comparable to the performance of large DNN models.

04.
arXiv (math.PR) 2026-06-19

A Cycle Walk for Sampling Measures on Spanning Forests for Redistricting

arXiv:2509.08629v2 Announce Type: replace-cross Abstract: We introduce the Cycle Walk, a new Markov chain Monte Carlo method for sampling distributions on balanced graph partitions, motivated by applications in political redistricting. The method operates on spanning forests and combines two types of updates: local "cycle" moves within districts and global moves that exchange population between adjacent districts while preserving balance constraints. This construction enables efficient Metropolis–Hastings correction while allowing proposals at multiple spatial scales. We show that the Cycle Walk naturally interpolates between existing approaches based on local updates and a class of global update methods derived from recombination (RECOM). Through a range of numerical experiments on synthetic graphs and real-world precinct data, we demonstrate that the Cycle Walk exhibits improved empirical convergence diagnostics for distributions that place weaker weight on spanning-tree counts, a regime that is challenging for existing methods. In particular, the algorithm remains effective when incorporating alternative compactness measures that more closely reflect policy-relevant criteria. These results suggest that the Cycle Walk provides a flexible and computationally efficient framework for sampling from a broader class of redistricting distributions than previously accessible with MCMC techniques.

05.
arXiv (CS.CV) 2026-06-16

Landmark-free Assessment of Lower-limb Alignment with Implicit Neural Shape Functions from Knee Radiographs

Radiographic assessment of lower-limb alignment (LLA) is important for predicting joint health and surgical outcomes in total knee arthroplasty. Traditional measurement methods are manual and time-consuming, while recent machine learning approaches typically rely on locating a fixed set of anatomical landmarks. This dependence limits flexibility and may require re-annotation when clinical definitions change. To address this, we propose an automated workflow using Implicit Neural Shape Functions (INSF). Rather than relying on explicit landmark coordinates, we encode the anatomy into a compact latent space and regress clinical alignment measurements directly from these latent codes. This architecture allows for rapid extendability to new tasks without altering the backbone representation. We trained our method on an internal dataset of 566 knee radiographs, each annotated with the outline of the femur and tibia. We evaluated it on both an internal test dataset of 50 patients and a separate external set of 402 preoperative cases from the MRKR dataset. Manual clinical measurements are available for these data, and the MRKR measurements will be made publicly accessible. Performance was comparable to state-of-the-art landmark-based methods and manual agreement, while offering a flexible shape representation that can be extended to additional measurement tasks.

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

Fantastic Pretraining Optimizers and Where to Find Them II: Hyperball Optimization

arXiv:2606.16899v1 Announce Type: new Abstract: Matrix based optimizers such as Muon can substantially speed up language model pretraining, but their gains over AdamW are observed to shrink as model size and data scale grow when using standard constant decoupled weight decay. We propose Hyperball, a simple optimizer wrapper that addresses this issue. Given a base optimizer such as Adam or Muon, Hyperball sets the Frobenius norms of weight matrices and their corresponding optimizer updates to fixed constants. On Qwen3 style models up to 1.2B parameters, Muon Hyperball achieves 20–30% token equivalent speedup over weight decay baselines. Hyperball also improves learning rate transfer across widths and depths compared to decoupled weight decay. This method is motivated by prior theory showing that training with weight decay leads to an equilibrium weight norm that only depends on the training hyperparameters. Through this mechanism, the weight decay then decides the angular learning rate, i.e. how fast the direction of the weight matrix changes.

07.
arXiv (quant-ph) 2026-06-19

Quantum Computing Applications for Flight Trajectory Optimization

arXiv:2304.14445v2 Announce Type: replace Abstract: Major players in the global aerospace industry are shifting their focus toward achieving net carbon-neutral operations by 2050. A considerable portion of the overall carbon emission reduction is expected to come from new aircraft technologies, such as flight path optimization. In pursuing these sustainability objectives, we delve into the capacity of quantum computing to tackle computational challenges associated with flight path optimization, an essential operation within the aerospace engineering domain with important ecological and economic considerations. In recent years, the quantum computing field has made significant strides, paving the way for improved performance over classical algorithms. In order to effectively apply quantum algorithms in real-world scenarios, it is crucial to thoroughly examine and tackle the intrinsic overheads and constraints that exist in the present implementations of these algorithms. Our study delves into the application of quantum computers in flight path optimization problems and introduces a customizable modular framework designed to accommodate specific simulation requirements. We examine the running time of a hybrid quantum-classical algorithm across various quantum architectures and their simulations on CPUs and GPUs. A temporal comparison between the conventional classical algorithm and its quantum-improved counterpart indicates that achieving the theoretical speedup in practice may necessitate further innovation. We present our results from running the quantum algorithms on IBM hardware and discuss potential approaches to accelerate the incorporation of quantum algorithms within the problem domain.

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

Emergent Strategic Reasoning Risks in AI: A Taxonomy-Driven Evaluation Framework

arXiv:2604.22119v2 Announce Type: replace Abstract: As reasoning capacity and deployment scope grow in tandem, large language models (LLMs) gain the capacity to engage in behaviors that serve their own objectives, a class of risks we term Emergent Strategic Reasoning Risks (ESRRs). These include, but are not limited to, deception (intentionally misleading users or evaluators), evaluation gaming (strategically manipulating performance during safety testing), and reward hacking (exploiting misspecified objectives). Systematically understanding and benchmarking these risks remains an open challenge. To address this gap, we introduce ESRRSim, a taxonomy-driven agentic framework for automated behavioral risk evaluation. We construct an extensible risk taxonomy of 7 categories, which is decomposed into 20 subcategories. ESRRSim generates evaluation scenarios designed to elicit faithful reasoning, paired with dual rubrics assessing both model responses and reasoning traces, in a judge-agnostic and scalable architecture. Evaluation across 11 reasoning LLMs reveals substantial variation in risk profiles (detection rates ranging 14.45%-72.72%), with dramatic generational improvements suggesting models may increasingly recognize and adapt to evaluation contexts.

09.
arXiv (quant-ph) 2026-06-12

Geometric Algebra Quantum Gate Decomposition

arXiv:2606.12480v1 Announce Type: new Abstract: Quantum gates are usually described through matrix and tensor-product formalisms that often obscure their geometric structure. In this work, we formulate the Pauli and Clifford groups within the complex Geometric Algebra (GA) framework. We show that the Pauli group is naturally identified with the group of blades up to a global phase, thereby providing a geometric interpretation of Pauli operators and their commutation relations in terms of oriented subspaces. We further prove that Clifford operators are generated by products of {\pi}/4-Pauli rotors and introduce a greedy Pauli rotor decomposition algorithm whose empirical behavior suggests unexpectedly compact decompositions for Clifford operators. Finally, we show that Clifford+T universality admits a natural geometric interpretation through {\pi}/8-rotors within this framework.

10.
arXiv (CS.CL) 2026-06-18

GateMem: Benchmarking Memory Governance in Multi-Principal Shared-Memory Agents

Memory benchmarks for LLM agents largely assume single-user settings, leaving shared assistants for hospitals, workplaces, campuses, and households understudied. In these deployments, multiple principals write to a common memory pool and query it under different roles, scopes, and relationships, so memory quality requires governance as well as recall. We introduce GateMem, a benchmark for multi-principal shared-memory agents. GateMem jointly evaluates utility for legitimate long-horizon requests with state updates, access control across contextual authorization boundaries, and agent-facing active forgetting after explicit deletion requests. It spans medical, office, education, and household domains, with long-form multi-party episodes, incremental memory injection, hidden checkpoints, structured judging, and leak-target annotations. Across diverse baselines and backbone models, no method simultaneously achieves strong utility, robust access control, and reliable forgetting. Long-context prompting often yields the best governance score at high token cost, while retrieval-based and external-memory methods reduce cost yet still leak unauthorized or deleted information. These results show current memory agents remain far from reliable shared institutional deployment.

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

TimeLens: On-Device Artifact Recognition with Retrieval-Augmented Question Answering for the Grand Egyptian Museum

TimeLens is an AI-powered bilingual mobile guide for the Grand Egyptian Museum (GEM). Pointing a phone at an exhibit, a visitor sees the artifact recognized in real time and can ask follow-up questions answered in English or Arabic. The work addresses three problems specific to in-gallery deployment: fine-grained visual similarity among 51 catalogued artifacts (many near-identical Ramesside statues), the gap between curated training data and handheld camera conditions, and the risk of an AI guide stating unsupported historical facts. Two engineering contributions are reported. First, an on-device artifact detector was developed through a data-quality-driven iteration study – from foundation-model auto-annotation (YOLO-World), through spatial label-cleaning rules, to a fully hand-annotated dataset – isolating label quality as the decisive factor: the final YOLOv8n model resolves every previously failing class while remaining a 5.97 MB TensorFlow Lite asset that runs in real time on a mid-range phone (mAP@0.5 = 0.995, mAP@0.5:0.95 = 0.924). Second, a bilingual Retrieval-Augmented Generation (RAG) guide, grounded in a 108-record ChromaDB knowledge base, was benchmarked across seven candidate language models, with Gemma 4 E2B (Q4 K M) selected; ten targeted optimizations reduce end-to-end latency from over 30 s to approximately 10 s. Both subsystems are integrated in a production Flutter application with bilingual interface, museum location gating, and text-to-speech support.

12.
arXiv (math.PR) 2026-06-11

On Skorokhod Problems for Reflected and Singular Stochastic Heat Equations

arXiv:2606.11951v1 Announce Type: new Abstract: We prove a Skorokhod decomposition for the Markov processes $X^a$ and $X$ associated to the gradient Dirichlet forms with respect to the measures $\rho^a\mu^{\beta}$ and $\rho\mu^{\beta}$, respectively. Here, $\mu^{\beta}$ is the law of the standard Brownian bridge $\beta$, while $\rho^a$ and $\rho$ denote densities which are given by $\rho^a(z) := \mathbf{1}_{[0,\infty)}(\bar{z}_a)$ and $\rho(z) := \int_0^1 \mathbf{1}_{[0,\infty)}(\bar{z}_x) \, dx$, respectively, for all $z\in L^2(0,1)$ which have a (unique) continuous representative $\bar{z}$ which vanishes at zero and one. To this end, we derive infinite-dimensional integration by parts formulas (IbPFs) w.r.t. $\rho^a\mu^{\beta}$ and $\rho\mu^{\beta}$, which contain Hida distributions alongside the usual drift terms. We represent these Hida distributions by integration w.r.t. vector measures of bounded variation. The vector measures in question are constructed via an approximation argument, making use of a generalization of Prokhorov's theorem for vector measures. We further prove that, almost surely, the sample paths of $X^a$ and $X$ take values in the equivalence class of continuous functions vanishing at zero and one for all and $dt$-almost all times, respectively. The main motivation for studying $\rho^a\mu^{\beta}$ and $\rho\mu^{\beta}$ lies in the fact that the distributional terms in their IbPFs are simplifications of the distributional term in the IbPF w.r.t. the law of the reflected Brownian bridge on the unit interval $\mu^{|\beta|}$. Representing the latter by integration w.r.t. a vector measure of bounded variation is still an open problem.

13.
arXiv (CS.CV) 2026-06-18

When Cars Have Stereotypes: Auditing Demographic Bias in Objects from Text-to-Image Models

While prior research on text-to-image generation has predominantly focused on biases in human depictions, demographic bias in generated objects remains relatively underexplored. We introduce SODA (Stereotyped Object Diagnostic Audit), a novel framework for systematically measuring these biases through automated attribute discovery and three standardized metrics: Base vs. Demographic Divergence (BDS), Cross-Demographic Disparity (CDS), and Visual Attribute Concentration (VAC). Applying SODA to 8,000 images across five state-of-the-art models and eight object categories (e.g., cars), we find that "neutral" prompts produce outputs most visually similar to middle-aged and White people, suggesting these groups are implicitly over-represented in model defaults. Furthermore, demographic cues trigger highly skewed stereotypical outputs: 26.6% of object-model-demographic combinations produce results where all 20 generated images share the exact same attribute value (e.g., rose gold laptops for women). Finally, prompt-level debiasing reduces inter-group disparity but paradoxically collapses within-group diversity, replacing one stereotype with another. SODA offers a practical pipeline for making these implicit associations measurable, serving as a step toward more responsible AI development.

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

Exploring Extrinsic and Intrinsic Properties for Effective Reasoning with Code Interpreter

Reasoning with a Code Interpreter (CI) has emerged as an effective paradigm for enhancing the reasoning capabilities of large language models (LLMs) through executable computation and iterative verification. Despite its growing adoption, the behavioral properties underlying effective code reasoning remain largely underexplored. In this work, we investigate code reasoning from two distinct perspectives inspired by prior studies of natural language reasoning: extrinsic properties, represented by crucial tokens, and intrinsic properties, represented by code-specific cognitive behaviors. Across multiple LLMs, we find that stronger CI reasoning models consistently exhibit a higher prevalence of crucial tokens and cognitive behaviors, particularly verification, backtracking, and backward chaining. Building on these observations, we examine how these properties can be leveraged during both inference and training. At inference time, appending code-specific crucial tokens improves performance on several reasoning capabilities, including mathematical, ordering, and optimization, while yielding limited benefits elsewhere. At training time, augmenting a state-of-the-art framework with code-specific cognitive behaviors improves supervised fine-tuning and reinforcement learning performance in two of three evaluated models. Further analysis shows that these behaviors reduce overthinking in incorrect responses and improve token efficiency, while also revealing factors that limit gains in a certain model. Our findings provide the first systematic characterization of effective reasoning with CI and demonstrate both the potential and limitations of leveraging key properties to improve CI-based reasoning.

15.
PLOS Medicine 2026-05-13

On the evolution of the company we keep: Implications for infectious disease modeling

by Joël Mossong Whom we meet shapes how infections spread. Where earlier focus of mathematical epidemiology was on incorporating age, more recent work has begun to reveal the importance of socioeconomic aspects for understanding and managing future epidemics. In this Perspective, Joël Mossong discusses the importance of understanding social contacts and how they have evolved for infectious disease modeling, and the need to factor in additional considerations such as ethic and socioeconomic backgrounds.

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

Benchmarking Instance-Dependent Label Noise with Controlled Corruptions

arXiv:2606.14965v1 Announce Type: new Abstract: Synthetic instance-dependent label noise (IDN) benchmarks are widely used to evaluate noisy-label learning methods, yet existing approaches typically generate noise through imperfect annotators or classifier raters, leaving the source of ambiguity implicit. We introduce CILN, a benchmark generation framework that creates IDN through controlled input corruptions. A diverse voter pool labels corrupted instances, producing benchmark datasets in which both the source and severity of ambiguity are explicit and controllable. Using CIFAR10, MNIST, and Adult, we construct 90 benchmark settings spanning multiple corruption families and severity levels. Our experiments show that the resulting benchmarks exhibit genuine instance-dependent noise, provide diverse confusion structures, and, on CIFAR-10, can produce label distributions that are closer to human uncertainty than an existing synthetic IDN benchmark. We further demonstrate that corruption-mediated IDN can expose failure modes of popular noisy-label learning methods, including Co-Teaching and DivideMix, that are not observed under comparable levels of rater-fallibility noise. These findings suggest that noise structure, not only noise rate, plays an important role in benchmark difficulty and algorithm behavior. By making ambiguity generation explicit and controllable, CILN provides a complementary benchmarking framework for studying noisy-label learning under diverse sources of instance difficulty.

17.
arXiv (quant-ph) 2026-06-11

Controlled ion-ion interactions and cavity-enhanced emission of a coherent dinuclear Eu$^{3+}$ complex

arXiv:2606.11947v1 Announce Type: new Abstract: Molecular rare-earth-ion complexes offer unique opportunities for quantum technologies by combining the intrinsic coherence properties of rare-earth ions with chemically tunable molecular environments. A crucial capability is the realization of multi-qubit architectures with defined qubit couplings to enable two-qubit quantum gates. Here, we investigate the optical coherence properties and excitation-induced interactions of two Eu$^{3+}$-based molecular complexes, comparing a mononuclear reference system with a dinuclear analogue in which two Eu$^{3+}$ ions are positioned at a well-defined intramolecular distance of about 7 Angstrom. Using cryogenic ensemble spectroscopy, including spectral hole burning, free-induction decay, and photon echo measurements at temperatures down to 100 mK, we demonstrate long optical coherence times $T_{2,o}$ of up to 9 $\mu$s. As a key step toward scalable multi-qubit architectures, a control-target sequence was implemented to probe conditional ion-ion interactions, revealing a stronger interaction-induced dephasing in the dinuclear complex. Finally, we show the integration of the dinuclear complex into a fiber-based optical microcavity, and observe an 380-fold emission enhancement of the $\mathrm{}^5\mathrm{D}_0\rightarrow\mathrm{}^7\mathrm{F}_0$ transition. Together, these results position molecular rare-earth complexes as versatile and chemically tunable building blocks for scalable quantum technologies.

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

BrainFusionNet: a deep learning and XAI model to understand local, global, and sequential features of MRI images for improved brain tumour detection

The noise of Magnetic Resonance Imaging MRI poses challenges for Deep Learning DL when tumor boundaries are obscured tumor location and appearance are complex Therefore we develop BrainFusionNet that combines Convolutional Neural Networks CNNs Vision Transformers ViT and Gated Recurrent Units GRUs to extract spatial contextual and sequential features from MRI images for improved brain tumor classification Furthermore explainable AI such as SHAP LIME and GradCAM are integrated to visualise and highlight image regions that contribute to BrainFusionNets decisionmaking process The proposed BrainFusionNet model is evaluated on two publicly available MRI datasets Kfold validation suggests 98 accuracy on both datasets The model was compared with the six stateoftheart SOTA CNNs and transfer learning Among the SOTA CNNs DenseNet121 and VGG16 achieved the highest accuracy of 96 The novelty of BrainFusionNet is that the hybrid model effectively extracts local and global features from MRI images even in smallscale tumor regions and small tumor sizes The model has a balanced sequential CNN architecture to capture lowlevel and deeperlayer features a customized ViT that captures local features stabilizes gradient flow and reduces the risk of vanishing gradients during MRI image training The CNN and ViT outputs are fed into a GRU for final classification Furthermore we analyze pixel intensities to determine whether MRI image quality affects image classification Our findings are very novel in image interpretation as we found that the distribution of pixel intensities in MRI images affects DL performance

19.
arXiv (CS.CV) 2026-06-15

$\mu_0$: A Scalable 3D Interaction-Trace World Model

World models that capture how actions induce physical change enable scalable robot learning without reliance on embodiment-specific action labels. Pixel-space video models provide broad visual priors but expend model capacity on dense appearance reconstruction, while direct action models require embodiment-specific labels that hinder scalability. We present $\mu_0$, a scalable world model based on 3D traces. Rather than predicting dense pixels or directly modeling actions, $\mu_0$ forecasts smooth 3D trajectories for salient interaction points such as objects, tools, hands, and contact regions, yielding a compact, embodiment-agnostic motion interface. To enable training from diverse video sources, our TraceExtract system automatically extracts 3D supervision by selecting keypoints, constructing globally aligned traces, and associating motion segments with hierarchical language captions. This TraceExtract supervision pretrains $\mu_0$ by combining a pretrained vision-language backbone with a modular trace expert, which represents each query via B-spline control points and predicts future traces. Experiments show that $\mu_0$ outperforms baselines in both 2D and 3D trace prediction, including trace prediction models and tokenized VLM methods. Because $\mu_0$ is frozen and reusable, it can be paired with action experts for downstream robot embodiments. Despite action-free pretraining, the resulting trace-conditioned policies achieve performance competitive with VLA models pretrained with action supervision, such as $\pi_0$. These results establish 3D traces as a scalable and transferable representation for cross-embodiment manipulation.

20.
arXiv (CS.LG) 2026-06-15

A Unified Framework for Structured Flow Modeling: From Representation to Verification and Model Discovery

arXiv:2605.18250v3 Announce Type: replace-cross Abstract: Many dynamical systems can be described in terms of structured flows combining source/sink behavior, cyclic dynamics, and topology-constrained transport. These features arise across a wide range of physical, engineered, and data-driven systems. The objective of this work is to establish a unified perspective on such systems, to identify modeling approaches that balance expressivity, interpretability, computational complexity, and data requirements, and to investigate how highly expressive models can be used to uncover the dominant mechanisms underlying observed dynamics. Starting from the Helmholtz-Hodge decomposition of continuous vector fields, we review the recently proposed Graph Vector Field (GVF) framework and its discrete representation on simplicial complexes. We then introduce a hierarchy of alternative approaches, including parametric conditional models, linear graph dynamical systems, and reduced Hodge representations. Finally, we propose a verification and validation methodology based on benchmark datasets from well-understood physical systems and on systematic model-reduction and ablation studies. The resulting family of structured-flow models within a common framework, ranging from low-dimensional parametric representations to full GVF formulations, supports a diagnostic methodology in which gradient, curl, harmonic, and topological contributions are systematically assessed through ablation studies. This process enables the identification of dominant mechanisms underlying the observed dynamics and guides the construction of simplified models tailored to the available data and operational constraints. By separating structural verification, behavioral verification, and domain-specific validation, the proposed approach provides a foundation for scalable and interpretable analysis of complex dynamical systems across multiple application domains.

21.
arXiv (math.PR) 2026-06-17

Spectral recovery of a planted triangle-dense subgraph

arXiv:2606.17604v1 Announce Type: cross Abstract: Given a simple graph on $n$ vertices and a parameter $k$, the triangle-densest-$k$-subgraph problem is known to be computationally hard in the worst case. To circumvent the computational hardness, we study an average-case model where a triangle-dense subgraph on $k$ vertices is planted in an Erdős-Rényi random graph on $n$ vertices. For the recovery of the planted subgraph, we propose a simple spectral algorithm and a semidefinite program, both of which use a graph matrix whose entries are local signed triangle counts. Theoretical guarantees for these algorithms are established through spectral analysis of the graph matrix. Finally, we provide evidence showing a statistical-to-computational gap analogous to that for the planted clique problem. The computational threshold in terms of the subgraph size $k$ is at least $\sqrt{n}$ in the framework of low-degree polynomial algorithms, while the information-theoretic threshold is at most logarithmic in $n$.

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

Benchmarking Physics-Informed Time-Series Models for Operational Global Station Weather Forecasting

The development of Time-Series Forecasting (TSF) models is often constrained by the lack of comprehensive datasets, especially in Global Station Weather Forecasting (GSWF), where existing datasets are small, temporally short, and spatially sparse. To address this, we introduce WEATHER-5K, a large-scale observational weather dataset that better reflects real-world conditions, supporting improved model training and evaluation. While recent TSF methods perform well on benchmarks, they lag behind operational Numerical Weather Prediction systems in capturing complex weather dynamics and extreme events. We propose PhysicsFormer, a physics-informed forecasting model combining a dynamic core with a Transformer residual to predict future weather states. Physical consistency is enforced via pressure-wind alignment and energy-aware smoothness losses, ensuring plausible dynamics while capturing complex temporal patterns. We benchmark PhysicsFormer and other TSF models against operational systems across several weather variables, extreme event prediction, and model complexity, providing a comprehensive assessment of the gap between academic TSF models and operational forecasting. The dataset and benchmark implementation are available at: https://github.com/taohan10200/WEATHER-5K.

23.
arXiv (CS.CV) 2026-06-16

Unified Multimodal Model for Brain MRI Imputation and Understanding

Multimodal large language models (MLLMs) hold great potential for medicine, as they inherit knowledge from LLM and allow multiple data modalities to be integrated, analysed and interpreted in natural language. However, the field of medical MLLMs is constrained by non-trivial challenges, notably the scarcity of high-quality training data and the frequent occurrence of missing data in the real-world clinical setting. Here, we propose a novel unified multimodal model, UniBrain, for brain magnetic resonance image (MRI) analysis. To address potential missing brain MRI modalities, we employ a unified training strategy to perform joint imaging modality imputation and brain image understanding. During training, an interleaved and description-enriched data flow is constructed to train the model in an autoregressive manner, enabling medical reasoning with generated multimodal data. A self-alignment strategy is introduced to leverage dense image embeddings to learn fine-grained anatomical features without requiring detailed image captions. Furthermore, we propose a dynamic hidden state mechanism to alleviate the exposure bias during long-context multimodal inference. Extensive experiments on multi-disease brain MRI dataset demonstrate that UniBrain achieves high performance for brain image imputation, understanding, and disease diagnosis under various extents of modality incompleteness.

24.
arXiv (CS.CL) 2026-06-19

ShoppingBench: A Real-World Intent-Grounded Shopping Benchmark for LLM-based Agents

Existing benchmarks in e-commerce primarily focus on basic user intents, such as finding or purchasing products. However, real-world users often pursue more complex goals, such as applying vouchers, managing budgets, and finding multi-products seller. To bridge this gap, we propose ShoppingBench, a novel end-to-end shopping benchmark designed to encompass increasingly challenging levels of grounded intent. Specifically, we propose a scalable framework to simulate user instructions based on various intents derived from sampled real-world products. To facilitate consistent and reliable evaluations, we provide a large-scale shopping sandbox that serves as an interactive simulated environment, incorporating over 2.5 million real-world products. Experimental results demonstrate that even state-of-the-art language agents (such as GPT-4.1) achieve absolute success rates under 50% on our benchmark tasks, highlighting the significant challenges posed by our ShoppingBench. In addition, we propose a trajectory distillation strategy and leverage supervised fine-tuning, along with reinforcement learning on synthetic trajectories, to distill the capabilities of a large language agent into a smaller one. As a result, our trained agent achieves competitive performance compared to GPT-4.1.

25.
arXiv (CS.LG) 2026-06-17

Questioning the Coverage-Length Metric in Conformal Prediction: When Shorter Intervals Are Not Better

arXiv:2601.21455v2 Announce Type: replace-cross Abstract: Conformal prediction(CP) has become a cornerstone of distribution-free uncertainty quantification, conventionally evaluated by its coverage and interval length. This work critically examines the sufficiency of these standard metrics. We demonstrate that the interval length might be deceptively improved through a counter-intuitive approach termed Prejudicial Trick(PT), while the coverage remains valid. Specifically, for any given test sample, PT probabilistically returns an interval, which is either null or constructed using an adjusted confidence level, thereby preserving marginal coverage. While PT potentially yields a deceptively lower interval length, it introduces practical vulnerabilities: the same input can yield completely different prediction intervals across repeated runs of the algorithm. We formally derive the conditions under which PT achieves these misleading improvements and provide extensive empirical evidence across various regression and classification tasks. Furthermore, we introduce a new metric interval stability which helps detect whether a new CP method implicitly improves the length based on such PT-like techniques. Code is available at https://github.com/benben-cd/PT-Conformal-Prediction.