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01.
arXiv (CS.AI) 2026-06-18

WebSP-Eval: Evaluating Web Agents on Website Security and Privacy Tasks

arXiv:2604.06367v2 Announce Type: replace-cross Abstract: Web agents automate browser tasks, ranging from simple form completion to complex workflows like ordering groceries. While current benchmarks evaluate general-purpose performance~(e.g., WebArena) or safety against malicious actions~(e.g., SafeArena), no existing framework assesses an agent's ability to successfully execute user-facing website security and privacy tasks, such as managing cookie preferences, configuring privacy-sensitive account settings, or revoking inactive sessions. To address this gap, we introduce WebSP-Eval, an evaluation framework for measuring web agent performance on website security and privacy tasks. WebSP-Eval comprises 1) a manually crafted task dataset of 200 task instances across 28 websites; 2) a robust agentic system supporting account and initial state management across runs using a custom Google Chrome extension; and 3) an automated evaluator. We evaluate a total of 8 web agent instantiations using state-of-the-art multimodal large language models, conducting a fine-grained analysis across websites, task categories, and UI elements. Our evaluation reveals that current models suffer from limited autonomous exploration capabilities to reliably solve website security and privacy tasks, and struggle with specific task categories and websites. Crucially, we identify stateful UI elements are a primary reason for agent failure, with toggles causing more than 45% task failure across many models.

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

Vision-Encoder Behavioral Fingerprints of Image-to-Image Generative Models: A Training-Paradigm-Driven Taxonomy of Six Commercial APIs

作者:

We study six production image-to-image AI systems (gpt-image-1, Gemini 2.5 Flash Image, Flux Kontext, SDXL img2img, SD3 img2img, and Qwen Image Edit) under a content-adaptive sub-JND adversarial perturbation pipeline, scoring all outputs by frozen DINOv2 ViT-B/14 token distances against clean references. Across a 3,588-call corpus spanning COCO photographs, CelebA-HQ portraits, and AI-generated inputs, the six systems partition into two image-invariant behavioral bands on a 2D (patch_mean, ssim_clean) plane: edit-trained models (Flux Kontext, Qwen Edit, Gemini) cluster in a tight band, while T2I-base models adapted at sampling time (SDXL, SD3, gpt-image-1) cluster in a drift band.

03.
arXiv (CS.LG) 2026-06-16

Scalar-pathway fidelity improves physical accuracy in short-range equivariant interatomic potentials

arXiv:2606.15892v1 Announce Type: new Abstract: Accurate interatomic potentials enable molecular dynamics of materials, molecules, and interfaces beyond density-functional-theory length and time scales. Equivariant neural network potentials have improved the representation of local geometry. However, their deployable energy surfaces ultimately manifest through invariant scalar channels, whose aggregation and spectral resolution remain comparatively underexamined. Here we use Physics-Aware Neighborhood (PAN) pooling and Physics-Guided Spectral (PGS) mixers as controlled scalar-pathway probes: lightweight, symmetry-preserving modifications that act only on \(\ell=0\) channels while leaving the equivariant tensor backbone unchanged. Using MACE as a high-body-order mechanistic scaffold, PAN adds coordination-sensitive amplitude modulation, whereas PGS augments edge and readout scalar features with radial and tapered spectral bases. Across metallic Ag, covalent Si, a short-range ionic LiF/Li–F subset, and MD17/rMD17 molecules, this scalar-pathway correction reduces MACE force errors by 22–27\% and energy errors by 19–22\%; on systems with stress labels, stress errors decrease by 27–28\%, at approximately 5\% additional inference-FLOPs cost. Directionally consistent gains in Allegro and NequIP further indicate that the correction is portable across distinct short-range equivariant backbones, although effect sizes remain architecture-dependent. These results identify scalar-pathway fidelity as a practical design dimension for short-range equivariant interatomic potentials.

04.
arXiv (CS.AI) 2026-06-16

Safe Exploration via Policy Priors

arXiv:2601.19612v3 Announce Type: replace-cross Abstract: Safe exploration is a key requirement for reinforcement learning (RL) agents to learn and adapt online, beyond controlled (e.g. simulated) environments. In this work, we tackle this challenge by utilizing suboptimal yet conservative policies (e.g., obtained from offline data or simulators) as priors. Our approach, SOOPER, uses probabilistic dynamics models to optimistically explore, yet pessimistically fall back to the conservative policy prior if needed. We prove that SOOPER guarantees safety throughout learning, and establish convergence to an optimal policy by bounding its cumulative regret. Extensive experiments on key safe RL benchmarks and real-world hardware demonstrate that SOOPER is scalable, outperforms the state-of-the-art and validate our theoretical guarantees in practice.

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

Beyond Classification: A Cough Regression Benchmark for Respiratory Acoustic Foundation Models

arXiv:2606.15436v1 Announce Type: cross Abstract: Respiratory acoustic foundation models (FMs) excel at cough classification, yet their ability to predict continuous health quantities from cough audio remains largely unexplored, despite the clinical value of passive age, BMI, and disease probability estimation in settings where physical measurements are unavailable. We introduce the multi-model, multi-target cough regression benchmark evaluating five FMs (OPERA-CT, OPERA-CE, OPERA-GT, HeAR, M2D+Resp) across six targets on three datasets under subject-disjoint protocols, comparing linear, MLP-small, and full MLP regression heads. MLP-small beats the mean-predictor baseline on all tasks and linear probing in 23 of 30 model x task cases, with full MLP overfitting on small clinical data but recovering on larger sets, revealing a dataset size x head-capacity trade-off. HeAR leads within-dataset age regression on Coswara (9.12 yr MAE); its CIDRZ result is excluded from headline claims owing to possible HeAR-CIDRZ pretraining overlap. OPERA-GT is favored over OPERA-CT on age in all three datasets, with the CIDRZ margin within seed variance, extending a generative-pretraining advantage from breath to cough. HeAR and M2D+Resp reach near-full performance at N = 50 samples while OPERA models require N = 400. Cross-dataset transfer is strongly asymmetric as large diverse data generalises to small clinical populations (CoughVID to CIDRZ: -0.17 yr) but not vice versa (CIDRZ to Coswara: +2.43 yr, +26.6%).

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

Smol-GS: Compact Representations for Abstract 3D Gaussian Splatting

We present Smol-GS, a novel method for learning compact representations for 3D Gaussian Splatting (3DGS). Our approach learns highly efficient splat-wise features to model 3D space, which capture abstracted cues, including color, opacity, transformation, and material properties. We propose octree-derived positional encoding, which explicitly models spatial locality and enhances representation efficiency. We further apply entropy-based compression to exploit feature redundancy and compress splat coordinates using a recursive voxel hierarchy. This design enables orders-of-magnitude reduction in storage while preserving representation flexibility. Smol-GS achieves state-of-the-art compression performance on standard benchmarks with high-level rendering quality.

07.
arXiv (CS.CV) 2026-06-17

Critique of World Model: A Generative Latent Prediction Architecture for World Modeling

World Model, the algorithmic simulator of the real-world environment which biological agents experience and act upon, has been an emerging topic in recent years due to the rising need to develop virtual agents with artificial (general) intelligence. There has been much discussion on what a world model really is, how to build it, how to use it, and how to evaluate it. In this essay, starting from the imagination in the famed Sci-Fi classic Dune, and drawing inspiration from the concept of ``hypothetical thinking'' in psychology literature, we argue the primary goal of a world model to be {\it simulating all actionable possibilities of the real world for purposeful reasoning and acting}. We examine the key design dimensions of world modeling: data, representation, architecture, learning objective, and usage, surveying existing approaches and analyzing their tradeoffs. Building on this examination, we propose a new Generative Latent Prediction (GLP) architecture for a general-purpose world model, based on stateful, hierarchical, multi-level, and mixed continuous/discrete representations, and a generative and self-supervised learning framework, with an outlook of a Physical, Agentic, and Nested (PAN) AGI system enabled by such a model.

08.
arXiv (CS.CV) 2026-06-12

Multi-Label Test-Time Adaptation with Bayesian Conditional Priors

Multi-label recognition with frozen Vision-Language Models (VLMs) is brittle under distribution shift: standard zero-shot inference scores labels independently, ignoring co-occurrence structure and producing incoherent label sets where dominant concepts suppress weaker but compatible labels. We introduce Bayesian Conditional Priors (BCP) Estimation, a gradient-free test-time adaptation method that injects label dependency without tuning the backbone. BCP views zero-shot logits as a proxy for marginal posteriors under a fixed image-text likelihood and attributes shift-induced errors mainly to a mismatched label prior. For each test image, it selects a high-confidence anchor label and applies an anchor-conditioned Bayesian refinement. This update is closed-form in logit space and admits a pointwise mutual information (PMI) interpretation, explicitly promoting compatible labels and suppressing incompatible ones. BCP operates without target annotations by estimating anchor-conditioned priors online from the unlabeled test stream via lightweight second-order co-occurrence statistics, adding negligible overhead beyond a single forward pass. Across standard multi-label benchmarks and multiple CLIP backbones, BCP consistently outperforms strong TTA baselines, e.g., improving RN50 average mAP from 57.31 to 69.22 and ViT-B/16 from 62.61 to 71.79.

10.
arXiv (CS.CL) 2026-06-12

Marginal Alignment Does Not Guarantee Joint-Distribution Fidelity: An Official-Reference Audit of Nemotron-Personas-Korea with Cross-Locale Replication

Synthetic persona datasets cite alignment with official demographics as a basis for trust, yet downstream users consume them as joint structures across age, sex, region, occupation, education, name, and institutional status. Marginal alignment does not imply that these joints are preserved. We propose the Independence-Assumption Footprint (IAF), an audit primitive that operates on the attribute combinations a dataset card itself documents as treated independently. For each such combination, IAF compares the synthetic joint against an external official or institutional reference, using direct joint tables where available and rule-implied checks otherwise. Applied to NVIDIA Nemotron-Personas-Korea (one million Korean synthetic personas), IAF finds that NPK aligns with KOSIS marginals while three joints fail. The major-by-occupation distribution against the KEIS graduate universe carries a large conditional mismatch. The age profile of military service is institutionally inconsistent. Female representation in male-dominated occupations is substantially over-flattened toward parity, with the strict screening verdict mapping-dependent and age-robust under direct standardisation. A transferability demonstration across six further NPK locales finds locale-dependent rather than universal diagnostics, with reference-taxonomy cardinality confounding cross-locale flag counts. For synthetic personas used as silicon samples, marginal claims must therefore be paired with disclosure-anchored joint audits before reuse. The released audit artefacts (reference manifests, occupational crosswalks, derived metrics, reproducibility scripts) instantiate this protocol on the NPK family and are released for retargeting at other synthetic persona resources.

11.
arXiv (CS.AI) 2026-06-16

Integrating Multi-Label Classification and Generative AI for Scalable Analysis of User Feedback

arXiv:2601.23018v1 Announce Type: cross Abstract: In highly competitive software markets, user experience (UX) evaluation is crucial for ensuring software quality and fostering long-term product success. Such UX evaluations typically combine quantitative metrics from standardized questionnaires with qualitative feedback collected through open-ended questions. While open-ended feedback offers valuable insights for improvement and helps explain quantitative results, analyzing large volumes of user comments is challenging and time-consuming. In this paper, we present techniques developed during a long-term UX measurement project at a major software company to efficiently process and interpret extensive volumes of user comments. To provide a high-level overview of the collected comments, we employ a supervised machine learning approach that assigns meaningful, pre-defined topic labels to each comment. Additionally, we demonstrate how generative AI (GenAI) can be leveraged to create concise and informative summaries of user feedback, facilitating effective communication of findings to the organization and especially upper management. Finally, we investigate whether the sentiment expressed in user comments can serve as an indicator for overall product satisfaction. Our results show that sentiment analysis alone does not reliably reflect user satisfaction. Instead, product satisfaction needs to be assessed explicitly in surveys to measure the user's perception of the product.

12.
arXiv (CS.CV) 2026-06-15

Temporal Backtracking Search for Test-time Generative Video Reasoning

While test-time scaling has revolutionized reasoning in large language models, generative video reasoning remains bottlenecked by a single-shot paradigm. We demonstrate that searching over denoising steps cannot rescue logically flawed rollouts because spatial trajectories commit early in the diffusion process. Root-level Best-of-N (BoN) sampling is similarly inefficient: reasoning errors cluster early in the temporal axis, and resampling blindly discards verified upstream progress. To unlock effective test-time scaling for video models, we introduce Temporal Backtracking Search (TBS), which shifts the search space to the temporal axis. TBS transforms video generation into an iterative generate-verify-restart loop via three core mechanisms: (1) variable-K conditioning to resume generation from arbitrary clean prefixes; (2) temporal process verification to localize failures and extract valid restart anchors; and (3) prefix-based search to reallocate compute toward extending correct trajectories rather than root resampling. Across algorithmic, navigation, and robotics domains, TBS Pareto-dominates matched-budget BoN. In a strict out-of-distribution setting where one-shot generation collapses (0.7% for BoN), TBS achieves 22.7%, with every solved episode stemming from a restarted branch. Ultimately, TBS reveals that the local reasoning competence of video models far exceeds what single-shot rollouts indicate, providing a scalable test-time framework to unlock it.

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

Symbolic Informalization: Fluent, Productive, Multilingual

作者:

Symbolic informalization enables a reliable conversion of formal mathematics to natural language. It has the potential to make machine-checked content human-readable without loss of precision. In a traditional proof system usage, symbolic informalization generalizes the limited mechanisms of syntactic sugar into the ordinary language of mathematics. In a setting where proofs are constructed by artificial intelligence and autoformalization, symbolic informalization can explain what precisely has been constructed. This paper outlines the project Informath, which aims to show how symbolic informalization can produce fluent text with a reasonable development effort and address multiple formal and natural languages. Informath is based on an interlingual architecture, where Dedukti works as a hub between different proof systems (Agda, Lean, Rocq) and Grammatical Framework (GF) takes care of linguistic correctness and variation in different natural languages.

14.
arXiv (CS.CV) 2026-06-18

Where Will They Go? Modelling Multimodal Pedestrian Manoeuvres from Ego-centric Videos

Pedestrian trajectory prediction from an ego-centric camera is challenging since it depends on complex interactions with vehicles and scene context, as well as the intention of the pedestrian. By modelling correlation and intent from the historical and future trajectories of the pedestrian, it will usually result in a multimodal (i.e. multiple modes) distribution. Existing stochastic predictors often sample multiple futures from a single unimodal distribution, which can yield sub-optimal 'mixed-mode' trajectories that lie between distinct motion patterns and become implausible in real scenes. In this paper, we propose MMPM, a mode-aware framework that separately models future trajectory distributions into semantically meaningful modes based on the pedestrian's crossing behavior. MMPM consists of two modules: behavior-aware Pedestrian Interaction Module (PIM) that jointly captures pedestrian-vehicle and pedestrian-environment interactions by introducing gaze, head and hand gesture, and a CVAE-based Mode-aware Trajectory Predictor (MTP) module to model the future trajectory distributions on two modes, crossing and non-crossing the road, separately. A query-based decoder further enforces mode consistency during decoding. Experiments on PIE and JAAD datasets show that our method surpasses state-of-the-art baselines. Our proposed MTP is model-agnostic, which can be integrated into existing frameworks such as BiTrap-NP and SGNet-ED to further improve future trajectory prediction performance. We additionally introduce a data-driven validation protocol that matches predictions to spatio-temporally consistent ground-truth trajectories, demonstrating improved frame-wise displacement errors over previous work.

15.
arXiv (quant-ph) 2026-06-17

Entanglement transition in unitary system-bath dynamics

arXiv:2512.06081v3 Announce Type: replace Abstract: The evolution of a system coupled to baths is commonly described by a master equation that, in the long-time limit, yields a steady-state density matrix. However, when the same evolution is unraveled into quantum trajectories, it is possible to observe a transition in the scaling of entanglement within the system as the system-bath coupling increases - a phenomenon that is invisible in the trajectory-averaged reduced density matrix of the system. Here, we go beyond the paradigm of trajectories from master equations and explore whether a qualitatively analogous entanglement-scaling transition emerges in a single unitary evolution of the combined system-bath setup, without monitoring the dynamics of the system. We investigate the scaling of entanglement in a unitary quantum setup composed of a two-dimensional lattice of free fermions, where each site is coupled to a fermionic bath. As the system-bath coupling increases, the logarithmic fermionic negativity reveals an entanglement transition from logarithmic-law to area-law scaling. This occurs while the system's steady-state properties are trivial, highlighting that the signatures of these different scalings are within the bath-bath correlations. Evidence of the transition is also found in the mutual information and the correlations of the full system-bath setup, suggesting that the entanglement transition is underpinned by a change in the spatial structure of quantum information.

16.
Nature (Science) 2026-06-11

‘Footballers are not superheroes’: we must tackle the mental and physical pressures of elite sport

作者:

As the men’s football World Cup gets under way, how the game weighs on the health of athletes still isn’t talked about enough, says player-turned-medic Vincent Gouttebarge. As the men’s football World Cup gets under way, how the game weighs on the health of athletes still isn’t talked about enough, says player-turned-medic Vincent Gouttebarge.

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

Efficient Financial Language Understanding via Distillation with Synthetic Data

Large instruction-following models are powerful but costly to deploy, particularly in finance, where labelled data are limited by confidentiality and expert annotation cost. We present an efficient framework for financial sentiment analysis through distillation with synthetic data, transferring knowledge from a large instruction-tuned teacher to compact student models. The framework is designed for low-resource conditions, where a small set of real examples are collected and labelled by hand. The framework then clusters the examples and uses the clusters to select seeds for generating synthetic examples via structured few-shot prompting. Experiments show that clustering-based seed selection yields more representative synthetic data than random sampling, enabling compact models to achieve strong performance with minimal supervision. Notably, on a more complex and noisy text domain, the compact model trained on the complete synthetic-seed corpus even outperforms the teacher model, while remaining competitive on formal text. The framework provides a practical route toward resource-efficient domain adaptation in financial NLP with minimal human labelling effort.

18.
arXiv (CS.AI) 2026-06-19

Bridging Distribution Shift and AI Safety: Conceptual and Methodological Synergies

arXiv:2505.22829v2 Announce Type: replace-cross Abstract: This paper bridges distribution shift and AI safety through a comprehensive analysis of their conceptual and methodological synergies. While prior discussions often focus on narrow cases or informal analogies, we establish two types connections between specific causes of distribution shift and fine-grained AI safety issues: (1) methods addressing a specific shift type can help achieve corresponding safety goals, or (2) certain shifts and safety issues can be formally reduced to each other, enabling mutual adaptation of their methods. Our findings provide a unified perspective that encourages deeper integration between distribution shift and AI safety research.

19.
arXiv (quant-ph) 2026-06-11

Super-Link Fragility in Asymmetric W-Class States under Quantum Noise

arXiv:2606.12307v1 Announce Type: new Abstract: The asymmetric three-qubit W-class state $|\overline{W_3^L}\rangle$ defines an isosceles entanglement-network geometry, (a) two vertex-base (VB) links form stronger bipartite connections, (b) while the base-base (BB) link is weaker. This suggests that concentrating entanglement into a super-link may be advantageous for quantum-network tasks. Here, we show that this intuition is incomplete. We analytically compare the bipartite concurrence dynamics of the symmetric |W> state and the asymmetric $|\overline{W_3^L}\rangle$ state, which differ both in entanglement-network geometry and excitation sector under standard noise models. In the absence of noise, the concurrence hierarchy is C_{VB} > C_W > C_{BB}$. Under phase damping, this hierarchy is preserved for all noise strengths and no entanglement sudden death occurs. Under amplitude damping, however, the hierarchy is reordered. The symmetric |W> state becomes the most robust, while the base-base concurrence of $|\overline{W_3^L}\rangle$ vanishes at the finite threshold of parameter $\gamma$. We term this reordering as the Super-Link Fragility Effect. The same structural asymmetry that produces a stronger vertex-base link also makes it more vulnerable to energy dissipation when coupled with multi-excitation amplitudes. Under depolarization, the asymmetry advantage is erased, with $C_W$ and $C_{VB}$ sharing the same sudden-death threshold for some value of the parameter p, while $C_{BB}$ disappears earlier at some other value of the parameter p. The generalized amplitude damping channel continuously connects the damping-dominated regime to the pure-excitation limit, where the initial hierarchy is restored. These results show that entanglement robustness in $W$-class resources is controlled not by initial concurrence alone, but by the joint structure of entanglement-network geometry, excitation sector, and noise symmetry.

20.
arXiv (CS.AI) 2026-06-19

SPOT-E: Test-Time Entropy Shaping with Visual Spotlights for Frozen VLMs

arXiv:2606.20244v1 Announce Type: cross Abstract: Vision-language models (VLMs) often underperform on evidence intensive tasks because decisive visual evidence are small, localized, and easy to overlook, leading to failures in evidence readout even when high-level reasoning is intact. Prior inference-time visual interventions can improve grounding without retraining, but they are largely open-loop and lack a mechanism to verify whether highlighted evidence is actually used. We study answer-span prediction entropy as a model-internal feedback signal and show that naive entropy minimization is ambiguous, since low entropy may arise from evidence-grounded confidence or shortcut collapse. To resolve this ambiguity, we introduce low-entropy anchors and an entropy-shaping objective that reduces answer uncertainty while preserving baseline high-confidence tokens. We instantiate this principle in SPOT-E, a plug-and-play test-time method that produces question-conditioned spotlights, optimized per instance via light-weight tuning based on Group Relative Policy Optimization (GRPO). Across all benchmarks and different VLM families, SPOT-E yields consistent gains and improved robustness under visual corruptions. Code is publicly available at: \url{https://github.com/YinBo0927/SPOT-E}

21.
arXiv (CS.AI) 2026-06-11

DiffCold: A Diffusion-based Generative Model for Cold-Start Item Recommendation

arXiv:2606.12245v1 Announce Type: cross Abstract: Cold-start item recommendation remains a persistent challenge in real-world systems due to the absence of interaction histories. While prior models attempt to bridge this gap using item content features, they universally suffer from the seesaw dilemma: enhancing performance for cold items inevitably degrades performance for warm items, and vice versa. We identify that this dilemma stems from a fundamental distributional disparity: warm item embeddings occupy a complex ``behavioral manifold" shaped by rich interaction signals, whereas cold item embeddings are constrained to a ``semantic manifold" derived solely from auxiliary content. Existing methods often force a rigid mapping between these inconsistent spaces, causing the model to sacrifice the precision of warm representations to accommodate cold ones. To address this, we propose DiffCold, a diffusion-based generative model that unifies warm and cold representations. Unlike GANs or VAEs, DiffCold leverages conditional diffusion to reconstruct warm item embeddings from content, preserving the underlying manifold structure without degradation. We further tailor this paradigm with two specific designs: a Retrieval-enhanced Aggregator that initializes generation using semantically similar warm items to bypass inefficient noise, and a Simulation-based Representation Alignment module that enforces distribution consistency between generated and real embeddings via contrastive learning. Experiments on three benchmarks confirm that DiffCold resolves the seesaw dilemma, consistently outperforming state-of-the-art methods across all metrics.

22.
arXiv (CS.CL) 2026-06-11

Which Models Are Our Models Built On? Auditing Invisible Dependencies in Modern LLMs

Modern LLM training pipelines increasingly rely on other models to generate data, filter corpora, judge outputs, and guide development decisions. These dependencies are recursive: a model may depend on an upstream artifact whose own dependencies are documented only in separate releases and artifacts. As a result, the full dependency structure is fragmented across heterogeneous public artifacts, with complexity and recursive depth far outpacing humans' ability to trace. We introduce ModSleuth, an agentic system that recursively reconstructs LLM dependency graphs from public artifacts with source-grounded evidence. We find that the primary challenge is no longer information extraction, but defining what constitutes a dependency and reconciling artifact references across inconsistent documentation. We address these challenges through a formalization that distinguishes direct and indirect dependencies, represents heterogeneous pipeline roles through operation-centered relationships, and resolves artifact identities across names, versions, and repositories. Applying ModSleuth to four public-artifact-rich LLM releases, we recover 1,060 source-verified dependencies and construct large-scale dependency graphs of modern LLM development. These graphs reveal multi-hop license obligations, train-evaluation coupling, discrepancies between released and training-time artifacts, and documentation inconsistencies that would otherwise be difficult to uncover. We release ModSleuth and the resulting dependency graphs to support transparent analysis of the increasingly complex ecosystems underlying modern LLMs.

23.
arXiv (math.PR) 2026-06-15

Stability of Synthetic Ricci Curvature Lower Bounds for Inverse Limit Extended Metric Measure Spaces

arXiv:2606.14322v1 Announce Type: cross Abstract: We show that every Polish extended metric measure space arises as an inverse limit of metric measure spaces up to isomorphism. We then prove that synthetic Ricci curvature lower bounds and several functional inequalities, including the log-Sobolev, Talagrand, Poincaré, and dimension-free Harnack inequalities are stable under inverse limit. We discuss applications to infinite-dimensional spaces, including abstract Wiener spaces and their quotient spaces.

24.
arXiv (math.PR) 2026-06-11

Hierarchical Random Measures without Tables

arXiv:2505.02653v2 Announce Type: replace-cross Abstract: The hierarchical Dirichlet process is the cornerstone of Bayesian nonparametric multilevel models. Its generative model can be described through a set of latent variables, commonly referred to as tables within the popular restaurant franchise metaphor. The latent tables simplify the expression of the posterior and allow for the implementation of Gibbs sampling algorithms to approximately draw posterior samples. However, managing their assignments can become computationally expensive, especially as the size of the dataset and the number of levels increase. In this work, we identify a prior for the concentration parameter of the hierarchical Dirichlet process that (i) induces a quasi-conjugate posterior distribution, and (ii) removes the need for tables, leading to more interpretable expressions for the posterior, with both a scalable and an exact algorithm to sample from it. Remarkably, this construction extends beyond the Dirichlet process, leading to a new framework for defining normalized hierarchical random measures and a new class of algorithms to sample from their posteriors. The key analytical tool is the independence of multivariate increments, that is, their representation as completely random vectors.

25.
Nature Medicine 2026-06-15

Activity-dependent adaptive deep brain stimulation improves gait in Parkinson’s disease

Parkinson’s disease leads to a spectrum of locomotor deficits that vary in severity with the nature of daily activities and the fluctuating physiology of patients. Many of these deficits remain inadequately addressed by existing deep brain stimulation therapies that rely on activity-agnostic parameters optimized for cardinal motor symptoms. By contrast, therapies embedding activity-specific parameters have the potential to better address the entire range of symptoms. Here we expose physiological principles that enable real-time decoding of ongoing locomotor activities across motor fluctuations from the neural dynamics of the subthalamic nucleus. This decoding steered activity-dependent adaptations of deep brain stimulation therapies that improved locomotor deficits while preserving efficacy for cardinal motor symptoms across activities of daily living. Our activity-dependent framework provides a blueprint for next-generation neuromodulation therapies that continuously select parameters optimized to the behavioral context and fluctuating physiology of each patient. ClinicalTrials.gov registration NCT06791902 . Neural decoding algorithms that leverage physiological principles of locomotor encoding support activity-dependent deep brain stimulation therapies that improve locomotor deficits in people with Parkinson’s disease.