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

NeuroClaw Technical Report

Agentic artificial intelligence systems promise to accelerate scientific workflows, but neuroimaging poses unique challenges: heterogeneous modalities (sMRI, fMRI, dMRI, EEG), long multi-stage pipelines, and persistent reproducibility risks. To address this gap, we present NeuroClaw, a domain-specialized multi-agent research assistant for executable and reproducible neuroimaging research. NeuroClaw operates directly on raw neuroimaging data across formats and modalities, grounding decisions in dataset semantics and BIDS metadata so users need not prepare curated inputs or bespoke model code. The platform combines harness engineering with end-to-end environment management, including pinned Python environments, Docker support, automated installers for common neuroimaging tools, and GPU configuration. In practice, this layer emphasizes checkpointing, post-execution verification, structured audit traces, and controlled runtime setup, making toolchains more transparent while improving reproducibility and auditability. A three-tier skill/agent hierarchy separates user-facing interaction, high-level orchestration, and low-level tool skills to decompose complex workflows into safe, reusable units. Alongside the NeuroClaw framework, we introduce NeuroBench, a system-level benchmark for executability, artifact validity, and reproducibility readiness. Across multiple multimodal LLMs, NeuroClaw-enabled runs yield consistent and substantial score improvements compared with direct agent invocation. Project homepage: https://cuhk-aim-group.github.io/NeuroClaw/index.html

02.
arXiv (CS.CV) 2026-06-17

Reinforcing Dual-Path Reasoning in Spatial Vision Language Models

Spatial VLMs have made substantial progress in geometric perception, yet complex spatial reasoning requiring multi-step inference over depth, distance, and scene relations remains challenging. Moreover, different spatial queries call for fundamentally different strategies: some are best addressed through purely linguistic, step-by-step deduction, while others require explicit 3D grounding before quantitative inference. We present Dual-Path Spatial Reasoning via Reinforcement Learning for Spatial VLMs (SR-REAL), a unified framework that equips a spatial VLM with two complementary reasoning paths: Language-Only Reasoning (LOR), which performs step-by-step linguistic deduction, and Detect-Then-Reason (DTR), which detects 3D geometric cues (e.g., centers or bounding boxes) via region tokens before explicit geometric inference. SR-REAL begins with a cold-start supervised fine-tuning stage that constructs LOR and DTR chain-of-thought supervision and exposes a region-to-3D interface, followed by RL that optimizes the policy model with accuracy and format rewards; for DTR, a discrete center-based detection reward further refines geometric alignment. Across diverse spatial benchmarks, SR-REAL significantly outperforms spatial VLM baselines: (i) a single RL-trained model supports both reasoning paths, with DTR excelling in region-aware tasks through precise 3D localization and LOR enhancing general spatial reasoning; (ii) jointly training both paths fosters mutual reinforcement; (iii) high-quality, blended cold-start data is crucial for stable RL optimization; and (iv) the model generalizes across datasets and domains without per-task tuning, demonstrating positive transfer between LOR and DTR.

03.
medRxiv (Medicine) 2026-06-22

Substantia Nigra and Subthalamic Nucleus Deep Brain Stimulation Exert Opposing Effects on Novelty Recognition in Parkinson's Disease

Episodic memory plays a critical role in supporting adaptive behavior; however, whether it can be causally regulated in humans via deep subcortical stimulation remains unclear. In the present study, we investigated the differential effects of substantia nigra (SN) and subthalamic nucleus (STN) stimulation on episodic memory, as well as the underlying mechanisms of its associated brain networks, using a recognition memory task combined with concurrent functional magnetic resonance imaging in patients with Parkinson's disease. SN-DBS increased recognition sensitivity and reduced false alarms at both frequencies, whereas 10 Hz STN-DBS reduced sensitivity and increased false alarms. Functional connectivity analyses in the absence of DBS stimulation identified a false recognition-related network linking nigral, pallidal, subthalamic, medial temporal, frontal, and occipital regions. SN-DBS-related false alarm reduction tracked modulation of this circuit and was marked by its baseline vulnerability state. These behavioral effects mapped onto target-dependent parieto-occipital and SN-visual retrieval pathways, supporting a model in which DBS bidirectionally regulates recognition memory through target- and frequency-dependent subcortical-cortical circuits.

04.
arXiv (CS.CL) 2026-06-17

Implicit vs. Explicit Prompting Strategies for LVLMs in Referential Communication

Two recent studies (Jones et al. (2026); Zeng et al. (2026)) reach apparently contradictory conclusions about whether LVLMs can coordinate on efficient referring expressions. We control for task differences between the studies while directly comparing their prompting styles. We replicate the finding that models can coordinate efficient referring expressions when explicitly prompted to do so, suggesting that other task differences are not responsible for divergent results. However, we also find that the same models fail to infer the need for communicative efficiency from a more implicit prompt, highlighting critical differences between how humans and AI systems communicate.

05.
arXiv (quant-ph) 2026-06-11

Entanglement preservation and Clauser-Horne nonlocality in electromagnetically induced transparency quantum memories

arXiv:2507.15453v4 Announce Type: replace Abstract: Entanglement preservation in noisy quantum memories represents a central challenge in quantum information science. While experiments have shown that electromagnetically induced transparency (EIT) memories can store entangled photons, a quantitative theoretical analysis of whether nonlocal quantum correlations can survive storage loss induced by ground-state decoherence remains limited. Here we combine the dark-state polariton formalism with a reduced density-operator treatment to derive an EIT-specific effective pure-loss description for the retrieved photonic state in the ground-state-decoherence-limited regime. The analysis reveals that decoherence transforms an initially pure Bell state into a mixed state with a vacuum component and predicts a protocol-dependent storage-efficiency benchmark of 89.7% for violating the chosen unconditional Clauser-Horne (CH) inequality. Above this benchmark, the retrieved photonic state violates the CH inequality without post-selection, whereas below it, this unconditional CH violation is no longer obtained. This framework provides a quantitative theoretical description of entanglement retention, retrieved photonic density operators, and protocol-dependent Bell-test benchmarks in EIT quantum memories.

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

A Technical Taxonomy of LLM Agent Communication Protocols

arXiv:2606.19135v1 Announce Type: cross Abstract: As large language models (LLMs) advance and multi-agent systems aim to overcome the limits of standalone agents, robust communication protocols are becoming essential infrastructure for distributed agent networks. Nonetheless, the fragmented protocol landscape presents a significant interoperability challenge. This study develops a technical taxonomy to classify and analyze LLM agent communication protocols. Following an established iterative method, we defined the taxonomy's purpose, meta-characteristic, and ending conditions, then performed five iterations, three empirical-to-conceptual and two conceptual-to-empirical, on nine actively maintained open-source protocols with demonstrable adoption. The taxonomy comprises five dimensions: counterparty, payload, interaction state, discovery mechanism, and schema flexibility. Classification reveals recurring architectural patterns: all sampled agent-to-agent protocols combine hybrid payloads with session-state persistence; most protocols support multiple predefined schemas, and two negotiate schemas at runtime, indicating a trend toward schema flexibility; decentralized discovery remains rare. Analysis suggests short-term convergence pressure toward protocols unifying agent-to-agent and agent-to-context (tool and data) communication. Long-term, however, no single protocol is likely to maximize versatility, efficiency, and portability simultaneously. The field will more likely evolve toward a federated, layered protocol stack. The framework guides protocol selection and highlights open research gaps such as privacy and policy enforcement.}

07.
arXiv (CS.LG) 2026-06-15

Code Correctness Signals in LLM Hidden States: Pre-Generation Probing and Repair Geometry

arXiv:2606.14530v1 Announce Type: new Abstract: Large language models encode rich information in their hidden states. This work asks whether code correctness is legible in the hidden states of Qwen3-4B-Instruct-2507, before it generates and as it repairs a failed attempt, studied on 444 LiveCodeBench tasks. It reports two findings connected by a single confound-control tool: residualization. First, the correctness of the model's first-attempt code is linearly decodable from the prompt-final hidden state, with a leakage-free held-out AUC of 0.931 +/- 0.008 across 50 outer splits. After the linear effect of prompt length is removed from each hidden state dimension, the probe still reaches 0.911 +/- 0.010, well above a prompt-length baseline of 0.754 +/- 0.014. Second, on 236 cleaned cases where the model attempts to repair a failed first attempt, the hidden state shift from the failing attempt to its repair carries a statistically detectable contrastive direction, significant on both a magnitude and a split-half test against label-shuffled nulls. This direction does not survive a conditional residualization against repair-context covariates that differ between successful and failed repairs, marking it as a correlate of repair success driven by the repair context rather than an isolated repair-comprehension feature. The probe layer is selected by nested cross-validation, and the same residualization approach that upholds the pre-generation correctness result overturns the repair-direction interpretation. The contribution is as much methodological as empirical: a diagnostic honest enough to report a negative result alongside a positive one.

08.
arXiv (math.PR) 2026-06-11

Persistent Homology of the Planar Wiener Sausage: Brownian Scaling and a Logarithmic Expectation Law

arXiv:2606.11248v1 Announce Type: new Abstract: We study degree-one persistent homology of the planar Wiener-sausage filtration generated by standard Brownian motion without drift. In the drifted case, regeneration along the drift direction leads to linear-in-time laws for persistent-homological observables. In the recurrent zero-drift case, this renewal structure disappears. The organizing mechanism is instead Brownian self-similarity: the persistence diagram at time $T$ is equal in law to the image of the unit-time diagram under spatial dilation by $\sqrt T$. Consequently, large-time questions on fixed radius windows are transformed into small-radius questions for the unit-time Brownian trace. Let $B$ be standard planar Brownian motion, let $K_T=B\left(\left[0,T\right]\right)$, and let $K_T^{\left(r\right)}$ be the radius-$r$ Wiener sausage. Since $K_T^{\left(r\right)}$ is connected, its first Betti number $\beta_1^T\left(r\right)$ is the number of bounded complementary components of $K_T^{\left(r\right)}$. For a bounded nonnegative Borel function $\psi$ supported in a compact interval $\left[a,b\right]\subset\left(0,\infty\right)$, we consider the smoothed Betti-curve observable $\left[r_0,r_1\right] \mathrm{\Phi}_\psi \left(T\right) = \int_{r_0}^{r_1} \beta_1^T \left( r \right) \psi \left( r \right) dr$. We prove that there exist absolute constants 0

09.
arXiv (CS.CV) 2026-06-11

Latent Geometric Chords for Query-Efficient Decision-Based Adversarial Attacks

While decision-based black-box adversarial attacks present a severe security threat, current methodologies suffer from fundamental limitations. Pixel-wise attacks frequently introduce unnatural, high-frequency visual artifacts, while latent-space frameworks are confined by the limited search space of low-dimensional manifolds and inherent reconstruction flaws. To resolve these limitations, we propose Latent Geometric Chords (LGC) for Query-Efficient Decision-Based Adversarial Attacks alongside a variant, LGC-H. At its core, LGC navigates decision boundaries by executing a curvature-aware geometric search within a compressed semantic manifold. To guarantee high visual fidelity and circumvent dimensionality bottlenecks, we introduce a Residual-based Adversarial Generation (RAG) mechanism. RAG isolates semantic perturbations as geometric chords and superimposes them directly onto the original source image. RAG substantially resolves baseline reconstruction flaws and effectively doubles the permissible search space dimensions. Experimental results demonstrate that LGC achieves robust cross-dataset transferability and substantially outperforms state-of-the-art baselines. Notably, our method, LGC, minimizes perturbation magnitudes while achieving state-of-the-art visual fidelity–with a Structural Similarity Index Measure (SSIM) exceeding 0.99 and a Learned Perceptual Image Patch Similarity (LPIPS) below 0.01 at 5000 queries–and sustaining high attack success rates under stringent perceptual constraints, successfully compromising adversarially trained robust models. The source code is available at: https://github.com/eihmuekhine/Latent-Geometric-Chords.

10.
arXiv (quant-ph) 2026-06-19

All-valid-state HOBO encoding for constrained combinatorial optimization on NISQ devices

arXiv:2606.20017v1 Announce Type: new Abstract: Continued advancements in quantum computing have stimulated growing interest in translating quantum technologies into real-world applications. Consequently, the investigation of practically motivated NP-hard problems is of significant value. This study investigates the performance of a variational quantum eigensolver (VQE) in addressing the traveling salesperson problem (TSP) through noiseless simulations representative of noisy intermediate-scale quantum (NISQ) devices using higher-order binary optimization (HOBO) encodings. We construct a HOBO Hamiltonian with an efficient binary representation and propose an all-valid-state HOBO (AVS-HOBO) scheme based on cyclic mapping that eliminates one penalty term and reuses states that would otherwise be invalid. Using TSP instances of up to 20 cities, we compare the original HOBO and AVS-HOBO encodings from multiple perspectives, including the energy convergence behavior and the approximation, tour-length, and feasibility ratios. In addition to simulations, we perform computations on real quantum hardware with different device architectures, where we not only compare the performances of different chips but also investigate the effects of different error-mitigation methods on actual quantum machines. The results indicate that AVS-HOBO encoding enhances the practical reliability of VQE on NISQ devices and improves scalability for larger TSP instances, with broader applicability to constrained quantum optimization problems.

11.
arXiv (quant-ph) 2026-06-24

Reinforcement Learning to Disentangle Multiqubit Quantum States from Partial Observations

arXiv:2406.07884v3 Announce Type: replace Abstract: Using partial knowledge of a quantum state to control multiqubit entanglement is a largely unexplored paradigm in the emerging field of quantum interactive dynamics with the potential to address outstanding challenges in quantum state preparation and compression, quantum control, and quantum complexity. We present a deep reinforcement learning (RL) approach using an actor-critic algorithm for constructing short disentangling circuits for states with up to 16 qubits. With access to only two-qubit reduced density matrices, our agent decides which pairs of qubits to apply two-qubit gates on; requiring only local information makes it directly applicable on modern NISQ devices, as we demonstrated experimentally on a trapped-ion quantum computer. Utilizing a permutation-equivariant transformer architecture, the agent can autonomously identify qubit permutations within the state, and adjusts the disentangling protocol accordingly. Once trained, it provides circuits from different initial states without further optimization. We demonstrate the agent's ability to identify and exploit the entanglement structure of multi-qubit states. We analyze the disentangling circuits constructed by the agent for 4- and 5-qubit Haar-random states, and observe strong correlations between consecutive gates and among the qubits involved. Through extensive benchmarking, we show the efficacy of the RL approach to find disentangling protocols with minimal gate resources. We explore the resilience of our trained agents to noise, highlighting their potential for real-world quantum computing applications. Analyzing optimal disentangling protocols, we report a general circuit to prepare an arbitrary 4-qubit state using at most 5 two-qubit (10 CNOT) gates.

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

Stochastic epidemic model with varying infectivity and waning immunity: the law of large numbers with unbounded infectivity

arXiv:2606.11845v1 Announce Type: new Abstract: We revisit the large population limit of our epidemic model with infection age dependent infectivity and progressive immunity waning, under the assumption that the supremum in $t$ of the random infectivity function has a finite expectation, while the previous proofs assumed that this supremum admits a deterministic upper bound.

13.
arXiv (CS.AI) 2026-06-15

CisTransCell: Single-Cell Perturbation Prediction via Gene Function, Regulatory Control, and Cellular Context

arXiv:2606.13713v1 Announce Type: cross Abstract: Predicting cellular transcriptional responses to genetic perturbations is a central problem in single-cell biology, especially in the zero-shot setting where the perturbed gene or gene combination is unseen during training. A major difficulty is that perturbation effects are not determined by expression state alone: they depend on how the perturbed gene product influences other genes and proteins, how those downstream factors act on cis-regulatory elements, and which regulatory programs are active in the current cell state. To better capture this biological complexity, we propose CisTransCell, a cell-conditioned multi-modal framework for single-cell perturbation prediction that augments each gene with two complementary priors: a regulatory-sequence prior that captures how the gene is controlled, and a coding-sequence prior that captures what the gene product does. By integrating these priors with cellular expression state, CisTransCell models perturbation response as a cascade from gene function to regulatory control to downstream transcriptional change. Experiments on benchmark single-cell perturbation datasets show that CisTransCell achieves strong performance in zero-shot perturbation prediction.

14.
arXiv (CS.CV) 2026-06-19

LaTtE-Flow: Layerwise Timestep-Expert Flow-based Transformer

Recent advances in multimodal foundation models unifying image understanding and generation have opened exciting avenues for tackling a wide range of vision-language tasks within a single framework. Despite progress, existing unified models typically require extensive pretraining and struggle to achieve the same level of performance compared to models dedicated to each task. Additionally, many of these models suffer from slow image generation speeds, limiting their practical deployment in real-time or resource-constrained settings. In this work, we propose Layerwise Timestep-Expert Flow-based Transformer (LaTtE-Flow), a novel and efficient architecture that unifies image understanding and generation within a single multimodal model. LaTtE-Flow builds upon powerful pretrained Vision-Language Models (VLMs) to inherit strong multimodal understanding capabilities, and extends them with a novel Layerwise Timestep Experts flow-based architecture for efficient image generation. LaTtE-Flow distributes the flow-matching process across specialized groups of Transformer layers, each responsible for a distinct subset of timesteps. This design significantly improves sampling efficiency by activating only a small subset of layers at each sampling timestep. To further enhance performance, we propose a Timestep-Conditioned Residual Attention mechanism for efficient information reuse across layers. Experiments demonstrate that LaTtE-Flow achieves strong performance on multimodal understanding tasks, while achieving competitive image generation quality with around 6x faster inference speed compared to recent unified multimodal models.

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

EnvShip-Bench: An Environment-Enhanced Benchmark for Short-Term Vessel Trajectory Prediction

arXiv:2606.15240v1 Announce Type: new Abstract: Vessel trajectory prediction is important for intelligent shipping, maritime surveillance, and navigation safety. However, existing public maritime AIS resources are often limited by inconsistent forecasting protocols, uneven data quality, and the lack of benchmark-ready contextual annotations, which hinder fair comparison and context-aware modeling. To address this gap, we present EnvShip-Bench, a unified benchmark for short-term vessel trajectory prediction built from large-scale raw AIS data from the Danish Maritime Authority (DMA) and NOAA through a common processing pipeline. EnvShip-Bench adopts a standardized forecasting protocol with 10 minutes of observation, 10 minutes of prediction, and 20-second sampling in vessel-centric local metric coordinates. Beyond the large-scale core benchmark, it provides a quality-first compact subset for efficient and reproducible experimentation, together with synchronized environmental and nearby-vessel context extensions. As a result, EnvShip-Bench supports trajectory-only, environment-aware, and interaction-aware forecasting under a unified evaluation framework. Extensive benchmark statistics and analysis demonstrate that EnvShip-Bench offers a standardized, extensible, and context-aware foundation for maritime trajectory forecasting research.

16.
bioRxiv (Bioinfo) 2026-06-11

DyMoTree decodes early cell state transitions and drivers from single-cell transcriptomes using a tree-structured neural network

Inferring early cell fate from single-cell RNA-sequencing data is essential for identifying cellular origins and fate plasticity in development and disease. However, existing methods often fail to exploit tree-structured lineage trajectories, limiting the accuracy and interpretability of fate mapping. Here we present DyMoTree, a computational framework that models cell fate decisions as nonlinear mappings between progenitor and terminal cell states under explicit lineage constraints. By integrating lineage graphs with a tree-structured neural architecture, DyMoTree learns lineage-resolved cell-state transition maps from single-cell transcriptomes, enabling robust inference of early fate bias and identification of fate-specific progenitor substates and driver genes. Across simulations, lineage-tracing experiments, and in vivo systems, DyMoTree outperformed existing methods in resolving early fate biases. Applications to mouse embryogenesis, lung adenocarcinoma progression, and CAR-T immunotherapy revealed regulatory programs underlying developmental and disease-associated transitions. DyMoTree provides a general framework for modeling lineage-resolved cell-state dynamics underlying development and disease progression.

17.
bioRxiv (Bioinfo) 2026-06-12

The Geometry of Allostery: A Laplacian Minor Hierarchy for Many-Body Protein Communication

Quantifying how cooperative, many-body relationships drive allostery in protein networks remains a major challenge. To address this, we develop the Laplacian minor hierarchy, a mathematical framework that characterizes the geometric invariants of a protein network. Lower-order minors yield standard metrics including the partition function and effective distances, whereas higher-order minors define novel topological measures: cooperation indices, each bounded between zero and one, that characterize pathway correlations at increasing levels of complexity, the third-order minor determines whether allosteric pathways are correlated or uncorrelated, and the fourth-order minor quantifies how distinct pathways communicate through intermediary residues. We apply this framework to analyze the evolutionary adaptation of the PSD95pdz3 domain from Class I to Class II ligand specificity via mutations G330T and H372A. The cooperation index demonstrates a distinct evolutionary hierarchy: the G330T mutation establishes distributed pathway couplings that the H372A mutation subsequently exploits, whereas H372A alone produces minimal global changes. Furthermore, the fourth-order analysis identifies His317 as a critical intermediary node bridging the class-switching (330-372) and class-bridging (330-400) allosteric pathways. These results demonstrate that allosteric dependencies emerge only when mutations accumulate in specific combinations, with a hierarchical organization of pathways structured around position 330 and intermediary nodes His317 and Phe400. Rather than predicting allosteric mechanisms, this framework provides a mechanistic explanation for why and how allostery emerges during protein evolution.

18.
arXiv (CS.CV) 2026-06-15

Rendering-Aware Sparse Sampling for BRDF Acquisition

Accurate BRDF acquisition is essential for realistic rendering, but dense gonioreflectometer measurements are slow and expensive. We study how to select a small set of BRDF measurements that is most informative for reconstructing material appearance under a learned BRDF prior. Existing sparse-acquisition methods often optimize samples for BRDF-space reconstruction for all materials, while the perceptual importance of a adaptive measurement ultimately depends on its effect on each rendered appearance. We therefore formulate sparse adaptive acquisition as a rendering-aware optimization problem. Our method combines a set encoder for sparse coordinate–value observations, a pretrained hypernetwork-based/PCA-based BRDF reconstructor, and a differentiable renderer. During sampler training, the reconstructor remains fixed, and gradients from a rendered-image loss optimize the measurement locations. This separates acquisition design from prior fitting and encourages the sampler to choose directions that are informative under the learned material distribution. To make the comparison controlled, we evaluate the uniform baseline, meta-learning method, HyperBRDF method, and our learned sampler under matched sample numbers, train/test split, rendering scene, object mask, image mapping, and metrics. Our central claim: rendering-aware sampling improves extremely sparse BRDF acquisition when final rendered appearance is the target. BRDF-space and combined losses are reported only as ablations, together with joint refinement and image-only latent fitting for unseen materials.

19.
arXiv (CS.LG) 2026-06-16

Anomaly Detection via Mean Shift Density Enhancement

arXiv:2602.03293v2 Announce Type: replace Abstract: Unsupervised anomaly detection stands as an important problem in machine learning. Existing unsupervised anomaly detection algorithms rarely perform well across different anomaly types, often excelling only under specific structural assumptions. This lack of robustness also becomes particularly evident under noisy settings. We propose Mean Shift Density Enhancement (MSDE), a fully unsupervised framework that detects anomalies through their geometric response to density-driven manifold evolution. MSDE is designed as a general purpose anomaly detection framework, based on the principle that normal samples, being well supported by local density, remain stable under iterative density enhancement, whereas anomalous samples undergo large cumulative displacements as they are attracted toward nearby density modes. To operationalize this idea, MSDE employs a weighted mean-shift procedure with adaptive, sample-specific density weights derived from a manifold learning-based fuzzy neighborhood graph. We evaluate MSDE on an anomaly detection benchmark comprising 46 real-world tabular datasets, four realistic anomaly generation mechanisms, and six noise levels. Compared to 13 established unsupervised baselines, MSDE achieves consistently strong, balanced and robust performance for several standard classification metrics, at several noise levels and on average over several types of anomalies. These results demonstrate that displacement-based scoring provides a robust alternative to the existing state-of-the-art for unsupervised anomaly detection.

20.
arXiv (math.PR) 2026-06-11

Exact Fourier dimensions of dyadic Mandelbrot cascades on curves of nonvanishing curvature under minimal integrability

arXiv:2606.11758v1 Announce Type: new Abstract: We prove an exact Fourier-dimension formula for scalar dyadic Mandelbrot cascades pushed forward to fixed C^2 Jordan curves with nonvanishing curvature. Let W be in the minimal Kahane-Peyriere regime, let the scalar dyadic cascade live on T = R/Z, and let gamma map T to R^2 be a fixed C^2 Jordan curve with nonvanishing curvature, parametrized at constant speed. For the push-forward measure mu_gamma, we prove that, almost surely on non-extinction, its Fourier dimension is A_loc(W), the usual local exponent obtained by optimizing over q>1 from the moment expression involving E[W^q]. The upper bound follows from the scalar circle local-dimension theorem, bi-Lipschitz transfer to the fixed curve, and a deterministic curved-support obstruction for Fourier dimension. The lower bound follows from a fixed-curve finite-r annular theorem, which gives summable annular Fourier decay under a single finite moment witness. The main analytic input is a deterministic phase-geometry package for fixed nondegenerate C^2 curves: stationary tubes, derivative bands, and phase-bin coefficient estimates replacing the explicit trigonometric structure available on the unit circle.

21.
arXiv (CS.AI) 2026-06-15

Quantile-Free Uncertainty Quantification in Graph Neural Networks

arXiv:2605.04847v2 Announce Type: replace-cross Abstract: Uncertainty quantification (UQ) in graph neural networks (GNNs) is crucial in high-stakes domains but remains a significant challenge. In graph settings, message passing often relies on strong assumptions such as exchangeability, which are rarely satisfied in practice, and achieving reliable UQ typically requires costly resampling or post-hoc calibration. To address these issues, we introduce Quantile-free Prediction Interval GNN (QpiGNN), a framework that builds on quantile regression (QR) to enable GNN-based UQ by directly optimizing coverage and interval width without requiring quantile inputs or post-processing. QpiGNN employs a dual-head architecture that decouples prediction and uncertainty, and is trained with label-only supervision through a quantile-free joint loss. This design allows efficient training and yields robust prediction intervals, with theoretical guarantees of asymptotic coverage and near-optimal width under mild assumptions. Experiments on 19 synthetic and real-world benchmarks show QpiGNN achieves average 22% higher coverage and 50% narrower intervals than baselines, while ensuring efficiency and robustness to noise and structural shifts.

22.
arXiv (CS.LG) 2026-06-15

On Rate-Optimal Partitioning Classification from Observable and from Privatised Data

arXiv:2312.14889v4 Announce Type: replace-cross Abstract: In this paper we revisit the classical method of partitioning classification and prove novel convergence rates under relaxed conditions, both for observable (non-privatised) and for privatised data. We consider the problem of classification in a $d$ dimensional Euclidean space. Previous results on the partitioning classifier worked with the strong density assumption (SDA), which is restrictive, as we demonstrate through simple examples. Here, we study the problem under much milder assumptions. We presuppose that the distribution of the inputs is a mixture of an absolutely continuous and a discrete distribution, such that the absolutely continuous component is concentrated on a $d_a$ dimensional subspace. In addition to the standard Lipschitz and margin conditions, a novel characteristic of the absolutely continuous component is introduced, by which the convergence rate of the classification error probability is computed, both for the binary and for the multi-class cases. This bound can reach the minimax optimal convergence rate achievable using SDA, but under much milder distributional assumptions. Interestingly, this convergence rate depends only on the intrinsic dimension of the continuous inputs, $d_a$, and not on $d$. Under privacy constraints, the data cannot be directly observed, and the constructed classifiers are functions of the randomised outcome of a suitable local differential privacy mechanism. In this paper we add Laplace distributed noises to the discretisations of all possible locations of the feature vector and to its label. Again, tight upper bounds on the convergence rate of the classification error probability can be derived, without using SDA, such that this rate depends on $2d_a$.

23.
arXiv (CS.LG) 2026-06-15

Deep Spectral Learning of Embedded Latent Transfer Operators for Stochastic Dynamical Systems

arXiv:2606.14079v1 Announce Type: new Abstract: We propose a spectral learning method for stochastic nonlinear dynamical systems represented with embedded latent transfer operators in deep feature spaces. We instantiate the method as Deep Spectral Encoder (DSE), an operator-based latent state-space model in which a time-invariant neural encoder implements learnable nonlinear feature maps from observations, and these features define Markovian latent states whose temporal evolution and observation mapping are described by the transfer and observation operators, respectively. Functional canonical correlation analysis in a learnable Galerkin-projected feature space provides state coordinates from past and future observations, and the two linear operators are estimated on the state coordinates as ridge-regularized closed-form solutions that coincide with Galerkin projections of the associated covariance operators. On this representation, we generalize sequential Bayesian filtering and Koopman spectral mode decomposition in feature space. Experiments on several scenarios show stable and superior performance with sequential Bayesian filtering and dynamic mode decomposition baselines even under noise and partial observability.

24.
arXiv (math.PR) 2026-06-12

Sub-Riemannian spectral distance

arXiv:2606.12804v1 Announce Type: cross Abstract: We study eigenvalues and eigenfunctions of the ``div-grad type" sub-Laplacian with respect to Popp's volume on a compact equiregular sub-Riemannian manifold $M$. Since Popp's volume is canonically determined by the sub-Riemannian structure of $M$, the spetra of the sub-Laplacian carry geometric meanings. In this paper, we first embed $M$ into the Hilbert space of square-summable sequences using eigenfunctions and then define a spectral distance between two compact equiregular sub-Riemannian manifolds. Our result is a sub-Riemannian analogue of Berard-Besson-Gallot's classical work in the Riemannian case.

25.
bioRxiv (Bioinfo) 2026-06-16

DynamicDemiLog: A Single Sketch for Ultrafast Similarity, Frequency, and Cardinality Estimation

Probabilistic cardinality estimators (HyperLogLog), similarity sketches (MinHash), and frequency estimators (Count-Min Sketch) are fundamental approximate data structures that each target one primary problem. We present DynamicDemiLog (DDL), a sketch that unifies cardinality estimation, set similarity, containment, element frequency and composition in one tiny data structure built from a single pass over the input stream. Using an inverted index over 200,687 RefSeq sketches (159,567 organisms), DDL performs all-to-all sketch similarity comparison of the full database in 30 seconds (128 threads, indexed) - over 375x faster per query than Mash's brute-force all-to-all comparison of 91,282 sketches, or 31x faster without the index, at double the sketch resolution. DDL extends the LogLog register with a mantissa: each register stores a floating-point-encoded hash value consisting of an integer exponent (the leading-zero count) and a fractional mantissa (the sub-leading-zero bits), rather than the integer leading-zero count alone. This preserves enough hash information for meaningful register-by-register comparison - a property that standard 6-bit registers lack - while improving on LogLog's cardinality estimation machinery, including DynamicLogLog's early exit mask for high-throughput streaming. With a default 10 mantissa bits (16-bit registers, 2,048 buckets, 4 KB), DDL achieves a per-register false-match rate of 0.018% on unrelated random same-size sets (compared to 17.0% for LL6, a basic HyperLogLog implementation), enabling Weighted Kmer Identity (WKID), Average Nucleotide Identity (ANI), containment, and completeness estimation from register comparison alone. A 16-bit per-register observation counter provides element frequency information at trivial additional computation cost, and an additional byte tracks element composition (GC content, for biological data). Furthermore, DDL's high-specificity registers enable an inverted index structure (DDLIndex) that answers similarity queries against a database of N sketches in O(B + M) time, where M is the number of matching index entries, compared to O(NxB) for pairwise comparison.