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01.
medRxiv (Medicine) 2026-06-16

Upper airway disease in primary ciliary dyskinesia: Clinical management and factors influencing decision-making, a multicentre analysis

Background Upper airway disease is common in primary ciliary dyskinesia (PCD), but management evidence is limited. We aimed to describe management practices and identify factors influencing management decisions. Methods Using data from the Ear-Nose-Throat (ENT) Prospective International Cohort of patients with PCD (EPIC-PCD) and an ENT-specialist survey across participating centres, we described management practices recorded at routine follow-up. We assessed clinical factors associated with practices via mixed-effects logistic regression models. In a subgroup of patients, we assessed factors associated with initiation or discontinuation of practices. Results We included 579 patients: median age 15 years, 46% female. Nasal rinsing (54%) and nasal corticosteroids (22%) were most frequently prescribed. Among 466 patients with available data, 47 had grommets (10%) and 42 hearing aids (9%). Nasal corticosteroids and rinsing were more frequently prescribed in patients with polyps (odds ratio [OR] 3.74, 95% confidence interval [CI] 1.80-7.76; OR 3.39, 95% CI 1.37-8.37) or turbinate hypertrophy (OR 1.89, 95% CI 1.03-3.47; OR 2.89, 95% CI 1.55-5.38), and upper airway nebulisation in patients with frequent nasal symptoms (OR 2.86, 95% CI 1.11-7.39). Management practices differed between centres, as seen also by the specialists survey responses. In 177 patients with multiple visits, initiation of nasal rinsing was associated with frequent nasal symptoms (OR 3.18, 95% CI 1.24-8.18) and turbinate hypertrophy (OR 3.21, 95% CI 1.20-8.59). Conclusion Upper airway disease management in PCD varies and is partly guided by symptom burden and clinical findings. This variation across centres highlights the need for care standardisation and PCD-specific management guidelines.

02.
arXiv (CS.LG) 2026-06-15

Anytime-Valid Confirmation of Label-Shift Corrections

Authors:

arXiv:2606.14028v1 Announce Type: cross Abstract: In small-batch scientific deployments, labeled target outcomes may be too scarce for reliable shift estimation even when unlabeled target inputs are available. We address the complementary setting where the practitioner has a pre-specified label-shift correction from domain knowledge and asks whether incoming labeled outcomes support it. We show that the per-observation likelihood ratio between a label-shift-corrected predictive and the source predictive is a conditional e-value, so its running product is a nonnegative martingale and Ville's inequality yields an anytime-valid confirmation rule. The log martingale equals the cumulative negative log-predictive density (NLPD) gap between the source and the corrected predictive, converting routine model monitoring into a formal sequential test. Rejection means the incoming data support the posited correction relative to the source predictive, but it is not a precise estimate of the degree of shift. Closed forms are available for GP sources with Gaussian label-shift ratios. GP regression simulations validate Type I control, finite-sample power, miscalibration sensitivity, and the small-batch advantage of a reliable prior over label-based re-estimation.

03.
medRxiv (Medicine) 2026-06-15

Bidirectional associations between cannabis use, oddball performance, and P3 event-related potential

Importance: Cannabis use remains prevalent in youth despite concerns regarding its potential impact on cognitive function. Unraveling whether the association between cannabis use and cognition is partially due to preexisting differences or primarily related to use is vital to understanding underlying mechanisms. Objective: To estimate the longitudinal association between cannabis initiation and cognitive trajectories, indexed by task performance and P3 event-related potential (ERP), and to estimate whether baseline cognition is associated with cannabis initiation. Design: Data were analyzed from the ongoing longitudinal Collaborative Study on the Genetics of Alcoholism (COGA) cohort, which was followed up approximately every 2-5 years from 2004 to 2025. Setting: 6 sites across the United States. Participants: Adolescent and young adult offspring of past COGA participants and control families who reported on their cannabis use and who had Visual Oddball (VOP) performance and P3 ERP data (N=4814; 52.4% female, 68.4% white) were grouped based on the timing of cognitive data collection relative to cannabis initiation into Pre-onset (n=2,449; [&ge;]1 assessment) and Post-onset (n=998; [&ge;]3 assessments) subsamples. Main Outcomes and Measures: VOP measures include performance accuracy (%), reaction times (ms), and P3 amplitude (V) and latency (ms) during target trials. Cannabis measures included lifetime use of cannabis (i.e., ever used) and age at first use. Results: High P3 amplitude, and prolonged P3 latency and reaction time were associated with a reduced hazard of cannabis initiation (All Hazards Ratio, [H.R.s]< 0.91, p's

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

Elastic ODYN: Differentiable Optimization for Infeasible Control and Learning in Robotics

arXiv:2606.16564v1 Announce Type: cross Abstract: Robotic systems routinely encounter conflicting objectives, modeling errors, and degenerate contact conditions that render quadratic programs (QPs) infeasible. Yet most optimization solvers and differentiable QP layers assume feasibility, leading to numerical failures, unstable gradients, or solver breakdown when constraints cannot be simultaneously satisfied. We present Elastic ODYN, a primal–dual non-interior-point QP solver that handles infeasibility through smooth squared-$\ell_2$ elastic relaxations. The resulting formulation remains well posed under ill-conditioning and degeneracy, supports warm starting, and converges to closest-to-feasible solutions when no feasible point exists. A lightweight refinement stage recovers physically meaningful dual variables from the elastic solution. Building on this framework, we develop Elastic OdynLayer, a differentiable QP layer with stable gradients under infeasibility, and Elastic OdynSQP, an infeasibility-aware SQP method that resolves inconsistent subproblems and intrinsically infeasible optimal control tasks through selective constraint relaxation. We evaluate the framework on benchmark QPs, singular contact mechanics, differentiable parameter identification, and quadrupedal and humanoid trajectory optimization. Across all settings, Elastic ODYN consistently outperforms state-of-the-art elastic QP solvers in robustness, warm-start performance, and convergence reliability, enabling optimization, simulation, control, and learning beyond the feasibility assumptions of existing methods.

05.
arXiv (CS.CL) 2026-06-12

Operads for compositional reasoning in LLMs

Question decomposition, i.e. breaking a complex query into simpler sub-queries whose answers are composed to produce a final answer, is a widely used strategy for improving LLM reasoning, yet it currently lacks a rigorous mathematical foundation. In this paper, we propose operads, mathematical structures that model many-in, one-out operations and compositions thereof, as a natural framework for describing question decomposition. We define the questions operad $Q$, in which operations correspond to question templates and composition corresponds to substitution of sub-answers, and show how QA models can be interpreted as algebras over $Q$. Beyond reframing existing practice, this operadic perspective points toward new methods, in particular a notion of operadic consistency, which measures whether a QA model's answers agree across the partial collapses of a question decomposition tree. Empirical evaluation of operadic consistency is reported in our companion paper (Bottman, Liu, and Richardson, 2026), which finds it strongly correlated with accuracy across twelve LLMs and four multi-hop QA datasets and outperforming standard temperature-based self-consistency baselines. We argue that operads are the natural mathematical home for question decomposition, and that invariants such as operadic consistency open new directions for analyzing and improving the reliability of multi-step reasoning.

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

Geometrical fairness in graph neural networks

arXiv:2606.17684v1 Announce Type: cross Abstract: Graph-based learning methods have become increasingly prominent due to their strong performance across diverse applications. Among these, recent frameworks grounded in diffusion processes provide a unifying perspective that extends traditional graph neural network formulations while addressing limitations of standard message-passing mechanisms. Despite these advances, concerns remain regarding the fairness of such models, as they may propagate or amplify biases present in the data. In this work, we introduce a fairness-aware adaptation of graph-based diffusion by modifying the underlying Laplacian operator. Our approach incorporates multiple complementary transformations, including subspace projections, spectral adjustments, and frequency-based filtering, to mitigate bias-related components. Leveraging the intrinsic smoothing properties of graph diffusion, we provide a principled analysis of the resulting behavior and establish theoretical insights into fairness properties. We evaluate the proposed framework on both synthetic and real-world datasets, demonstrating that it achieves competitive performance while improving fairness metrics with limited additional computational cost.

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

Optimal multi-spectral squeezing via deterministic 2D-phase optimization

arXiv:2606.20192v1 Announce Type: new Abstract: Optimization routines are ubiquitous in quantum information technologies and essential to reach the resource levels required by quantum protocols. Specifically, multi-spectral squeezing for use in such protocols requires that losses be kept minimal at every stage, including coherent detection, which is performed by interfering the signal with a classical local-oscillator beam. This in turn requires control over all optical degrees of freedom of the beam in order to optimize the detection. The most general framework for this optimization relies on agnostic, off-the-shelf machine-learning techniques. Here we take the opposite approach: by focusing on a physical description of the specific optical process, we develop a deterministic sequential algorithm that provably reaches the global maximum of the visibility in a pixel basis and scales linearly with the number of pixels, thereby offering an efficient and theoretically grounded alternative to black-box optimization. In our waveguide-based setup, the optimized mask increases the visibility from 76% to 84%, corresponding to a 20% gain in mode-matching efficiency. Multi-spectral squeezing measurements confirm that this improvement translates directly into quantum readout: for the most squeezed spectral mode, the squeezing increases from $-2.08$ dB to $-2.64$ dB, consistent with the inferred efficiency gain. These results establish deterministic spatial phase shaping as an effective, interpretable route to enhanced multimode squeezing in waveguide platforms.

08.
arXiv (quant-ph) 2026-06-11

On the Addressability Problem on CSS Codes

arXiv:2502.13889v4 Announce Type: replace Abstract: Recent discoveries in asymptotically good quantum codes have intensified research on their application in quantum computation and fault-tolerant operations. This study focuses on the addressability problem within CSS codes: we ask what circuits might implement logical gates on strict subsets of logical qubits. With some notion of fault-tolerance, we prove several impossibility results: for CSS codes with non-zero rate, one cannot address a logical $H$, $HS$, $SH$, or $\mathsf{CNOT}$ to any non-empty strict subset of logical qubits using a circuit made only from 1-local Clifford gates. Furthermore, we show that one cannot permute the logical qubits in a code purely by permuting the physical qubits, if the rate of the code is (asymptotically) greater than 1/3 and the distance is at least 3. We can show a similar no-go result for $\mathsf{CNOT}$s and $\mathsf{CZ}$s between two such high-rate codes, albeit under a more restrictive assumption on the circuit, which we call "global" (though recent addressable CCZ gates use global circuits). This work pioneers the study of distance-preserving addressability in quantum codes, mainly by considering automorphisms of the code. This perspective offers new insights and potential directions for future research. We argue that studying this trade off between addressability and efficiency of the codes is essential to understand better how to do efficient quantum computation.

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

Phase Transitions in Attention: A Bayesian Theory of Copy Head Emergence

arXiv:2606.12058v1 Announce Type: cross Abstract: Attention is the key mechanism underlying in-context learning in transformers, and attention patterns have been observed empirically to emerge abruptly during training. We present a Bayesian theory of feature learning in attention; we then focus on how the copy subcircuit in the first layer of an induction head is learned by analyzing a single-layer softmax attention network trained on a copy task. We derive a closed-form posterior over the attention matrix and reduce it to a low-dimensional order parameter space. This reduction reveals a phase transition in the amount of training data, which we verify using both Bayesian sampling and standard training with Adam. We contrast our results with linear attention and find that softmax attention exhibits a first-order phase transition while in linear attention an initial second-order phase transition is followed by a smooth, continuous evolution toward the structured attention pattern (crossover). Our work provides a first-principles theoretical account of the abrupt emergence of the copy subcircuit, reminiscent of the one observed in training large language models.

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

NRITYAM: Language Models Meet Art and Heritage of Dance

Language models have become essential tools in shaping modern workflows. However, their global effectiveness hinges on a nuanced understanding of local socio-cultural contexts. To address this gap, we present NRITYAM, a comprehensive benchmark for evaluating the cultural comprehension capabilities of language models in the context of global dance traditions. NRITYAM comprises 9,260 carefully curated question-answer pairs spanning 12 languages, making it the largest dataset dedicated to evaluating cultural knowledge in dance. The dataset has been developed from the ground up through close collaboration with native dance artists and native speakers of the languages, who authored and validated culturally relevant questions specific to their regions. We evaluate a broad set of models, including large language models, small language models, multimodal large language models, and small multimodal language models. As a multilingual and multicultural benchmark, NRITYAM sets a new standard for evaluating the ability of AI systems to understand and reason about traditional performing arts. Detailed dataset samples are available at~\url{https://github.com/niladrighosh03/NRITYAM}.

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

UniT: Unified Multimodal Chain-of-Thought Test-time Scaling

Unified models can handle both multimodal understanding and generation within a single architecture, yet they typically operate in a single pass without iteratively refining their outputs. Many multimodal tasks, especially those involving complex spatial compositions, multiple interacting objects, or evolving instructions, require decomposing instructions, verifying intermediate results, and making iterative corrections. While test-time scaling (TTS) has demonstrated that allocating additional inference compute for iterative reasoning substantially improves language model performance, extending this paradigm to unified multimodal models remains an open challenge. We introduce UniT, a framework for multimodal chain-of-thought test-time scaling that enables a single unified model to reason, verify, and refine across multiple rounds. UniT combines agentic data synthesis, unified model training, and flexible test-time inference to elicit cognitive behaviors including verification, subgoal decomposition, and content memory. Our key findings are: (1) unified models trained on short reasoning trajectories generalize to longer inference chains at test time; (2) sequential chain-of-thought reasoning provides a more scalable and compute-efficient TTS strategy than parallel sampling; (3) training on generation and editing trajectories improves out-of-distribution visual reasoning. These results establish multimodal test-time scaling as an effective paradigm for advancing both generation and understanding in unified models.

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

Pathwise integration beyond Young via Faber–Schauder energy spaces

Authors:

arXiv:2606.13331v1 Announce Type: cross Abstract: We develop a pathwise integration theory based on Faber–Schauder energy spaces. The approach replaces the classical Hölder–Young and finite-variation Young conditions by dyadic summability conditions expressed in terms of Faber–Schauder coefficients. On the normalized interval $[0,1]$, these conditions define Banach spaces $\mathcal{E}^p$, which we call Faber–Schauder energy spaces. For $p,q>1$ satisfying $1/p+1/q\ge1$, we prove that every pair $f\in\mathcal{E}^p$ and $g\in\mathcal {E}^q$ admits a continuous pathwise integral $I_{f,g}$, constructed from dyadic left Riemann sums. We call $I_{f,g}$ the Faber–Schauder integral, and show that it depends boundedly and bilinearly on $(f,g)$ in the corresponding energy norms. The integral satisfies additivity, integration by parts, and a dyadic Young–Loève estimate. It is also the uniform limit of classical Riemann–Stieltjes integrals of finite Faber–Schauder approximations. The Faber–Schauder integral agrees with the classical Young integral whenever the latter is available, but also applies to deterministic and Gaussian examples for which neither the Hölder–Young condition nor the finite-variation Young condition can be verified. In this sense, it provides a Faber–Schauder coefficient-based extension of Young's framework.

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

Adaptive $k$NN graph model

arXiv:2601.16509v2 Announce Type: replace-cross Abstract: The $k$-nearest neighbors ($k$NN) algorithm is a cornerstone of non-parametric classification in artificial intelligence, yet its deployment in large-scale applications is persistently constrained by the computational trade-off between inference speed and accuracy. Existing approximate nearest neighbor solutions accelerate retrieval but often degrade classification precision and lack adaptability in selecting the optimal neighborhood size ($k$). Here, we present an adaptive graph model that decouples inference latency from computational complexity. By integrating a Hierarchical Navigable Small World (HNSW) graph with a pre-computed voting mechanism, our framework completely transfers the computational burden of neighbor selection and weighting to the training phase. Within this topological structure, higher graph layers enable rapid navigation, while lower layers encode precise, node-specific decision boundaries with adaptive neighbor counts. Benchmarking against eight state-of-the-art baselines across six diverse datasets, we demonstrate that this architecture significantly accelerates inference speeds, achieving real-time performance, without compromising classification accuracy. These findings offer a scalable, robust solution to the inherent inference bottleneck of $k$NN, laying an adaptive structural foundation for graph-based nonparametric learning.

14.
arXiv (CS.CL) 2026-06-11

LibriConvo: Simulating Conversations from Read Literature for ASR and Diarization

We introduce LibriConvo, a synthetic conversational speech corpus for speaker diarization and automatic speech recognition (ASR), built by instantiating the previously proposed Speaker-Aware Simulated Conversation (SASC) framework in a dataset and benchmarking setting. The main contribution of this paper is a corpus construction pipeline and benchmark derived from that framework. To make the data more suitable for downstream ASR and diarization, conversational timing statistics are estimated from English CallHome using external voice activity detection, long pauses are compressed, LibriTTS utterances are grouped by book to improve local semantic continuity, and room impulse responses are selected with a spatial-plausibility heuristic. The resulting corpus contains 240.1 hours of audio across 1,496 dialogues involving 830 speakers, partitioned into speaker-disjoint train, validation, and test splits. We report baseline results for both diarization and ASR. On the test split, Sortformer outperforms the pyannote pipeline in diarization (11.1\% vs.~24.4\% DER). For ASR, a Fast Conformer-CTC XLarge model fine-tuned with Serialized Output Training achieves 7.29\% WER and 6.97\% cpWER, outperforming zero-shot Whisper-large-v3. These results position LibriConvo as a practical benchmark for studying synthetic conversational speech and for evaluating multi-speaker speech processing systems.

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

Ricci-Filtration: Boosting Retrieval-Augmented Generation Reranker to Query-Answer Tasks by Discrete Ricci Flow

arXiv:2606.15482v1 Announce Type: cross Abstract: Ricci flow is a curvature-guided diffusion process that deforms space by shrinking regions of high positive curvature and expanding those with negative curvature. Similarly, discrete Ricci flow on weighted graphs modifies edge weights by shrinking edges with positive Ricci curvature and stretching those with negative Ricci curvature, effectively increasing the separation between clusters. Inspired by these two cornerstone works, we propose a geometry-based RAG reranker enhancement procedure called Ricci-Filtration. By modeling the input query and initial retrieved chunks as a network, where the input query and chunks serve as nodes and embedding-based pairwise relations define an initial graph, Ricci-Filtration leverages discrete curvature and Ricci flow to evaluate the structural importance of each chunk with respect to the user query. The system first filters the initial chunks based on their geometric curvature relative to the query; then, a reranker processes the remaining chunks to enhance generative performance. We theoretically prove that normalized discrete Ricci flow can detect community structures by identifying distinct asymptotic behaviors in edge weights. This supports the removal of ``noisy'' document chunks characterized by large weights and negative Ricci curvature relative to the query node. Extensive experiments confirm that Ricci-Filtration outperforms several baseline reranking methods in accuracy, precision, recall, and F1 scores. Furthermore, ablation studies demonstrate that the Ricci-Filtration generally outperforms the baseline under various settings, highlighting the framework's robustness across different architectures.

16.
arXiv (math.PR) 2026-06-12

Sphere Packings in Higher Dimension (after Boaz Klartag)

arXiv:2606.13313v1 Announce Type: cross Abstract: Let $\delta_n^L$ be the maximal density of a lattice sphere packing in the $n$-dimensional Euclidean space. We explain how Boaz Klartag proved the inequality $\delta_n^L \geq c n^2 2^{-n}$ where $c>0$ is a universal constant. In higher dimension, even for non-lattice sphere packings, this new lower bound is a substantial improvement. Klartag's proof uses the probabilistic method in two different ways. The first, very standard, relies on the statistical properties of a uniformly chosen random lattice. The second, completely new, studies the stochastic evolution of an ellipsoid constrained to contain non nonzero lattice points in the interior.

17.
arXiv (CS.LG) 2026-06-24

Managing Task Execution for Unknown Workloads in Batteryless IoT: A Hardware-Agnostic Evaluation

arXiv:2606.24340v1 Announce Type: new Abstract: In recent years, the Internet of Things (IoT) paradigm has been shifting toward batteryless, energy-harvesting architectures. Sustaining reliable operation in these systems requires intelligent management of highly volatile stored energy. As edge applications grow in complexity, traditional energy-aware schedulers struggle with unpredictable workloads due to their reliance on static execution thresholds or pre-measured, hardware-specific task profiles. To overcome this, we propose two novel, hardware-agnostic dynamic scheduling strategies treating applications as a "black box," requiring no prior energy information: a model-free Reinforcement Learning (RL) agent and an on-the-fly Approximated Prediction (AP) method. We evaluate these methods against an adaptive task rate approach (AsTAR) and optimized static thresholds using a custom-built, physically accurate simulation framework driven by real-world solar data and dynamic LoRa transmission profiles. Rather than claiming universal superiority, our analysis exposes the distinct operational trade-offs of each method: the AP approach delivers lightweight, near-oracle task throughput; the RL agent provides tunable survival-execution balancing; and AsTAR excels at execution pacing across long energy gaps. Finally, we demonstrate that while these advanced strategies provide critical resilience for severely constrained systems with small capacitors, devices with larger energy buffers can efficiently rely on simpler, less computationally expensive static policies.

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

Render-FM: Feedforward Model for Real-time Photorealistic Volumetric Rendering

arXiv:2505.17338v3 Announce Type: replace-cross Abstract: Photorealistic volumetric rendering of CT scans greatly benefits clinical workflows, yet neural approaches such as Neural Radiance Fields (NeRF) and 3D Gaussian Splatting (3DGS) require prohibitive per-scan optimization (hours for NeRF, about 30 minutes for 3DGS), making them impractical in clinical settings. We propose Render-FM, a feedforward model that eliminates this bottleneck by directly regressing 6D Gaussian Splatting (6DGS) parameters from a CT volume in a single 2.8-second forward pass, a 500x speedup over per-scan optimization. To bridge the domain gap between natural scene reconstruction and medical volumetric rendering, we introduce Anatomy-Guided Priming (AGP), which incorporates segmentation masks and transfer functions as structural and appearance priors, information that existing Gaussian splatting methods overlook. Built on an nnU-Net-inspired 3D U-Net trained on diverse CT scans, Render-FM predicts per-voxel 6DGS parameters and supports immediate real-time rendering. Unlike per-scan methods, it generalizes to unseen anatomies, novel transfer functions, and enables compositional organ visualization with zero additional preparation time. Optional 89-second fine-tuning further improves quality, surpassing per-scan optimized baselines. Project page: https://gaozhongpai.github.io/renderfm/.

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

MeshLoom: Feed-Forward Non-Rigid Registration of Mesh Sequences

We present MeshLoom, a feed-forward registration network that directly reconstructs vertex deformations across mesh sequences. Our approach advances non-rigid registration beyond existing models, which are typically constrained by costly per-instance optimization, narrow object categories, pairwise-only inputs, or merely intermediate outputs. The network is simple and efficient, registering multiple meshes within seconds. At its core lies a topology-aware encoder–decoder design. Specifically, we first introduce a topology-aware point representation that encodes the anchor (reference) mesh's topology into its per-vertex features. This representation strengthens the network's understanding of the anchor-mesh geometry and disambiguates points that are Euclidean-close yet geodesically distant. We then propose a multi-modal encoder that fuses this anchor-mesh representation with complementary cues from each frame, such as shape latents and image features. These multi-source signals are compressed into a compact global motion embedding that captures dense inter-frame correspondence. A lightweight decoder then queries this global embedding with the anchor-mesh point representation, retrieving per-vertex deformations at target timestamps. Through extensive experiments across diverse motions and object categories, we show that MeshLoom achieves state-of-the-art results on non-rigid registration. In addition, we find that our global embedding-then-query paradigm naturally enables the network to generate deformations at intermediate timestamps, which extends MeshLoom to motion interpolation and mesh morphing. Project page: https://meshloom.github.io/ .

20.
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.

21.
arXiv (CS.CV) 2026-06-12

DuET: Dual Expert Trajectories for Diffusion Image Editing

Recent diffusion editors perform diverse instruction-based edits while conditioning on the source image at every denoising step. Yet persistent source-image conditioning can limit how fully an edit is executed and how natural the result appears, especially when the target scene diverges substantially from the input. We introduce DuET (Dual Expert Trajectories), a training-free inference method that temporarily relaxes source-image conditioning by transitioning through a text-to-image phase before returning to edit mode, allowing the denoising trajectory to move toward the target distribution while retaining the structural benefits of image-conditioned editing. Without modifying model weights or increasing sampling cost, DuET consistently improves instruction relevance, semantic fidelity, and perceptual quality across diverse models and benchmarks. In some cases, these gains come with a modest reduction in source-image preservation, revealing a predictable trade-off between source preservation and edit fidelity.

22.
arXiv (math.PR) 2026-06-12

Characterizing metric-space-valued processes: separating classes and weak invariance principles for measure-theoretic inference

arXiv:2606.13084v1 Announce Type: cross Abstract: This article investigates stochastic processes taking values in metric spaces that lack a topological vector space structure, a regime characterized by intricate interplay between topological, geometric, and temporal dependence structures. It is formally established that spaces admitting an isometric Hilbertian embedding constitute a strict subclass within the much broader class of metric spaces possessing the ball property. While traditional kernel methods are susceptible to geometric distortion when the underlying space cannot be isometrically embedded into a Hilbert space, we bypass such limitations by exploiting a fundamental structural property inherent to this broader class; namely, that Borel probability measures are uniquely determined by their values on balls. These separating classes provide the foundation for the subsequently introduced measure-theoretic inference methodology. We derive uniform convergence of a family of time-dependent random measures, alongside weak invariance principles for the corresponding nonstationary random fields. This framework explicitly exposes how dependence and geometric complexity influence sample path regularity. Furthermore, because the rapid decay of small-ball probabilities can prohibit the existence of limiting distributions for supremum-based discrepancy measures, we develop $L^p$-based alternatives. By directly leveraging the introduced convergence results, this approach circumvents the need for higher-order $U$-process formulations. Finally, for spaces that do admit an isometric Hilbertian embedding, and where $U$-processes naturally arise, we establish limit theory for both degenerate and nondegenerate multi-parameter $U$-processes, and demonstrate that local discrepancy tests maintain asymptotic stability under dynamic parameter regimes.

23.
arXiv (math.PR) 2026-06-12

Temporal Conductance and Bounds on the Voter Model for Dynamic Networks

arXiv:2606.13374v1 Announce Type: cross Abstract: The voter model is a classical stochastic process that models how opinions might spread through a network: at each step, every node lazily adopts the opinion of a random neighbour; eventually all nodes share the same opinion (consensus). Stronger connectivity should yield faster consensus. Berenbrink, Giakkoupis, Kermarrec, and Mallmann-Trenn (ICALP 2016) make this precise via the network's conductance: if the network has $m$ edges, minimum degree $d_{\min}$, and conductance at least $\phi$, then the voter model reaches consensus in expected $O(m/(d_{\min}\phi))$ steps. Their results extend to dynamic networks with fixed vertex degrees by considering the network's conductance at each time step. We introduce temporal conductance $\Phi$, a more general connectivity measure for dynamic networks. Unlike static conductance, which collapses to $0$ whenever some snapshot is disconnected, $\Phi$ captures connectivity through edges that appear at different times. We generalise the results of Berenbrink et al. from static conductance to temporal conductance, showing that the expected consensus time of the standard voter model is at most $O(m/(d_{\min}\Phi))$. Moreover, we prove that this bound is tight up to constant factors. We expect temporal conductance to be a useful primitive for analysing other dynamics on temporal networks, and potentially time-inhomogeneous Markov chains more generally.

24.
arXiv (math.PR) 2026-06-16

Universality in the target arrival statistics of non-conservative search processes

arXiv:2606.16025v1 Announce Type: cross Abstract: Stochastic search processes in which searchers are continuously introduced to and removed from a target search domain are fundamental to a wide class of physical and artificial systems. The theory of such non-conservative search processes is, however, much less developed than for search processes with a fixed number of particles. Here we exploit a natural mapping between non-conservative stochastic search and queueing theory to derive the full time-dependent distribution of target arrivals under minimal assumptions on the underlying search process. Remarkably, we find that the steady-state inter-arrival time distribution is exactly exponential, regardless of the details of the search process, showing a robust universality that emerges directly from the queueing framework. Thus, counterintuitively, the arrival statistics of a non-conservative search process are much simpler than sequential search-and-capture processes involving a fixed number of searchers. This has major implications for target resource accumulation, where the delivery of resources is counter-balanced by their downstream consumption.

25.
arXiv (quant-ph) 2026-06-17

The Standard Model, The Exceptional Jordan Algebra, and Triality

Authors:

arXiv:2006.16265v2 Announce Type: replace-cross Abstract: Jordan, Wigner and von Neumann classified the possible algebras of quantum mechanical observables, and found they fell into 4 "ordinary" families, plus one remarkable outlier: the exceptional Jordan algebra. We point out an intriguing relationship between the complexification of this algebra and the standard model of particle physics, its minimal left-right-symmetric $SU(3)\times SU(2)_{L}\times SU(2)_{R}\times U(1)$ extension, and $Spin(10)$ unification. This suggests a geometric interpretation, where a single generation of standard model fermions is described by the tangent space $(\mathbb{C}\otimes\mathbb{O})^{2}$ of the complex octonionic projective plane, and the existence of three generations is related to $SO(8)$ triality.