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01.
arXiv (quant-ph) 2026-06-15

The Magic Barrier before Thermalization

arXiv:2510.11681v2 Announce Type: replace Abstract: We investigate the time dependence of anti-flatness in the entanglement spectrum, a measure for non-stabilizerness and lower bound for non-local quantum magic resource, on a subsystem of a linear SU(2) plaquette chain during thermalization. Tracing the time evolution of a large number of initial states, we find that the anti-flatness exhibits a barrier-like maximum during the time period when the entanglement entropy of the subsystem grows rapidly from the initial value to the microcanonical entropy. The location of the peak is strongly correlated with the time when the entanglement exhibits the strongest growth. This behavior is found for generic highly excited initial computational basis states and persists for coupling constants across the ergodic regime, revealing a universal structure of the entanglement spectrum during thermalization. We conclude that quantitative simulations of thermalization for nonabelian gauge theories require quantum computing. We speculate that this property generalizes to other quantum chaotic systems, a conjecture supported by analogous behavior observed in real-time simulations of the mixed-field Ising model.

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

Rethinking One-Step Image Editing through ChordEdit: Reproduction, Simplification, and New Insights

One-step image editing is important for making text-guided editing fast, practical, and easy to deploy, but its underlying mechanism is still not fully understood. We revisit ChordEdit through reproduction, ablation, and simplification. Our analysis shows that a) the chord window $\delta$ largely acts as an effective timestep shift from $t$ to $t - \delta$; b) chord transport acts on high-noise images and mainly performs low-frequency semantic editing; and c) proximal alignment acts on low-noise images and complements it by adding high-frequency target details. In this view, ChordEdit naturally decomposes editing into a coarse low-frequency transport stage and a fine high-frequency alignment stage. These findings suggest a path toward prompt-conditioned dynamic timestep selection for adaptive image editing. All code and results can be found at \href{https://github.com/Harvard-AI-and-Robotics-Lab/ChordEdit-Reproduction}{link}.

03.
arXiv (CS.CV) 2026-06-12

HYDRA-X: Native Unified Multimodal Models with Holistic Visual Tokenizers

Holistic visual tokenizers are fundamental to unified multimodal models (UMMs) as they map diverse visual inputs into a unified representation space. In this paper, we present HYDRA-X, the first UMM that unifies image and video tokenization within a single Vision Transformer (ViT). Our design is driven by two core challenges: efficiently injecting spatiotemporal reconstruction capability into a native ViT, and embedding image- and video-level semantic awareness into the latent space. To address the first, comprehensive ablations reveal two key findings: (1) frame-level causal temporal attention suffices for visual reconstruction, whereas full spatiotemporal attention degrades it; and (2) hierarchical temporal compression substantially outperforms single-step alternatives. To tackle the second, we propose a lightweight decompressor that upsamples temporally compressed features under joint image-video teacher supervision, thereby enforcing complementary semantic structures within the compact latent space. Building on this holistic tokenizer, we further propose a principled improvement of the editing pipeline: source-target interaction should occur at the latent level inside the tokenizer rather than at the semantic level inside the LLM, substantially improving editing consistency and accelerating convergence. Instantiated at the 7B dense model, HYDRA-X achieves strong performance across image and video understanding and generation tasks, paving the way for future unified-tokenizer UMMs.

04.
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.

05.
bioRxiv (Bioinfo) 2026-06-10

When batch correction corrupts gene expression: uncovering distortions in correlation structures

Batch correction is essential for integrating datasets and enabling population-level insights into health and disease. Embedding-based approaches are among the most widely used solutions, but here we highlight a critical, overlooked limitation: these methods can distort feature-to-feature (e.g., gene gene) relationships, potentially undermining downstream analyses. We investigate this issue and introduce a novel metric to quantify it.

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

Decoupled Object-Centric Video Understanding for Generating Robotic Manipulation Commands

Translating video demonstrations into executable robot commands remains challenging because existing methods often fail to identify which objects are functionally involved in the demonstrated action. As a result, they may generate commands that are linguistically plausible but operationally ambiguous. We propose an object-centric video understanding framework that decouples action recognition from object identification to generate precise, grammar-free manipulation commands. Our approach integrates Temporal Shift Modules (TSM) for efficient spatio-temporal action classification with a novel Object Selection algorithm that identifies task-relevant objects through trajectory-based role classification, blur detection, and overlap minimization. The selected objects are then processed by Vision-Language Models (VLMs) for robust category recognition and zero-shot generalization. Evaluated on a modified Something-Something V2 dataset, our method achieves 86.79\% action classification accuracy and BLEU-4 scores of 0.337 on standard objects and 0.261 on novel objects. These results improve over the strongest task-specific baseline by 80.2\% and 143.9\%, respectively. Larger gains are observed in METEOR and CIDEr, reaching 157.9\% and 171.7\% on novel objects. Across all semantic metrics, our approach consistently outperforms task-specific methods and remains competitive with, or surpasses, large general-purpose VLMs while retaining a modular, object-centric design.

07.
arXiv (CS.LG) 2026-06-11

Learning What to Say to Your VLA: Mostly Harmless Vision Language Action Model Steering

arXiv:2606.12299v1 Announce Type: cross Abstract: Vision-Language-Action (VLA) models provide a natural language interface to robot control, but the mapping from language to behavior is often brittle and unintuitive: semantically similar instructions can induce drastically different behaviors, while some capabilities may not be elicitable through prompting alone. As a result, both human instructions and zero-shot language models can fail to reliably steer VLAs toward successful task execution. In this work, we propose a framework that interactively searches for language sequences that improve closed-loop VLA task performance, distills these sequences into a test-time language feedback policy (LFP), and learns an improvement head that predicts when language steering will improve performance. We conformalize this improvement head to prevent harmful steering interventions, where the LFP decreases task performance relative to the original instruction on out-of-distribution scenarios. Crucially, our approach operates on arbitrary frozen pre-trained VLAs, requiring neither access to the original training distribution nor fine-tuning of the underlying model. On seen environments, our conformalized LFP improves base VLA performance by 24.7% in simulation and 65.0% in hardware. On visual and semantic perturbations, our conformalized LFP has strong harmlessness guarantees, and produces recovery behaviors not observed with open-loop prompting.

08.
arXiv (quant-ph) 2026-06-16

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

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

09.
arXiv (math.PR) 2026-06-17

Analysis of the asymmetric shelf shuffle

arXiv:2606.18047v1 Announce Type: new Abstract: In an asymmetric shelf shuffle, a deck of $n$ cards is dealt sequentially from the bottom and assigned one of the $m$ shelves uniformly at random. The card is placed at the top of the assigned shelf with probability $p$, and at the bottom of the assigned shelf with probability $(1-p)$. Analysis of the shelf shuffle has gained much attention recently, and the case $p=1/2$ was first treated by Diaconis–Fulman–Holmes [Ann. Appl. Prob. 23 (2013), no. 4, 1692–1720]. In this paper, we extend the analysis of the shelf shuffle to general $p\in (0, 1)$. In particular, we study the distribution of cycles, cycle lengths, number of descents, number of valleys, number of inversions, and the RSK shape of a permutation obtained from an asymmetric shelf shuffle. Our results extend the analysis of Diaconis–Fulman–Holmes to arbitrary $p$. Furthermore, our analysis of the distribution of descents and inversions is new even for $p=1/2$.

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

TMR-GGNN: Credit Card Fraud Detection based on Time-Aware Multi-Relational Guided Graph Neural Network

arXiv:2606.18444v1 Announce Type: cross Abstract: In recent years, credit card fraud detection has faced significant challenges due to highly imbalanced data, evolving fraud patterns, and complex relational structures among transaction entities. To address these issues, this research proposes a novel framework called Timeaware Multi Relational Guided Graph Neural Network (TMR GGNN). Particularly, the proposed TMR GGNN extends the encoder decoder Graph Neural Network GNN architecture by modeling heterogeneous interactions across customers, merchants, devices, and IPs over temporal windows. Subsequently, the proposed TMR GGNN approach constructs a dynamic, multi relational graph and incorporates a time aware relational attention mechanism within the encoder to adaptively weigh the transaction relevance based on temporal proximity and semantic context. Consequently, the decoder employs a contrastive learning module to distinguish between real and synthesized transaction patterns, while improving the models generalization of rare fraud cases. Additionally, to effectively manage severe class imbalances and emphasize discriminative learning, a composite loss function combining Information Noise Contrastive Estimation (InfoNCE) based contrastive loss with Focal Loss is introduced. This integration assists in improving fraud identification while mitigating false negatives.

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

teasr: training-efficient any-step diffusion transformer for real-world image super-resolution

Diffusion models excel in Real-World Image Super-Resolution (Real-ISR) due to their powerful generative priors but suffer from slow iterative sampling. Although existing one-step distillation methods accelerate inference, they typically require auxiliary teacher models that inflate training memory and restrict scalability to large-scale architectures. Furthermore, these fixed-step models lack the flexibility to trade off speed for quality. In this paper, we propose TEASR, a training-efficient any-step diffusion framework for Real-ISR that enables both one-step and multi-step restoration within a unified model. Our key idea is to perform self-adversarial distillation within a single diffusion model, eliminating the need for auxiliary teachers or discriminators. Specifically, we propose a timestep-aware rectification strategy that stabilizes one-step generation across noise levels. These two designs further enables the distillation of 20B-parameter diffusion models on a single GPU, significantly improving training efficiency. Moreover, we introduce a dual-branch diffusion transformer with decoupled timestep condition to separate the current noise state and the denoising target to enhance sampling quality. Extensive experiments demonstrate that TEASR supports seamless any-step sampling and consistently outperforms state-of-the-art methods across multiple datasets.

12.
arXiv (CS.AI) 2026-06-12

Stubborn: A Streamlined and Unified Reinforcement Learning Framework for Robust Motion Tracking and Fall Recovery for Humanoids

arXiv:2606.12814v1 Announce Type: cross Abstract: Recent reinforcement learning approaches have shown great promise in improving humanoid motion tracking performance and achieving fall recovery under disturbances. However, most existing works treat motion tracking and fall recovery as different tasks and require multi-stage training with specialized recovery rewards and/or separate recovery policies. Moreover, existing reinforcement learning-based methods often terminate training episodes immediately after severe tracking failures, limiting recovery-oriented exploration in unstable or fallen states. To address the above issues, we propose Stubborn, a streamlined and unified reinforcement learning framework to achieve robust humanoid motion tracking and fall recovery. Specifically, Stubborn uses an asymmetric Actor-Critic architecture and consists of three major components. First, a yaw-aligned tracking representation is adopted to reduce sensitivity to global drift and heading disturbances while preserving gravity-related balance information. Second, we introduce a Bernoulli-based probabilistic termination mechanism that enables the policy to encourage exploration of fall-recovery behaviors under varying failure modes. Third, we propose a probabilistic termination and tracking-error-driven strategy that dynamically reshapes the sampling distribution based on tracking performance, increasing the training efficiency for difficult motion segments and unstable states. Extensive comparisons with SOTA methods and ablation studies show that Stubborn achieved competitive performance, and the proposed probabilistic termination mechanism and adaptive sampling strategy contributed to the performance and robustness gains. For real-world demonstrations, please refer to https://aislab-sustech.github.io/Stubborn/.

13.
arXiv (CS.CV) 2026-06-19

SA-VIS: Sparse frame Annotations for training Video Instance Segmentation

Recent online video instance segmentation (VIS) methods have achieved impressive results, thus becoming the preferred approach to segment instances in videos. Despite the resurgence of impressive single image models, the online (or semi-online) VIS approaches outperform single-image models (e.g., based on SAM) by using long sequences of densely annotated frames during training. However,such a training setup of VIS is expensive in the sense of compute as well as dense annotations required. In order to solve these major flaws, we argue that the effective modeling of the instances and their evolution in videos do not require densely annotated frames. To that end, we propose a simple and effective module, called Past-frames Feature Propagation (PFP) which aggregates low-dimensional features from the image encoder of multiple frames. This simple low-compute module provides tremendous learning capability in using sparse video frame labels for end-to-end training. Combined with a light-weight frame-specific Instance Queries, our Sparse frame Annotation VIS (SA-VIS) significantly improves performance over its baseline. Most interestingly, our simple design that avoids complexities effectively bridges the gap in accuracy between training on sparsely and densely annotated video sequences. This translates to a mere 0.4% drop in performance of SA-VIS when using annotations for only 1/5 of the images in the dataset. Empirically, SA-VIS shows strong improvements over the baseline on YouTube-VIS 2019/2021/2022 and Occluded VIS (OVIS) and an over 1% improvement in AP on the state-of-the-art in a limited annotations scenario.

14.
arXiv (CS.AI) 2026-06-12

AAbAAC: An Annotated Corpus for Autoimmunity Information Extraction

arXiv:2606.13051v1 Announce Type: new Abstract: Despite advances in information extraction driven by deep learning and large language models, performance gaps remain in highly specialized biomedical fields, where domainspecific complexity poses challenges for generalist models. In this work, we focus on the domain of autoimmunity, where the main entities of interest are autoimmune diseases, autoantibodies (i.e., molecules that may mark or cause these diseases), their molecular targets, their location in the body, and their associated clinical signs. Herein, we present AAbAAC (AutoAntibodies and Autoimmunity Annotated Corpus), a corpus of 115 abstracts selected from PubMed, where we manually annotated entities and their relationships. First, AAbAAC was used to evaluate several methods on the task of named entity recognition (NER), and secondly, to fine-tune NER models. Our study demonstrates the utility of AAbAAC for information extraction in the domain of autoimmunity, showing expected improvement in NER performance after finetuning. This illustrates the value of small-scale annotation efforts for specialized domains and contributes to the computational study of autoimmunity. The AAbAAC corpus is available at https://github.com/f-maury/AAbAAC.

15.
medRxiv (Medicine) 2026-06-15

VarEx: A Large Language Model Pipeline for Automated Extraction of Exposures, Outcomes, and Covariates from Epidemiologic Studies

Objective: Observational studies are essential for investigating risk factors for Alzheimer's disease and related dementias (ADRD), but inconsistent reporting and selection of covariates can contribute to residual confounding, omitted-variable bias, and reduced reproducibility. We developed and evaluated VAREX (Variable Extraction), a large language model (LLM)-based information extraction framework designed to automatically identify exposures, outcomes, and covariates from epidemiologic studies and populate structured evidence repositories. Materials and Methods: VAREX combines retrieval-augmented generation, biomedical language-model embeddings, semantic chunking, cross-encoder reranking, and prompt-engineered LLM workflows to extract epidemiologic variables from full-text biomedical articles. The framework was evaluated using a reference-standard corpus of observational studies examining blood pressure variability (BPV) and Alzheimer's disease-related dementias (ADRD), together with external validation datasets involving other exposure-outcome relationships. Extracted variables were compared with independently curated human reference standards using semantic matching and one-to-one assignment procedures. Covariates were additionally classified into ten epidemiologically relevant semantic categories. Results: In the primary BPV[->]ADRD corpus (10 studies), VAREX achieved a precision of 0.91, recall of 0.84, and F1-score of 0.87 for variable extraction. Covariate classification accuracy was 0.90, yielding a strict extraction-and-classification F1-score of 0.78. External validation datasets demonstrated comparable performance across diverse epidemiologic domains, with extraction F1-scores ranging from 0.73 to 0.85. Category-level performance was strongest for health behaviors (F1=0.96), sociodemographic variables (F1=0.90), and medication exposures (F1=0.89). Compared with published estimates of manual systematic-review effort, VAREX reduced processing time from approximately 61 minutes to 9 minutes per article, representing an 85.7% reduction in review time. Discussion: These findings demonstrate that LLM-based information extraction can accurately identify and classify epidemiologic variables across heterogeneous observational-study designs. Automated extraction enables scalable construction of structured repositories of exposures, outcomes, and covariates while substantially reducing the labor required for evidence synthesis and systematic reviews. Conclusion: VAREX provides an effective framework for automated extraction and classification of epidemiologic variables from the biomedical literature. By supporting large-scale evidence synthesis and structured knowledge resource development, VAREX may facilitate more rigorous observational research, improved confounder identification, and enhanced reproducibility in epidemiology.

16.
arXiv (CS.CV) 2026-06-17

PhaseWin: An Efficient Search Algorithm for Faithful Visual Attribution

Visual attribution is a fundamental tool for interpreting modern vision and vision-language models, particularly when their decisions must be inspected, diagnosed, or audited. Its goal is to explain how a model's decision depends on local regions of the visual input, typically by assigning an importance ordering over candidate image regions. Given an image partitioned into $n$ regions, faithful attribution can be cast as an ordered subset-search problem, in which progressively inserting the selected regions should recover the target model response as early as possible. Exhaustive search over region subsets incurs exponential cost, while the widely used greedy search still requires a quadratic number of model evaluations, because every selection step rescores all remaining candidates. We propose PhaseWin, an efficient subset-search algorithm for faithful visual attribution. PhaseWin reorganizes greedy region selection into a phased window-search procedure: rather than re-evaluating the full candidate set at every step, it alternates between global candidate screening, adaptive pruning, and localized window refinement, while preserving the essential region-ranking behavior of greedy search. We analyze PhaseWin under monotone evidence-accumulation conditions and show that, under feature-level structural assumptions, it attains controllable linear evaluation complexity together with near-greedy faithfulness guarantees. Extensive experiments on image classification, object detection, visual grounding, and image captioning show that, among all compared attribution methods, PhaseWin reaches high faithfulness with the fewest forward passes, empirically realizing the predicted reduction from $O(n^2)$ to $O(n)$. The code is available at https://github.com/Qihuai27/phasewin-va.

17.
arXiv (math.PR) 2026-06-19

Theory of uncertain probability: can we derive the probability density function of uncertain random experiments with continuously changing conditions?

作者:

arXiv:2606.20169v1 Announce Type: new Abstract: This paper aims to explore the formation mechanism of probability distribution in situations where the differences among random experiments are distinguishable, and these differences continue to evolve along with the dynamic changes in conditions and their mechanisms of action. To this end, we are motivated to devise a new theoretical system – theory of uncertain probability (TUP) with Kolmogorov's system and nonlinear theories as special cases. TUP develops a novel model that integrates probability and uncertainty as well as the known and unknown to more accurately depict numerous typical random phenomena under more realistic assumptions, and thus provides appropriate tools for greater variety of real needs. It also allows for pioneering interpretation of the causal mechanisms underlying many important distributional characteristics and incorporation of pathwise property to distribution model.

18.
arXiv (CS.CV) 2026-06-11

SpecLoR: Spectral Lookahead Rectification for Motion-Coherent Text-to-Video Generation

Flow Matching has enabled robust text-to-video generation via latent ODE sampling. However, velocity approximation and numerical discretization errors inevitably accumulate, causing sampling trajectories to drift. Consequently, generated videos often suffer from severe spatiotemporal inconsistencies. Nevertheless, directly correcting these drifted, noisy latents is challenging: (i) timestep-dependent noise obscures reliable structural cues; (ii) spatial interventions risk disrupting intricate local geometry while incurring heavy computational costs. To address this, we propose Spectral Lookahead Rectification (SpecLoR), a plug-and-play inference method that bypasses noise via lookahead prediction, and circumvents spatiotemporal entanglement by shifting corrections to the frequency domain, where universal statistical priors of natural videos are readily available. First, during early sampling stages, SpecLoR looks ahead to estimate the clean latent $z_{t,0}$ and computes its 3D spatiotemporal spectrum. Next, SpecLoR rectifies the amplitude spectrum to match the prior, leaving the phase intact. Finally, the corrected state is re-noised to resume ODE integration. Experiments on Wan2.2 demonstrate that SpecLoR significantly reduces physical artifacts and enhances motion coherence across multiple benchmarks with minimal computational overhead (4 additional NFEs).

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

ROSA-TFormer: A Radar-Optical Sensor-Aware Temporal Transformer for Pinus sylvestris Plantation Classification in Northern Shaanxi Using GEE-Derived Sentinel-1/2 Time Series

Accurate identification of Pinus sylvestris var. mongolica plantations is important for monitoring afforestation quality and ecological restoration in northern Shaanxi. This paper proposes ROSA-TFormer, a radar-optical sensor-aware temporal Transformer for P. sylvestris classification using Sentinel-1/2 time-series data generated on Google Earth Engine. The model integrates separate SAR and optical embedding branches, a sensor-aware gate, and temporal attention pooling to capture multi-source seasonal features. Experiments on monthly and half-month point-level datasets show that ROSA-TFormer achieves strong classification performance, with 99.67% overall accuracy, 99.56% macro F1, and 98.91% P. sylvestris F1 on the HalfMonth-dataBig dataset. Spatial block validation and ablation results further indicate the effectiveness of radar-optical temporal fusion and sensor-aware modeling. The results demonstrate the potential of ROSA-TFormer for point-level P. sylvestris plantation classification, while broader wall-to-wall validation remains necessary.

21.
arXiv (CS.LG) 2026-06-19

AgentArmor: A Framework, Evaluation, \& Mitigation of Coding Agent Failures

arXiv:2606.19380v1 Announce Type: cross Abstract: Software engineering and deployment are increasingly being delegated to AI coding agents. The scale of their adoption is surfacing rare, but highly destructive, failure modes. In this paper, we study these failure modes as stemming from three distinct mechanisms: underspecification, where default model behavior is unsafe; capability errors, where the safe action is available but the model does not adhere to it due to bias or capability limitations; and agent harness errors, where the model fails to execute the safe action through the harness. We evaluate these across 8 different evaluations, each inspired by real-life deployment failures, totaling 20 coding environments and 59 synthetic transcript templates. Based on this evaluation, we propose AgentArmor, an agent harness modification, to mitigate these errors. By adding an extended system prompt, a separate command classifier, a ``3 strikes'' policy, deterministic guardrails, and tools for the agent to edit its own context, we show that AgentArmor is safer across a statistically significant number of samples. Thus, we suggest concrete mitigations for current coding agents and a design philosophy for future agent harness features.

23.
arXiv (math.PR) 2026-06-17

Time and Killed Resolvents in Reflected Optimal Stopping with a Max Payoff

arXiv:2606.18214v1 Announce Type: cross Abstract: We study infinite-horizon optimal stopping for normally reflected two-dimensional diffusions in the positive quadrant with max payoff \(G(x_1,x_2)=x_1\vee\alpha x_2\). The non-smooth payoff produces a singular stopping-gain measure on the kink set \(\Delta=\{x_1=\alpha x_2\}\). We prove $\displaystyle \Gamma^\Delta(dx) = -\frac{n^\top a(x)n}{2\sqrt{1+\alpha^2}}\,\sigma_\Delta(dx)$, with $n=(1,-\alpha)$, so the diagonal component is non-positive and strictly negative under local ellipticity. This implies that every interior kink point lies in the continuation region. We further show that the correct value representation uses the resolvent killed at first entry into the stopping set, $\displaystyle V=G-R_r^{\mathcal C}\Gamma$, and give a closed-form reflected Brownian counter-example showing that the unrestricted reflected resolvent is generally wrong. A reflected Brownian benchmark and numerical experiments illustrate the local-time, resolvent-gap, and diagonal-avoidance mechanisms.

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

Weighted Bayesian Conformal Prediction

arXiv:2604.06464v2 Announce Type: replace Abstract: Conformal prediction provides distribution-free prediction intervals with finite-sample coverage guarantees, and recent work by Snell \& Griffiths reframes it as Bayesian Quadrature (BQ-CP), yielding powerful data-conditional guarantees via Dirichlet posteriors over thresholds. However, BQ-CP fundamentally requires the i.i.d. assumption. Meanwhile, weighted conformal prediction handles distribution shift via importance weights but remains frequentist, producing only point-estimate thresholds. We propose Weighted Bayesian Conformal Prediction (WBCP), which generalizes BQ-CP to arbitrary importance-weighted settings by replacing the uniform Dirichlet $\Dir(1,\ldots,1)$ with a weighted Dirichlet $\Dir(\neff \cdot \tilde{w}_1, \ldots, \neff \cdot \tilde{w}_n)$, where $\neff$ is Kish's effective sample size. We prove four theoretical results: (1)~$\neff$ is the unique concentration parameter matching frequentist and Bayesian variances; (2)~posterior standard deviation decays as $O(1/\sqrt{\neff})$; (3)~BQ-CP's stochastic dominance guarantee extends to per-weight-profile data-conditional guarantees; (4)~the HPD threshold provides $O(1/\sqrt{\neff})$ improvement in conditional coverage. We instantiate WBCP for spatial prediction as Geographical BQ-CP, where kernel-based spatial weights yield per-location posteriors with interpretable diagnostics. Experiments on synthetic and real-world spatial datasets demonstrate that WBCP maintains coverage guarantees while providing substantially richer uncertainty information.

25.
arXiv (math.PR) 2026-06-15

Scaling limits of multitype Bienaymé trees

arXiv:2507.23241v2 Announce Type: replace Abstract: We consider critical multitype Bienaymé trees that are either irreducible or possess a critical irreducible component with attached subcritical components. These trees are studied under two distinct conditioning frameworks: first, conditioning on the value of a linear combination of the numbers of vertices of given types; and second, conditioning on the precise number of vertices belonging to a selected subset of types. We prove that, under a finite exponential moment condition, the scaling limit as the tree size tends to infinity is given by the Brownian Continuum Random Tree. Additionally, we establish strong nonasymptotic tail bounds for the height of such trees. Our main tools include a flattening operation applied to multitype trees and sharp estimates regarding the structure of monotype trees with a given sequence of degrees.