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01.
arXiv (CS.CV) 2026-06-25

An Improved Variational Method for Image Denoising

The total variation (TV) method is an image denoising technique that aims to reduce noise by minimizing the total variation of the image, which measures the variation in pixel intensities. The TV method has been widely applied in image processing and computer vision for its ability to preserve edges and enhance image quality. In this paper, we propose a Mixed-norm TV (MixTV) model for image denoising and the associated numerical algorithm to carry out the procedure, which is particularly effective in removing several types of noise and their combinations. Our MixTV admits a unique solution and the associated numerical algorithm guarantees convergence. Numerical experiments are demonstrated to show improved effectiveness and denoising quality compared to other TV models. Such encouraging results further enhance the utility of the TV method in image processing. Our project page is available at https://angusbb.github.io/MixTV.

02.
arXiv (CS.LG) 2026-06-24

XConv: Low-memory stochastic backpropagation for convolutional layers

arXiv:2106.06998v5 Announce Type: replace Abstract: Training convolutional neural networks at scale demands substantial memory, largely because intermediate activations must be stored for backpropagation. Existing remedies (checkpointing, invertible architectures, or gradient-approximation methods such as randomized automatic differentiation) either add significant computation, impose architectural constraints, or require non-trivial code changes. We propose XConv, a near-drop-in replacement for standard 2D and 3D convolutional layers that addresses all three: it preserves standard backpropagation, imposes no architectural constraints, and integrates into existing codebases with minimal changes. XConv exploits the algebraic structure of convolutional weight gradients, storing highly compressed projections of the activations rather than the full tensors and approximating the gradients via multi-channel randomized trace estimation. The number of probing vectors sets a memory-accuracy tradeoff and recovers the exact gradient in the limit. We establish convergence guarantees and error bounds for the estimator, showing that its gradient-error variance is comparable to that of stochastic gradient descent. Empirically, XConv matches exact-gradient methods across classification, generative modeling, super-resolution, inpainting, and segmentation, with gaps that narrow as the number of probing vectors grows, while reducing activation memory by a factor of two or more when convolutional activations dominate, and remaining computationally competitive with optimized convolution kernels at larger batch sizes. At half precision the gradient-approximation error falls to the rounding floor, so XConv adds essentially no error beyond that of low-precision arithmetic. The savings matter most where activation memory rather than compute is the binding constraint, such as high-resolution and volumetric training and on-device finetuning.

03.
arXiv (math.PR) 2026-06-16

Sharp One-Dimensional Sub-Gaussian Comparison in Convex Order

作者:

arXiv:2604.26819v2 Announce Type: replace Abstract: We prove that any random variable $X$ whose moment generating function is point-wise upper bounded by that of $ G \sim \mathcal{N}(0,1) $ must be dominated by $ G/\mathbb{E}[|G|] $ in convex order, meaning $ \mathbb{E}[f(X)] \le \mathbb{E}[f(G/\mathbb{E}[|G|])] $ for all convex $f$. This is sharp as witnessed by $ X \sim \mathrm{Unif}(\{-1,1\}) $ and $ f(x) = |x| $.

04.
arXiv (CS.AI) 2026-06-12

Multiagent Protocols with Aggregated Confidence Signals

arXiv:2606.13591v1 Announce Type: new Abstract: Confidence is used for reliability, oversight, and a range of downstream decision tasks in Natural Language Processing (NLP), yet no existing method produces or evaluates a confidence for the output of a multiagent system. Prior work uses confidence within multiagent debate (MAD) to weight messages, trigger debate, or calibrate individual agents, but it never aggregates these into a single confidence for the system itself. We introduce three protocols that produce a final answer along with a single aggregated confidence by first transforming raw confidence signals to make them comparable across models, then combining them via soft voting or a probability fusion we call Bayesian fusion. This aggregated confidence is substantially more discriminative (AUARC) than that of the best single agent or the standard debate baselines, while correctness (F1-score) stays stable and recovers the losses MAD incurs on more ambiguous tasks. Analyzing two estimators, sequence probability and self-report, alongside parametric and non-parametric calibrators, we find that calibration improves F1 for both estimators while AUARC is less reliant on it. We evaluate six homogeneous and heterogeneous debating pairs per benchmark, across five benchmarks and four task types, spanning a range of model capabilities and sizes.

05.
arXiv (CS.CL) 2026-06-17

When AI Says "I have been in similar situations": Synthetic Lived Experience in Peer-Like Caregiver Support

Caregivers often turn to online communities for informational and emotional support. In these spaces, peer supporters frequently draw on personal narratives to respond to emotionally complex caregiving situations. As LLMs are increasingly designed as peer-like sources of support, they introduce a critical tension: AI can provide immediate, private, and nonjudgmental support, but it cannot authentically possess the lived experiences that make human peer support meaningful. Yet, when prompted to sound peer-like, LLMs may generate language that implies lived experience. This creates a synthetic lived experience paradox: the same experiential language that may make AI support feel warm, relatable, and peer-like can also falsely position the system as someone with lived experience. We examine this paradox in the context of family caregivers of people living with Alzheimer's Disease and Related Dementias (ADRD). Drawing on caregiver support exchanges from online communities and prompted peer-like responses from three LLMs – LLaMA, GPT-4o-mini, and MedGemma – we analyze how human peers use personal narratives and how AI incorporates similar narrative forms. Psycholinguistic analysis shows that peer responses used significantly more first-person and past-focused language than peer-like AI responses. Qualitatively, we identify seven types of personal narratives in human peer support and show that AI often captures their emotional work, but can fabricate experiential grounding. These findings reveal a narrative authenticity gap: peer-like AI can generate synthetic lived experience without the real experience that makes peer support meaningful. We argue that caregiver-support AI systems need mechanisms to distinguish supportive peer-like framing from fabricated lived experience, ensuring that models can offer warmth and validation without falsely positioning themselves as experiential peers.

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

SciRisk-Bench: A Risk-Dimension-Aware Benchmark for AI4Science Safety

arXiv:2606.18936v1 Announce Type: new Abstract: Large language models (LLMs) are increasingly embedded in AI for Science (AI4Science) workflows, from scientific question answering and literature analysis to laboratory planning and autonomous discovery. This progress creates an urgent need for safety benchmarks that evaluate not only scientific competence, but also whether models recognize and avoid risks in high-stakes scientific contexts. Existing AI4Science safety datasets cover several disciplines and task formats, leaving the underlying risk dimensions underspecified. We introduce SciRisk-Bench, a benchmark designed to evaluate AI4Science safety from two complementary perspectives: explicit risk dimensions and scientific disciplines. SciRisk-Bench covers 7 disciplines, 31 subdisciplines and 10 risk dimensions. In the experimental section, we evaluate both mainstream LLMs and science-oriented LLMs across risk dimensions, disciplines, and sub-disciplines, enabling fine-grained diagnosis of where scientific models remain unsafe.

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

Learning Object Manipulation from Scratch via Contrastive Interaction

arXiv:2606.11525v1 Announce Type: cross Abstract: Contrastive Reinforcement Learning (CRL) has seen recent success in a wide variety of goal-conditioned robotics tasks by learning structured representations of the dynamics. However, despite its success in locomotion and simpler control domains, CRL often struggles in interaction-rich manipulation. We argue that a key source of this difficulty is object-centric interaction, such as contact or grasping, that induces distinct changes in the underlying dynamic modes. In this work, we formulate manipulation dynamics as a piecewise-smooth Markov process and show that interaction-induced mode changes create piecewise nonlinear reachability structures that are difficult for standard CRL energy functions to represent and plan over. Based on this analysis, we introduce Interaction-weighted Resampling (IWR). IWR performs interaction-aware resampling around phases before, during, and after interactions, encouraging the learned representation to preserve the mode boundaries that determine future reachability to capture multi-modal and piecewise nonlinear reachability. Across interaction-centric environments, including 2D dynamic control, robotic manipulation, and robot air hockey, IWR improves both sample efficiency and overall performance over prior CRL methods, with 19.8% average improvement in simulation. Finally, using a sim-to-real pipeline with policies trained by IWR, we demonstrate the first real-world goal-conditioned robot air hockey agent capable of hitting goals, improving success from 25% to 60%. Project Page: IWR-arxiv.github.io.

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

Double-Helix Vision (DH-V2): A Geometry-Based Visual Sampler for Bandwidth-Constrained Perception

作者:

We present Double-Helix Vision (DH), a geometry-based visual sampler that compresses 2D images into compact 1D signals using paired golden-ratio-inspired spiral trajectories. Rather than processing every pixel uniformly, DH employs two phase-shifted helices (Alpha and Beta, offset by 180 degrees) to sample the image with biologically-inspired foveation: high density at the center, sparse coverage at the periphery. At 4K resolution, DH achieves a 1,433x compression ratio (99.93% reduction) while preserving the geometric structure of the scene. The full perception pipeline – including spatial mapping, temporal collision detection, and intra-frame structural disparity estimation – runs in 0.52 ms at 1080p on CPU-only hardware, with no neural network dependencies. On CIFAR-10 at extreme sampling budgets (K=128 points per helix), DH achieves a +6.03% accuracy gain over uniform random sampling. A JSON-serializable Robotics API is provided, delivering sub-millisecond spatial perception reports in 2.7 KB packets. Code and benchmarks are available under the MIT License.

09.
arXiv (CS.AI) 2026-06-18

A Knowledge Theory of Capital:The Value of Natural and Artificial Intelligence

arXiv:2606.18288v1 Announce Type: cross Abstract: This volume develops a knowledge theory of capital for economies in which productive capacity increasingly resides in software, data, models, routines, expertise, platforms, organizations, commons, and public epistemic infrastructure. Beginning from Adam Smith's theory of labour, stock, specialization, and market extent, it asks what changes when knowledge becomes stock-like, mobile across forms, scalable, governable, recombinable, and imperfectly visible in accounting. The book introduces knowledge-bearing stock as the central object and analyses how it is generated, converted into governable form, deployed, improved through feedback, enclosed or shared, measured, impaired, and used as input to future production. It distinguishes embodied, disembodied, institutionalized, commons, and public knowledge forms and develops concepts such as first conversion, cognitive enclosure, feedback capture, dark capital, and expected knowledge loss. The argument is conditional and testable: modern wealth depends not only on capital accumulation, but on how productive knowledge is governed.

10.
PLOS Medicine 2026-06-23

Multi-omics biomarkers of endothelial dysregulation preceding chronic lung allograft dysfunction: A prospective cohort study

by Giulia Iacono, Christina Begka, Bailey Cardwell, Carmel Daunt, Roxanne Chatzis, Celine Pattaroni, Alana Butler, Matthew Macowan, Bronwyn Levvey, Gregory I. Snell, Glen P. Westall, Benjamin J. Marsland Background Long-term survival of lung transplant recipients remains limited by chronic lung allograft dysfunction (CLAD). CLAD is only diagnosed following a persistent and substantial decline in lung function, after which irreversible damage to the lungs has occurred, limiting opportunities to effectively intervene at an early stage. There is a critical need for earlier detection prior to its clinical manifestation. The immunological drivers of CLAD remain unclear, limiting the development of predictive biomarkers and new therapies. Methods and findings In this hypothesis-generating, prospective cohort study, we profiled the microbial, metabolic, lipidomic, and gene expression dynamics of longitudinally collected broncho-alveolar lavages (BALs) from 56 CLAD-free lung transplant recipients up to 30 months post-transplant, and compared BALs from 13 CLAD-free patients to BALs from 13 patients who developed CLAD. In CLAD-free patients, the first 6 months post-transplant were hallmarked by diminished microbial diversity and increased abundance of Staphylococcus and Candida, coupled with upregulated innate and adaptive immune responses, and elevated nitric oxide metabolism (FDR 

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

On the convex hull of a planar Brownian bridge with a random Gaussian endpoint

arXiv:2606.24485v1 Announce Type: new Abstract: We consider a one-parameter family of isotropic planar Gaussian processes \[ X_\sigma(t) =B_t+\sigma t Z,\qquad 0\le t\le 1,\quad 0\le \sigma\le 1, \] where $B$ is a standard ($0$-to-$0$) planar Brownian bridge on $[0,1]$, and $Z\sim \mathrm N(0,I)$ is a standard Gaussian random vector independent of $B$. The family interpolates between standard planar Brownian bridge ($\sigma=0$) and standard planar Brownian motion ($\sigma=1$). As the main result of the paper we compute the expected perimeter and area of the convex hull of the random set $\left\{X_\sigma(t) \colon 0\le t\le 1\right\}$ as closed formulas in terms of $\sigma$, and recover the classical Brownian bridge and Brownian motion values at $\sigma=0$ and $\sigma=1$. We also consider the convex hull spanned by multiple independent processes of this type and the possibilities for closed formulas in special cases. The key observation in our argument is that the isotropy property reduces the expected perimeter and area to one-dimensional quantities through the support function and Cauchy's formulas.

12.
arXiv (CS.LG) 2026-06-17

ResAware: Cross-Environment Website Fingerprinting via Resource-Privileged Distillation

arXiv:2606.17462v1 Announce Type: new Abstract: While Website Fingerprinting (WF) attacks achieve high accuracy in controlled laboratory settings, they often degrade substantially in real-world environments due to spatio-temporal drift, browser heterogeneity, proxy obfuscation and etc. This limitation stems from their sole reliance on low-level traffic features that are noisy and highly sensitive to environmental perturbations. To address this problem, we propose ResAware, a cross-environment resource-aware distillation framework under a training-rich/inference-poor asymmetric setting. Specifically, ResAware trains a teacher model on resource-level features, and then distills the resulting privileged knowledge into a student model through heterogeneous knowledge distillation. At deployment time, the student model performs inference using only encrypted traffic, incurring zero additional cost. We evaluate ResAware on a large-scale dataset collected over five months from six globally distributed vantage points, comprising more than $160{,}000$ paired samples. The results show that ResAware significantly enhances the cross-environment robustness of diverse WF baselines. Under a 150-day temporal drift, for example, ResAware improves the F1-score of Var-CNN from $72.77\%$ to $81.49\%$ and the open-world $TPR@1\%FPR$ from $22.40\%$ to $27.20\%$. Our results demonstrate that resource-level supervision improves WF robustness without expanding online observation capabilities.

13.
arXiv (CS.AI) 2026-06-12

Before You Think: System 0, AI-Mediated Cognition and Cognitive Colonization

arXiv:2606.13658v1 Announce Type: new Abstract: This paper examines three recent frameworks for understanding the cognitive and epistemic consequences of artificial intelligence: Tri-System Theory, Thinkframes, and System 0. It argues that while the first two capture important dimensions of AI's influence on individual reasoning and collective epistemic practices, System 0 occupies a theoretically distinctive position that neither can fully replicate. The paper introduces the concept of cognitive colonization, according to which AI systems can embed external interests within the architecture of the self in ways that are difficult for users to perceive. Because such systems are already widely deployed, understanding these invisible forms of influence is an urgent philosophical and practical task.

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

ANCHOR: Error-Controlled Adaptive Numerical Correction for Neural Operator Time Marching

arXiv:2512.19643v2 Announce Type: replace Abstract: Numerical simulation of time-dependent partial differential equations (PDEs) is central to scientific and engineering applications, but high-fidelity solvers are often prohibitively expensive for long-horizon or time-critical settings. Neural operator (NO) surrogates offer fast inference across parametric and functional inputs; however, most autoregressive NO frameworks remain vulnerable to compounding errors, and ensemble-averaged metrics provide limited guarantees for individual inference trajectories. In practice, error accumulation can become unacceptable beyond the training horizon, and existing methods lack mechanisms for online monitoring or correction. To address this gap, we propose ANCHOR (Adaptive Numerical Correction for High-fidelity Operator Rollouts), an online, instance-aware hybrid inference framework for stable long-horizon prediction of nonlinear, time-dependent PDEs. ANCHOR treats a pretrained NO as the primary inference engine and adaptively couples it with a classical numerical solver using a physics-informed, residual-based error estimator. Inspired by adaptive time-stepping in numerical analysis, ANCHOR monitors an exponential moving average (EMA) of the normalized PDE residual to detect accumulating error and trigger corrective solver interventions without requiring access to ground-truth solutions. We show that the EMA-based estimator correlates strongly with the true relative L2 error, enabling data-free, instance-aware error control during inference. Evaluations on six canonical PDEs: 1D and 2D Burgers', 2D Allen-Cahn, 2D Cahn-Hilliard, 2D Navier-Stokes, and 3D heat conduction, demonstrate that ANCHOR reliably bounds long-horizon error growth, stabilizes extrapolative rollouts, and significantly improves robustness over standalone neural operators, while remaining substantially more efficient than high-fidelity numerical solvers.

15.
arXiv (CS.CL) 2026-06-15

CORA: Analyzing and bridging thinking-answer gap in Multimodal RLVR via Consistency-Oriented Reasoning Alignment

Reinforcement learning with verifiable rewards (RLVR) has successfully elicited the reasoning capabilities of large language models, motivating its extension to multimodal scenarios. Existing methods primarily focus on improving the visual coverage of reasoning traces and mitigating visual hallucinations, but underestimate the semantic inconsistency between the reasoning process and the final answer. In this paper, we delve into thinking-answer inconsistency in RLVR for large vision-language models (LVLMs), showing thorough analyses of rollouts collected throughout Group Relative Policy Optimization (GRPO) training process and post-RLVR evaluation outputs that this issue persists during training and remains present during inference. Motivated by the analysis, we propose Consistency-Oriented Reasoning Alignment (CORA), which introduces thinking-answer semantic consistency into RLVR through a lightweight plug-and-play consistency reward model, and further incorporates Hybrid Reward Advantage Splitting (HRAS) to stably coordinate task and consistency optimization. Extensive experiments across representative multimodal reasoning benchmarks and mainstream LVLMs show that CORA improves task performance while effectively mitigating thinking-answer inconsistency, leading to more faithful reasoning traces.

16.
arXiv (CS.LG) 2026-06-25

A Zeroth-Order Deep Learning Method for Fully Nonlinear Parabolic Partial Differential Equations with Unknown Coefficients

arXiv:2606.24999v1 Announce Type: new Abstract: High-dimensional partial differential equations (PDEs) with unknown coefficients arise widely in scientific machine learning, including continuous-time reinforcement learning, yet solving them efficiently in a data-driven way remains challenging. Existing deep learning solvers often rely on repeated automatic differentiation to evaluate differential operators, which can cause instability and amplify derivative errors in high dimensions, while probabilistic methods based on stochastic representations require explicit knowledge of the data-generating dynamics and therefore do not apply to black-box environments. We introduce two types of simulators as data-generating mechanisms, and take a ``representing-then-learning" approach that learns the solutions and their derivatives under settings where the underlying PDE operators are accessible only through simulations and pointwise evaluations. Our representation of derivatives relies on the zeroth-order derivative (ZOD) estimators derived from perturbed Monte Carlo trajectories. This fully model-free approach generates targets for the gradient and Hessian networks using only function evaluations. We provide a statistical learning analysis of the proposed approach, including a bias–variance tradeoff for ZODs. Assuming a standard contraction property of the underlying operator, we establish a non-asymptotic error bound that decomposes the total error into discretization error, approximation error, statistical error, and ZOD bias. Crucially, we derive the sample complexity of the learned representations in (weighted) Sobolev space, characterizing the error up to second-order derivatives. Numerical experiments illustrate the competitive performance of the method in moderate and high dimensions.

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

Density-Informed Pseudo-Counts for Calibrated Evidential Deep Learning

arXiv:2602.01477v2 Announce Type: replace-cross Abstract: Evidential Deep Learning (EDL) is a popular framework for uncertainty-aware classification that models predictive uncertainty via Dirichlet distributions parameterized by neural networks. Despite its popularity, its theoretical foundations and behavior under distributional shift remain poorly understood. In this work, we provide a principled statistical interpretation by proving that EDL training corresponds to amortized variational inference in a hierarchical Bayesian model with a tempered pseudo-likelihood. This perspective reveals a major drawback: standard EDL conflates epistemic and aleatoric uncertainty, leading to systematic overconfidence on out-of-distribution (OOD) inputs. To address this, we introduce Density-Informed Pseudo-count EDL (DIP-EDL), a new parametrization that decouples class prediction from the magnitude of uncertainty by separately estimating the conditional label distribution and the marginal covariate density. This separation preserves evidence in high-density regions while shrinking predictions toward a uniform prior for OOD data. Theoretically, we prove that DIP-EDL achieves asymptotic concentration. Empirically, we show that our method enhances interpretability and improves robustness and uncertainty calibration under distributional shift.

18.
arXiv (quant-ph) 2026-06-15

Nanostructure modelling with early fault tolerant quantum computers

arXiv:2606.06442v2 Announce Type: replace Abstract: Semiconductor nanostructures are central to many developing technologies. Notably, double quantum dots are especially important for semiconductor spin-qubit architectures, quantum sensing applications, and quantum-dot solar cells. Accurate modelling is highly desirable but conventional methods can struggle when dynamics involve more than two interacting electrons. In this work, we present a quantum simulation framework capable of addressing multi-electron double quantum dots. We adopt an efficiently scaling 1$^st$ quantised representation of the system and develop algorithms based on both Trotterisation and Qubitisation. Incorporating insights from classical simulations enables us to produce resource estimates that are more realistic than those obtained from theoretical error bounds. Using a standard surface code model with physical noise at $10^{-3}$, our results indicate that the ground-state energy of four electrons in a double quantum dot can be estimated in approximately 22 hours using 226k physical qubits, or an eight-electron system in 3.3 days with 314k qubits (with runtimes falling dramatically when more qubits are available). We anticipate that incorporating recent advances in surface code architectures may reduce these costs significantly further. Our results suggest that early fault-tolerant quantum computers may become valuable tools for designing mature-era quantum technologies.

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

Can Post-Training Turn LLMs into Good Medical Coders? An Empirical Study of Generative ICD Coding

Automated International Classification of Diseases (ICD) coding is a core medical-coding task for billing, epidemiology, and clinical decision support. Generative large language models (LLMs) are often reported as weak medical coders, but this finding mainly comes from inference-time settings such as prompting, retrieval, reranking, or tool use, leaving the role of task-specific post-training underexplored. We present a controlled empirical study of post-training for generative ICD coding, comparing discriminative baselines with LLM coders across prompting, supervised fine-tuning, and reinforcement learning under a common protocol and metric set. To our knowledge, this is the first study to evaluate RL-based post-training for generative LLM coders in ICD coding. We further introduce PHI, a diagnostic curriculum that extends GRPO to refine missed-code cases. Our results show that prompting-only evaluation substantially underestimates the potential of LLMs for ICD coding. SFT provides the main capability jump, GRPO further improves code-set prediction beyond SFT, and PHI provides targeted gains on macro-level performance. These findings suggest that the main bottleneck is not the generative formulation alone, but how the model is adapted and optimized for full-taxonomy recall. We release our code, data splits, and checkpoints at https://github.com/AlexandreWANG915/LLM4ICD.

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

Optimal Hidden-Target Learning for Online Inventory Optimization on General Convex Sets

arXiv:2606.14679v1 Announce Type: new Abstract: Online inventory optimization (OIO) is online convex optimization with physical memory: inventory carryover makes the feasible action set depend on the past. A natural principle, used in stochastic inventory learning and recently in OIO under a single linear capacity constraint, is to maintain a hidden target chosen by an online learner and implement its projection onto the currently feasible order-up-to set. We prove that this simple principle is optimal for OIO on arbitrary bounded convex capacity sets. With online gradient descent as the base learner, the method improves the best known regret guarantee for OIO on general convex sets from inverse to inverse-square-root dependence on the common-demand probability, and we prove a matching lower bound. The same principle gives the first polylogarithmic regret guarantee for strongly convex losses and the first dynamic regret guarantee adapting to Euclidean path variation on general convex capacity sets. The analysis introduces a norm alignment principle: the right state variable is the distance from the hidden target to the feasible set, measured in the same norm as the projection. Under norm alignment, this distance evolves pathwise as a scalar queue, with target movement as arrival and common demand as service. This reduction to one-dimensional queue control resolves the state dependence and extends the guarantees to general convex capacity sets, beyond the reach of prior productwise approaches. Experiments on synthetic and real-world inventory data corroborate the theory.

21.
arXiv (math.PR) 2026-06-11

Sharp log-Sobolev inequalities on finite cyclic groups

arXiv:2606.02847v2 Announce Type: replace-cross Abstract: Let $\mathbb Z_n$ be the cyclic group equipped with the uniform probability measure $\pi$, and let $A_{\psi_n}$ be the Laplacian with word length \[ \psi_n(k) = \min(k,n-k). \] We prove the sharp log-Sobolev inequality \[ Ent_{\pi}(f^2) \le 2\pi(f A_{\psi_n} f), \qquad f:\mathbb Z_n \to [0,\infty), \] for every $n \ge 4$. The proof is inspired by the recent work of Frank and Ivanisvili[FrankIvanisvili2026] on a sharp log-Sobolev inequality for nearest-neighbor simple random walk. We use their cubic-majorant reduction, which turns the problem into a 3rd moment estimate; the new point is a blockwise 3rd moment estimate adapted to the word-length multiplier. The same 3rd moment argument also recovers the log-Sobolev inequality for Poisson-semigroup on the circle, first proved by Weissler[Weissler1980]. The same sharp inequalities were also obtained recently by Yao[Yao2026] by a different method.

22.
arXiv (math.PR) 2026-06-19

Power-law hypothesis and (un)fairness of PageRank on undirected multi-type PAMs

arXiv:2606.19583v1 Announce Type: new Abstract: The preferential attachment model (PAM) describes the sequential growth of a network based on the "rich-get-richer" principle. Several versions of it have become established for modeling, e.g., citation networks, capturing a power-law degree distribution. Directed versions of the preferential attachment model where the edges are directed from the new to the old vertices have been the subject of extensive research. They have been shown to exhibit remarkable properties such as heavier tails for the limiting graph-normalized PageRank than for the in-degrees. By contrast, for the undirected version, we recently showed that PageRank has similar tails as the degree. In the present paper, we discuss the PageRank asymptotics for a multi-type version of the undirected PAM (here vertices have different colors), complementing previous results of Antunes, Bhamidi, Banerjee and Pipiras on the asymptotics of PageRank on similar directed multi-type or colored PAMs. Our studies are motivated by the aim to go beyond the rigid rule of edge orientation in directed preferential attachment models. As the main result, for the case of a finite set of colors, we show that the power-law hypothesis for PageRank is fulfilled also for the colored undirected PAM, where, by contrast to the directed case, the power-law exponent is color-dependent for some choices of the initial color distribution and the attractiveness function. For the specific case of a two-type model, we discuss implications of our results on fairness in sampling underrepresented nodes from the network.

23.
Nature (Science) 2026-06-10

The Amazon can be saved — with concerted action inside and outside Brazil

作者: 未知作者

As deforestation in the Amazon falls, fresh evidence shows that the rainforest can withstand global warming, but only if there is a worldwide effort to stop cutting it down. As deforestation in the Amazon falls, fresh evidence shows that the rainforest can withstand global warming, but only if there is a worldwide effort to stop cutting it down.

24.
arXiv (CS.CL) 2026-06-11

Causal Emotion Recognition in Conversation: Context Saturation and Discourse-Marker Evidence

We address two persistent gaps in Emotion Recognition in Conversation: which modeling choices materially affect performance, and how recognition findings connect to interpretable discourse-level patterns. We study both through a systematic investigation on IEMOCAP with cross-dataset validation on MELD. For recognition, we run controlled ablations with 10 random seeds and paired significance tests with multiple-comparisons correction, yielding three findings. First, conversational context is the dominant factor, but performance saturates quickly: roughly 90% of the gain is captured within the most recent 10-30 preceding turns, depending on the label set. Second, hierarchical sentence representations help most in utterance-only settings and show a clear advantage on MELD, but their benefit disappears once turn-level context is available, suggesting that conversational history subsumes much of the intra-utterance structure. Third, integrating an external affective lexicon does not improve results, consistent with pretrained encoders already capturing most of the affective signal needed for ERC. Under a strictly causal setting, our simple models achieve strong performance (82.69% 4-way; 67.07% 6-way weighted F1), showing that competitive accuracy is achievable without future turns. For linguistic analysis, we examine 5,286 discourse-marker occurrences and find a reliable association between emotion and marker position (p < .0001). Sad utterances show reduced left-periphery marker usage (21.9%) relative to other emotions (28-32%), consistent with accounts linking left-periphery markers to active discourse management. This aligns with our recognition results, where Sad benefits most from conversational context (+22 percentage points), suggesting sadness may be more context-dependent than emotions with stronger local pragmatic cues.

25.
arXiv (CS.CV) 2026-06-19

Addressing Detail Bottlenecks in Latent Diffusion for RGB-to-SWIR Image Translation

Latent diffusion models (LDMs) enable efficient image-to-image translation but discard fine spatial details during compression, degrading downstream perception tasks. We identify two bottlenecks: the autoencoder, which loses spatial information, and the conditioning pathway, which further degrades the source signal through naive downsampling. We propose two lightweight, backbone-agnostic fixes: a Source-Conditioned Autoencoder (SCAE) that injects high-resolution source features into the decoder via skip connections, and a Learnable Guidance Encoder (LGE) that replaces naive downsampling with a learned conditioning signal. Evaluated on RGB-to-SWIR translation for driving scenes with two denoiser backbones (U-Net and DiT), our approach improves detection mAP by up to 2x over the latent diffusion baseline, with up to 3.4x gains on small objects (COCO-small,