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01.
arXiv (CS.CV) 2026-06-11

Continual Learning with Support Boundary Experience Blending

Continual learning (CL) seeks to mitigate catastrophic forgetting when models are trained with sequential tasks. A common approach, experience replay (ER), stores past exemplars but only sparsely approximates the data distribution, yielding fragile and oversimplified decision boundaries. We address this limitation by introducing Support Boundary Data (SBD), generated via differential-privacy-inspired noise into latent features to create boundary-adjacent representations that implicitly regularize decision boundaries. Building on this idea, we propose Experience Blending (EB), a framework that jointly trains on exemplars and SBD through a dual-model aggregation strategy. EB has two components: (1) latent-space noise injection to generate support boundary data, and (2) end-to-end training that jointly leverages exemplars and SBD. Unlike standard experience replay, SBD enriches the feature space near decision boundaries, leading to more stable and robust continual learning. Extensive experiments on CIFAR-10, CIFAR-100, Tiny ImageNet, and ImageNet1K demonstrate consistent accuracy improvements of 10%, 6%, 13%, 2%, respectively.

02.
arXiv (math.PR) 2026-06-18

Power Partitions and Hayman Functions

arXiv:2602.18575v3 Announce Type: replace Abstract: We prove, within the probabilistic framework of Khinchin families, that the generating function $P_k$ of partitions into $k$-th powers is strongly Gaussian in the sense of Báez-Duarte, and even further that it is a Hayman function. Thus the Hardy–Ramanujan asymptotic formula for the number $p_k(n)$ of partitions of $n$ into $k$-th powers which reads \[ p_k(n) \sim \frac{\alpha_k}{n^{(3k+1)/(2k+2)}} \exp\!\Big(\beta_k\, n^{1/(k+1)}\Big), \qquad n\to\infty, \] where $\alpha_k$ and~$\beta_k$ are explicit constants depending only on $k$, follows directly from Hayman's asymptotic formula for strongly Gaussian power series. The proof of strong Gaussianity of $P_k$ combines a Gaussianity criterion for Khinchin families with certain bounds of Tenenbaum, Wu and Li on the generating function; the asymptotic formula is recovered by computing asymptotic approximations of the mean and variance of the associated family. Analogous results are presented for the generating function $Q_k$ of partitions into distinct $k$-th powers.

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

Effective Resistances and Commute Times in Sparse Random Geometric Graphs

arXiv:2606.14895v1 Announce Type: new Abstract: The commute time between two nodes in a network - the expected number of steps for a random walk to travel from one node to the other and then return - is a metric of broad importance arising in community detection, network routing, dimensionality reduction, and diffusion modeling. For random geometric graphs (RGGs), in which nodes are placed at random in a spatial domain and connected pairwise wherever their Euclidean distance is below a threshold radius, the relationship between commute times and the embedding geometry remains poorly understood outside very dense settings (where the role of the geometry disappears and commute times degenerate to a sum of inverse degrees). We develop and numerically validate a model for approximating commute times in sparse RGGs on a torus by combining theoretically motivated geometric contributions with an inverse degree sum. The geometric terms include a universal logarithmic contribution from the Laplacian, a quadratic correction encoding the compact topology of the torus, and a quartic angular term reflecting the square anisotropy of the domain. We fit this model to samples of node pairs across a range of graph sizes and mean degrees, demonstrating good predictive performance and that the geometric terms contribute significantly to model fit. We then study the continuous perturbation of the model from a regular square lattice to a fully random geometric graph, further validating the functional model form through this transition and showing how commute times in sparse RGGs retain meaningful geometric information about the embedding space.

04.
arXiv (CS.CL) 2026-06-18

Structured Inference with Large Language Gibbs

The knowledge encoded in large language models (LLMs) can serve as a substrate for structured reasoning over variables describing a complex world, but accessing this knowledge in a probabilistically coherent manner poses a difficult inference problem. We propose Large Language Gibbs, a scheme for structured probabilistic inference that uses conditional distributions of an LLM as transition operators. Rather than sampling structured objects through single-pass autoregressive generation, we iteratively resample individual variables conditioned on others using an LLM's next-token conditionals. This approach avoids order-dependent biases and produces a stationary distribution that reflects a compromise between all local conditionals. We apply this approach to sampling from synthetic distributions, consistent reasoning tasks, and Bayesian structure learning. The results suggest that the use of LLM conditionals in MCMC is a practical alternative to one-pass generation for structured probabilistic inference under a world prior accessible through noisy LLM conditionals.

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

Can LLM Agents Infer World Models? Evidence from Agentic Automata Learning

We propose agentic automata learning to evaluate the extent to which tool-calling LLM agents can uncover hidden environments through interaction. In our setup, an agent should uncover a hidden deterministic finite automaton (DFA) by interacting with an oracle through (1) membership queries ("Does this string belong to the target language?") and (2) equivalence queries ("Is this the target DFA?"). This yields a scalable testbed with controlled task complexity, measurable interaction efficiency, and strong baselines (classic automata-learning algorithms). Evaluating state-of-the-art LLMs, we find that performance drops sharply as DFA size increases. Reasoning models are markedly stronger than non-reasoning models, yet trajectory analyses reveal recurring failures in query planning, evidence integration, and hypothesis construction. Overall, our results show that current LLM agents can sometimes perform non-trivial interactive discovery, but remain far less robust and efficient than classic algorithms for the task.

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

Classical representation of the dynamics of quantum spin chains

作者:

arXiv:2502.10502v3 Announce Type: replace-cross Abstract: Since the advent of quantum mechanics, classical probability interpretations have faced significant challenges. A notable issue arises with the emergence of negative probabilities when attempting to define the joint probability of non-commutative observables. In this work, we propose a resolution to this dilemma for quantum spin chains, by introducing an exact representation of their dynamics in terms of classical continuous-time Markov chains (CTMCs). These CTMCs effectively model the creation, annihilation, and propagation of pairs of classical particles and antiparticles. The quantum dynamics then emerges by averaging over various realizations of this classical process.

07.
arXiv (CS.CV) 2026-06-18

Hallucination Detection and Correction in Medical VLMs via Counter-Evidence Verification

Vision-Language models (VLMs) reliability in medical diagnosis is challenged by trust-undermining hallucinations. Existing hallucination detection approaches mainly focus on identifying factual inconsistencies between generated text and reference data. While some studies analyze where models attend in images, they seldom verify whether such attention truly reflects the visual evidence supporting the generated text. To address this gap, we propose Co}unter-Evidence Verification (CoEV), a training-free plug-and-play framework that detects and corrects hallucinations through evidence-based factual consistency verification. CoEV performs bidirectional verification between textual assertions and visual evidence, testing whether each statement is supported by its corresponding evidence region, and assigns each statement into a four-quadrant diagnostic map capturing combinations of text factuality and visual grounding. CoEV detects hallucinated content and serves as a post hoc refinement tool, correcting hallucinations without retraining. Extensive experiments on four medical datasets show that CoEV combats hallucinations in VLMs.For hallucination detection, CoEV consistently outperforms existing methods, improving average PR-AUC and ROC-AUC by 3.0% and 3.9% absolute points respectively, with notable gains of up to 18.5% in specific VQA scenarios. For hallucination correction, it improves Micro-F1 by up to 12.5%, reduces hallucination rates by over 11.9% on medical report generation, and also boosts medical VQA accuracy. These results show that CoEV enables reliable detection and correction of hallucinations, providing clinicians with dependable, evidence-based cues for diagnosis. Code will be released upon acceptance.

08.
arXiv (CS.CV) 2026-06-19

Neural Events: Discrete Asynchronous Autoencoders for Event-Based Vision

Event cameras capture dynamic scenes with exceptional temporal fidelity by representing them as a continuous stream of microsecond resolution events. Each individual event, however, only carries minimal semantic value, merely signaling a localized brightness change. To derive meaningful signals, downstream algorithms need to quickly integrate cues from a potentially massive torrent of low-information events. Current architectures, however, are easily overwhelmed, struggling to balance capturing fine-grained temporal dynamics and maintaining a manageable data throughput. This paper proposes a framework to re-tokenize event streams into a small set of highly informative neural events, each representing a local spatio-temporal context window with a discrete learnable code. Every time this code flips, a neural event is triggered, yielding a highly compressed data stream. We demonstrate that, across object detection and classification, networks trained on neural events are on par or surpass the performance of state-of-the-art approaches while reducing the event rate by a factor of 2.0.

09.
arXiv (CS.AI) 2026-06-19

Zero-Inflated Gaussian Distributions Enable Parameter-Space Sparsity in Estimation-of-Distribution Algorithms

arXiv:2606.19369v1 Announce Type: cross Abstract: Estimation-of-distribution algorithms (EDAs) are a powerful class of evolutionary methods for black-box optimization, especially when little is known about the structure of the objective. Whereas classical evolutionary algorithms rely on hand-designed mutation and crossover operators, hard to devise for unknown problem structures, and a source of bias, EDAs sidestep operator design entirely: they fit a probability distribution to the best individuals and sample the next generation from it. EDAs are well established on continuous parameter spaces, but they have not previously been generalized to sparse ones, in which most coefficients of a good solution are exactly zero. Existing sparse black-box optimizers therefore reintroduce exactly what EDAs were designed to avoid: hand-crafted sparsity operators, bi-level schemes alternating between support set and active values, zeroing thresholds, and other baked-in assumptions. We close this gap by proposing multivariate zero-inflated Gaussian (ZIG) distributions as EDA sampling laws. A latent Gaussian model with separate indicator and value dimensions represents sparsity patterns, correlations among active parameters, and the interactions between the two, so sparsity patterns and active values are optimized jointly, hierarchy-free. We show that the latent parameters of this model are identifiable from observed samples, unlike in the missing-data settings where related constructions originate, and introduce practical amortized inversion-based estimators for them. The estimators accurately recover latent correlation structures, and on the Lunar Lander benchmark the resulting ZIG-EDA converges faster and reaches higher final returns than a dense Gaussian EDA, a hand-crafted sparse evolutionary algorithm, and an ad-hoc sparse EDA, while finding controllers with only a small fraction of parameters active.

10.
arXiv (quant-ph) 2026-06-11

A saturation-absorption rubidium magnetometer with multilevel optical Bloch-equation modeling for intermediate-to-high fields

arXiv:2601.09115v2 Announce Type: replace Abstract: We present SASHMAG (Saturated Absorption Spectroscopy High-field MAGnetometer), an atomic sensor designed for precision magnetic-field measurements in the intermediate-to-high field regime ($>0.2\,T$) using Rubidium-87 ($^{87}Rb$). The sensor operates in the hyperfine Paschen-Back regime, where the hyperfine and Zeeman interactions decouple, and utilizes counter-propagating pump-probe configuration in Faraday geometry to resolve isolated, Doppler-free Zeeman transitions. To interpret the resulting spectra in this strongly field-dependent regime, we developed a comprehensive multilevel optical Bloch-equation model solved explicitly in the uncoupled $\ket{m_I, m_J}$ basis, capturing state mixing and nonlinear saturation dynamics. This model reproduces measured spectra at sub-Doppler resolution and is consistent with analytical expectations for power broadening and thermal Doppler scaling. Magnetic field estimation is performed using a physics-constrained optimization routine that infers the magnetic field by minimizing the residual between experimentally extracted line centers and calculated transition frequencies from the field-dependent Hamiltonian. We demonstrate magnetic field retrieval from $0.2\,T$ to $0.4\,T$ with a precision of $\pm 0.0017 \,T$). Furthermore, the validated simulation establishes a foundation for generating synthetic training datasets, paving the way for autonomous, Machine Learning-enhanced magnetometry in applications ranging from MRI to fusion reactors.

11.
arXiv (CS.AI) 2026-06-12

Reasoning for Mobile User Experience with Multimodal LLMs: Task, Benchmark, and Approach

arXiv:2606.13192v1 Announce Type: new Abstract: User experience (UX) centered on usability, perceived consistency, and functional clarity is fundamental to real-world user interfaces (UI). The application of multimodal large language models (MLLMs) in the field of user interfaces is evolving rapidly, such as visual element grounding, graphical user interface (GUI) agents, and design-to-code generation. However, research efforts on evaluating UX based on UI screenshots are still immature. To address this, we propose UXBench, a novel multimodal benchmark consisting of 2,000 VQA data samples designed to assess MLLMs' ability to perform UI-based reasoning. UXBench includes 8 tasks based on real-world UI screenshots that require fine-grained diagnosis of UX issues across layout relationships, visual hierarchy, and content consistency. Our extensive evaluation of mainstream MLLMs shows that they remain fundamentally limited in their capacity for UI-based reasoning. The results underscore the need for further advancements in this area. To bridge this gap, we propose UI-UX, an MLLM based on Qwen3-VL-4B-Thinking foundation model and enhanced via reinforcement learning with two key innovations: a reward routing mechanism that dynamically balances perceptual understanding and logical reasoning during inference, and an asymmetric transition reward that suppresses redundant or insufficient reasoning steps. Experiments demonstrate that UI-UX achieves state-of-the-art (SOTA) performance on UXBench, attaining an accuracy of 0.7963 – surpassing Claude-4.5-Sonnet's 0.6550 – while exhibiting strong generalization across diverse UI tasks and maintaining low inference latency.

12.
arXiv (CS.CL) 2026-06-16

Does Traversal Order Matter? A Systematic Study of Tree Traversal Methods in Transformer Grammars

Transformer Grammars (TGs) enhance language modeling by incorporating syntactic tree structures. Despite the potentially significant impact on model performance of how syntactic trees are linearized in TGs, existing studies rely solely on Depth-First Traversal (DFT) for linearization. In this paper, we expand the traversal design space by exploring Breadth-First Traversal (BFT) and a novel hybrid traversal strategy, Production-Rule Traversal (PRT), which combines the structural lookahead of BFT with the early lexical generation of DFT. We integrate these traversal methods with varying tree configurations and masking strategies, and empirically evaluate their performance on language modeling, syntactic generalization and summarization. We reveal the inherent trade-offs between nested composition and global lookahead, providing actionable recommendations for designing task-aware Transformer Grammars.

13.
arXiv (CS.CV) 2026-06-18

SAMA: Semantic Anchor-aligned Augmentation for Unified Low-Resource Multimodal Information Extraction

Multimodal Information Extraction (MIE)-covering tasks such as Multimodal Named Entity Recognition (MNER), Relation Extraction (MRE), and Event Extraction (MEE)-is essential for understanding multimedia content but remains constrained by severe data scarcity. Although data augmentation is a promising remedy, existing approaches are impeded by coarse cross-modal alignment and fragmented, task-specific designs that fail to exploit shared semantic knowledge. To overcome these limitations, we introduce Semantic Anchor-aligned Multimodal Augmentation (SAMA), a unified framework for generating high-fidelity, task-aware synthetic data. SAMA constructs structured semantic anchors from ground-truth labels to guide a Collaborative Multi-Experts Multimodal Large Language Model (CME-MLLM), which integrates a Universal Adapter for shared semantics with Task-Specific Adapters to produce diverse yet constraint-compliant textual samples. For image synthesis, SAMA employs an Anchor-Preserving Diffusion mechanism that uses anchor-weighted prompts and latent conditioning to maintain critical semantic anchors while diversifying visual contexts. To eliminate the need for manual verification, SAMA further introduces a Dual-Constraint Filtering module that selects synthetic samples based on both cross-modal consistency and anchor fidelity. Extensive experiments across benchmark datasets for MNER, MRE, and MEE demonstrate that SAMA consistently outperforms state-of-the-art augmentation baselines under both fully supervised and low-resource settings, underscoring its versatility, robustness, and effectiveness.

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

Normative Robustness as a Frontier for Non-Verifiable Reasoning in LLMs

arXiv:2606.12731v1 Announce Type: new Abstract: As LLMs increasingly serve in advisory and deliberative roles, users rely on them for non-verifiable reasoning in domains lacking objective ground truths. However, traditional evaluations of LLM reasoning focus almost exclusively on fact-based domains, such as mathematics and science, leaving uncertainty over whether and to what degree models can handle ambiguous, subjective, or value-laden problems over time. To address this concern, we propose moral reasoning as a paradigmatic subdomain of non-verifiable reasoning. We define moral robustness as a model's capacity to exhibit sound moral reasoning across time and contexts, and we introduce a scalable, adversarial, multi-turn evaluation framework to empirically measure this capability. We simulate 48,000 user-agent moral deliberations across four frontier LLMs, varying premise relevance, premise order, conversation duration, and the user's stated moral view. We find that models successfully ignore morally-irrelevant distractors, but shift their reasoning by up to 6.5%, on average, towards the user's stated preferred moral view, and varying their reasoning depending on factors such as order (altering moral judgments by order in 13-22% of the cases) and duration (altering moral judgments between single-turn and multi-turn in 10-24% of the cases). Our analysis indicates that models tailor not just their final verdicts but their underlying justifications to align with a user's moral viewpoint - a failure mode we characterize as moral deliberative sycophancy.

15.
arXiv (math.PR) 2026-06-16

The Backward Stochastic Partial Differential Integral Equations: Solvability and Comparison Principle

arXiv:2606.16237v1 Announce Type: new Abstract: The paper is concerned with the well-posedness of backward stochastic partial differential equations with jumps, also called backward stochastic partial differential integral equations. We start from the proof for the existence and uniqueness of solution to backward stochastic evolution equation with jump in the Gelfand triple framework. Then the well-posedness of both weak solution and strong solution to backward stochastic partial differential integral equation is obtained with the Gelfand triple replaced by specific Sobolev spaces. Finally, the comparison principle for backward stochastic partial differential integral equation is proved, which has potential applications in financial mathematics.

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

Effective Gaussian Management for High-fidelity Object Reconstruction

This paper proposes an effective Gaussian management framework for high-fidelity scene reconstruction of both appearance and geometry. Unlike recent Gaussian Splatting (GS) pipelines that treat all primitives uniformly during optimization, our framework explicitly manages the attribute activation, representation and pruning of Gaussian. Specifically, our framework first introduces GauSep, a novel densification strategy that selectively activates Gaussian color or normal attributes to alleviate destructive gradient conflicts arising from dual supervision. We further propose GauRep, an adaptive Gaussian representation that dynamically adjusts spherical harmonics (SHs) orders and performs task-decoupled pruning to reduce redundancy at both the individual and global levels. To provide reliable geometric supervision for above mangement process, we additionally introduce CoRe, an regularized surface reconstruction module that distills robust normal fields from an SDF branch to the Gaussian representation through a confidence mechanism. Notably, the proposed Gaussian management is compatible with various reconstruction architectures and can be seamlessly integrated to improve performance while reducing size of the model. Extensive experiments demonstrate that our approach achieves superior or comparable performance in appearance and geometry reconstruction compared with state-of-the-art methods, while using significantly fewer parameters.

17.
arXiv (CS.LG) 2026-06-15

Implicit Variational Rejection Sampling

arXiv:2606.14235v1 Announce Type: new Abstract: Variational Inference (VI) is a fundamental inference technique in Bayesian machine learning for approximating complex posterior distributions. Traditional VI often relies on the mean-field factorization, which can inadequately capture true posterior complexity. Recent advancements have leveraged neural networks to model implicit distributions, offering increased flexibility. However, the practical constraints of neural network architectures still produces inaccuracies. In this paper, we propose a method called Implicit Variational Rejection Sampling (IVRS), which integrates implicit distributions with rejection sampling to improve the posterior approximation. Our method uses neural networks to construct implicit proposal distributions, and rejection sampling with a discriminator network that estimates the density ratio between the implicit proposal and the true posterior for refining the approximation. Towards this end, we introduce the Implicit Resampling Evidence Lower Bound (IR-ELBO) as a metric to characterize the resampled distribution's quality and derive a tighter variational lower bound. Experimental results demonstrate that our method outperforms traditional variational inference techniques.

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

3D-CBM: A Framework for Concept-Based Interpretability in Generative 3D Modeling

This research introduces a framework for incorporating Concept Bottleneck Models (CBMs) into 3D generative architectures to address the inherent 'semantic gap' in deep geometric learning. As deep models become central to 3D content creation, explainability shifts from a peripheral feature to a fundamental requirement for trust and accountability in safety-critical domains such as healthcare and manufacturing. CBMs provide an intrinsic interpretability solution by constraining latent representations to align with human-defined concepts, yet their application to unstructured 3D data remains largely unexplored. We design, implement, and validate a formal 3D-CBM architecture that maps raw geometric inputs, including point clouds and meshes, into a multi-tiered taxonomy of interpretable primitives and functional attributes. The framework further identifies strategic datasets, such as PartNet and ShapeNet, specialized for concept-based supervision. Experimental results from a 3D part-manipulation proof-of-concept experiment demonstrate the framework's efficacy, achieving a concept prediction accuracy of 88.8\% and a Chamfer Distance of 0.0115. Critically, the model enables precise test-time intervention, allowing for the interactive correction of structural errors. This work establishes a foundation for semantically-steerable 3D generation and invites further exploration into collaborative human-in-the-loop design systems.

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

Sub-Token Routing for KV Cache Compression

Transformer inference often requires a large KV cache, especially for long-context language modeling and multimodal generation. Existing compression methods usually reduce cache cost by selecting, evicting, quantizing, or compressing cached tokens, or by reducing the visual-token sequence before language-model inference. We introduce sub-token routing, a KV-compression method that adds a finer control axis inside retained tokens. It splits each retained value vector into groups and keeps only selected groups, while leaving query and key states unchanged. The method is designed to work after token-level reduction. First, a token-reduction method determines which tokens are retained. Then, sub-token routing compresses the value states inside those retained tokens. Experiments under matched KV budgets show that adding sub-token routing improves token-level reduction performance in both LLM and VLM settings, including Quest on LLaMA-2-7B and Qwen2.5-7B, and FastV/VisionZip across LLaVA and Qwen-VL models. The gains are larger at smaller KV budgets, suggesting that value-group routing is especially useful when further token removal becomes costly. Overall, token-level reduction and sub-token routing provide complementary ways to reduce KV cost.

20.
medRxiv (Medicine) 2026-06-10

Prediction of immunotherapy response using live tumor fragments from routine clinical biopsies

Functional ex vivo assays using live tumor tissues have demonstrated strong predictive accuracy for response to immune checkpoint inhibitors (ICIs) but are not scalable, requiring manual processing of large resections collected at academic centers. Here, an ex vivo live tumor fragment (LTF) platform was developed using standard-of-care biopsies from 228 patients with suspected malignancy collected across prospective, multicenter observational trials and biobanks. Hierarchical clustering of ICI-mediated changes in cytokine production identified two groups: responders and nonresponders. A binary classifier (elive index) using 8 cytokines achieved an AUC of 0.99 for cluster prediction. elive index correctly predicted clinical benefit in 93% (26/28) of patients (P = 3.2x10-5) and accurately identified 83% (10/12) of objective responders. Critically, elive responders were identified among biomarker-negative patients, highlighting the platform as a scalable approach that complements existing companion diagnostics and expands the population of patients identified to benefit from ICI therapy.

21.
arXiv (CS.AI) 2026-06-17

FoundCause: Causal Discovery with Latent Confounders from Observational Data

arXiv:2606.17516v1 Announce Type: cross Abstract: Causal discovery from observational data remains challenging due to the need to recover directed structure and latent confounding without interventions. We propose FoundCause, an amortized causal discovery model trained entirely on synthetic data that maps datasets directly to causal graphs in a single forward pass. By learning from large collections of simulated structural causal models, FoundCause captures transferable statistical patterns that generalize beyond individual datasets. The architecture incorporates several key inductive biases for causal discovery. It uses a permutation-invariant transformer encoder with alternating attention over samples and variables to jointly model cross-variable dependence and per-variable distributions. Pairwise statistical features derived from classical asymmetry measures are injected through statistics-conditioned attention, guiding the model toward known causal signals. A factorized decoder separates edge existence from direction, while a triangular refinement module enables reasoning over higher-order causal motifs such as chains and colliders. In addition, a dedicated confounder module based on learnable latent tokens explicitly models hidden common causes, and the model explicitly handles missing data via its masked input representation. To our knowledge, FoundCause is the first amortized causal discovery approach to explicitly model latent confounding. FoundCause outperforms 11 classical non-amortized methods (e.g., PC, GES, NOTEARS-style optimization) and 4 amortized causal discovery methods on 15 real-world datasets, achieving +9.6% improvement in $F_1$, +1.2% in AUROC, and an 18.9% reduction in structural Hamming distance relative to the strongest non-amortized methods, while performing inference in a single forward pass.

22.
arXiv (math.PR) 2026-06-11

Instability of a nonlinear oscillator with small friction and small additive noise

arXiv:2606.11389v1 Announce Type: new Abstract: Let $\lambda = \lambda(\beta,\sigma,a,b)$ denote the top Lyapunov exponent for the linearization along trajectories of the noisy damped non-linear oscillator $\ddot{x}+\beta \dot{x} + ax+bx^3 = \sigma \dot{W}_t$, where $a$, $b$ and $\beta$ are all positive and $\sigma \neq 0$. In 2004 Arnold, Imkeller and Sri Namachchivaya stated without proof that $\lambda(\varepsilon^2 \beta,\varepsilon \sigma,a,b) \sim \overline{\lambda} \varepsilon^{2/3}$ as $\varepsilon \to 0$ with $\overline{\lambda} > 0$. This paper contains a proof of this assertion.

23.
arXiv (CS.CV) 2026-06-17

NTIRE 2024 Challenge on Image Super-Resolution (x4): Methods and Results

This paper reviews the NTIRE 2024 challenge on image super-resolution ($\times$4), highlighting the solutions proposed and the outcomes obtained. The challenge involves generating corresponding high-resolution (HR) images, magnified by a factor of four, from low-resolution (LR) inputs using prior information. The LR images originate from bicubic downsampling degradation. The aim of the challenge is to obtain designs/solutions with the most advanced SR performance, with no constraints on computational resources (e.g., model size and FLOPs) or training data. The track of this challenge assesses performance with the PSNR metric on the DIV2K testing dataset. The competition attracted 199 registrants, with 20 teams submitting valid entries. This collective endeavour not only pushes the boundaries of performance in single-image SR but also offers a comprehensive overview of current trends in this field.

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

A polynomial-time approximation scheme for minimum-weight decoding of topological codes

arXiv:2606.18145v1 Announce Type: new Abstract: Two-dimensional topological translationally invariant (2D TTI) stabilizer codes lie at the heart of fault-tolerant quantum computation, but using them requires solving the decoding problem. Minimum-weight decoding of these codes was recently shown to be NP-hard, even in basic settings, such as the color code with Pauli $Z$ errors and the toric code with Pauli $X$, $Y$ and $Z$ errors. Here, we prove that minimum-weight decoding of 2D TTI codes nonetheless admits a polynomial-time approximation scheme (PTAS), i.e., for any constant $\varepsilon>0$, a recovery operator of weight within a multiplicative factor of $1+\varepsilon$ of the minimum can be found in polynomial time. Our approach builds on Arora's PTAS for Euclidean problems, such as the traveling salesman problem, and applies when decoding can be cast in terms of point-like excitations connected by string-like errors. It therefore extends beyond two dimensions, covering certain higher-dimensional topological codes and quantum memories, including the toric code with phenomenological or circuit-level noise.