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02.
arXiv (CS.CL) 2026-06-12

If LLMs Have Human-Like Attributes, Then So Does Age of Empires II

Much research has been carried out on large language models (LLMs) and LLM-powered agentic workflows. However, many works within the field state emergence of, ascribe to, or assume, generalised anthropomorphic attributes to them (e.g., morality or understanding of natural language). Our goal is not to argue in favour or against the existence of these attributes, but to point out that these conclusions could be incorrect. For this we build and train a simple neural network on the videogame Age of Empires II, and note that any entity in a sufficiently-powerful substrate, such as LEGO or the Greater Boston Area, could also present such attributes. Hence, the purported anthropomorphic attributes of LLMs are empirically non-unique: although some properties (e.g., responses to prompts) could remain invariant, others, such as the interpretation of their perceived behaviour, might change with the substrate. Thus, any empirically-grounded discussion on these attributes requires explicit measurement criteria; otherwise the interpretation is left to the representation. We then show that assuming that these attributes exist or not in a system, independent of the substrate and in a generalised way, leads to either circular or uninformative conclusions. This is regardless of the experimenter's viewpoint on the subject, or whether the outcome shows existence or non-existence. Finally we propose a 'null' assumption, where one assumes LLM non-uniqueness instead of assuming anthropomorphic attributes to set up an experiment, along with examples of it. We also discuss potential objections to our work, briefly survey the field, and prove that Age of Empires II is functionally- and Turing-complete.

03.
arXiv (CS.CV) 2026-06-18

On-Manifold Variational Learning with Heat-Kernel Priors

Learning unsupervised representations of medical imaging cohorts can reveal clinically meaningful prototypes without expert labels, which are often noisy and fail to capture true pathological heterogeneity. However, existing deep latent-variable models estimate Gaussian mixture priors via Euclidean averaging, producing prototypes that drift off the curved data manifold and degenerate as the number of sub-populations grows. We propose a manifold-anchored variational framework built on a geometry-aware Expectation-Maximization (EM) algorithm, whose M-step selects each sub-population prototype as the graph medoid with the highest diffusion centrality on a heat-kernel-weighted latent graph, ensuring that every prototype remains on-manifold. A Dirichlet energy regularizer enforces geometric smoothness of the latent space, and a per-sub-population uncertainty score enables label-free quality assessment. \rev{The manifold-anchored EM is a general-purpose geometric tool that extends standard EM and applies readily to other latent-variable models beyond this setting.} On cardiac scar and brain MRI benchmarks, our framework attains the highest accuracy among all compared methods, produces the sharpest prototypes reported to date, and remains stable at large sub-population counts where all baselines degenerate.

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

From Values to Tokens: An LLM-Driven Framework for Context-aware Time Series Forecasting via Symbolic Discretization

arXiv:2508.09191v2 Announce Type: replace-cross Abstract: Time series forecasting plays a vital role in supporting decision-making across a wide range of critical applications, including energy, healthcare, and finance. Despite recent advances, forecasting accuracy remains limited due to the challenge of integrating historical numerical sequences with contextual features, which often comprise unstructured textual data. To address this challenge, we propose TokenCast, a large language model (LLM) driven framework that leverages language-based symbolic representations as a unified intermediary for context-aware time series forecasting. Specifically, TokenCast employs a discrete tokenizer to transform continuous numerical sequences into temporal tokens, enabling structural alignment with language-based inputs. To effectively bridge the semantic gap between modalities, both temporal and contextual tokens are embedded into a shared representation space via a pre-trained LLM, further optimized with generative objectives. Building upon this unified semantic space, the aligned LLM is subsequently fine-tuned in a supervised manner to predict future temporal tokens, which are then decoded back into the original numerical space. Extensive experiments on real-world datasets demonstrate the effectiveness of our framework and highlight its potential as a generative framework for context-aware time series forecasting. The code is available at https://github.com/Xiaoyu-Tao/TokenCast.

05.
arXiv (CS.CV) 2026-06-18

Grids Often Outperform Implicit Neural Representations at Compressing Dense Signals

Implicit Neural Representations (INRs) have recently shown impressive results, but their fundamental capacity, implicit biases, and scaling behavior remain poorly understood. We investigate the performance of diverse INRs across a suite of 2D and 3D real and synthetic signals with varying effective bandwidth, as well as both overfitting and generalization tasks including tomography, super-resolution, and denoising. By stratifying performance according to model size as well as signal type and bandwidth, our results shed light on how different INR and grid representations allocate their capacity. We find that, for many tasks involving dense signals, a simple regularized grid with interpolation trains faster and to higher or comparable quality than any INR with the same number of parameters. We also find limited settings – namely fitting binary signals such as shape contours – where INRs outperform grids, to guide future development and use of INRs towards the most advantageous applications.

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

Adaptive $k$NN graph model

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

07.
medRxiv (Medicine) 2026-06-17

Waning protection of long-acting RSV monoclonal antibodies in infants: a Bayesian analysis of clesrovimab and nirsevimab trial data

Clesrovimab and nirsevimab are long-acting monoclonal antibodies used to prevent respiratory syncytial virus (RSV) disease in infants, but waning protection in the first year of life is incompletely characterised. We applied a published Bayesian inference framework to clesrovimab and pooled nirsevimab trial data to estimate time-varying efficacy against medically attended RSV lower respiratory tract infection (LRTI) and RSV-associated hospitalisation, accounting for differences in placebo-arm event timing between trials. Estimated clesrovimab efficacy declined from 60.7% (95% CrI: 46.3-72.6) shortly after dosing to 38.3% (8.6-52.9) at six months against medically attended RSV LRTI, and from 87.1% (71.2-96.2) to 49.6% (10.4-70.7) against RSV-associated hospitalisation. For nirsevimab, corresponding estimates declined from 86.9% (75.4-95.0) to 53.8% (27.4-69.7) against LRTI, and from 77.5% (52.6-91.8) to 49.7% (15.7-68.3) against hospitalisation. After accounting for differences in RSV exposure timing and LRTI endpoint definitions between trials, we found no evidence of a difference in efficacy or waning between clesrovimab and nirsevimab.

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

Simplifying the Modeling of Arbitrary Conditionals in Natural Language

Causal Transformers model sequences through an autoregressive factorization of the joint distribution, which enables efficient left-to-right decoding and conditional likelihood computation. However, they cannot tractably sample from or evaluate arbitrary conditionals – e.g., a block of text conditioned on past and future tokens. Recent work aims to solve this problem through novel architectures, but they often lead to sub-optimal modeling of such conditionals and degraded generations. We propose Arbitrary Conditionals GPT (AC-GPT) which introduces a simple modification to standard causal Transformers to enable evaluating and sampling from arbitrary conditionals – including past, future, and mixed contexts – within a single forward pass. Unlike prior approaches, our method preserves the standard left-to-right ordering and next-token prediction objective essential for both strong performance and efficient training on natural language. Crucially, this compatibility allows existing LLMs to be fine-tuned for arbitrary conditioning. Our empirical results indicate that our method outperforms baselines on modeling arbitrary conditionals, without degrading standard left-to-right performance.

09.
arXiv (CS.CL) 2026-06-17

Environment-Grounded Automated Prompt Optimization for LLM Game Agents

LLM agents in interactive environments are highly sensitive to their prompts, yet prompt engineering remains a manual, task-specific process. We introduce an automated prompt optimization framework for LLM agents that decomposes the observation-to-action pipeline into a goal-conditioned descriptor agent and an action selection agent, and iteratively refines each module's prompt through an LLM-driven evolutionary loop guided by environment returns. We propose a behavior analyzer to attribute episode outcomes to specific prompt components, and a mutator to propose targeted revisions to the prompt, before validating them through environment rollouts. We evaluate on all five BabyAI tasks in the BALROG benchmark, comparing our pipeline against BALROG's RobustCoTAgent under both plain and guided prompt initializations. Optimization improves performance consistently across tasks and conditions, without requiring updates to the model weights. On PutNext, a multi-step coordination task where the RobustCoTAgent achieves 0% success, our framework reaches up to 72.5% success rate using the same underlying LLM with optimized prompts. These results suggest that a multi-agent framework, combined with automatic prompt optimization, enhances LLMs without the need for fine-tuning or extensive human supervision.

10.
arXiv (CS.AI) 2026-06-11

Reinforcement Learning Disrupts Gradient-Based Adversarial Optimization

arXiv:2606.12251v1 Announce Type: cross Abstract: Gradient-based adversarial attacks remain a dominant threat to deep neural networks (DNNs), as they exploit gradient information to efficiently optimize adversarial perturbations. To address this, we investigate whether reinforcement learning (RL) training can disrupt the gradient structure used by attackers by training image classifiers with policy-gradient objectives and epsilon-greedy exploration. Through systematic experiments across CIFAR-10, CIFAR-100, and ImageNet-100 with multiple architectures, we find that RL-trained classifiers significantly disrupt gradient-based adversarial optimization. To explain this, we conduct a comprehensive mechanism analysis using loss landscape visualization, static and dynamic gradient indicators, and predictive entropy. Our analysis reveals that RL acts as an implicit regularizer, producing models with highly unstable gradient directions and smaller gradient magnitudes. This combination makes each PGD step both unreliable in direction and limited in magnitude, causing gradient-based attacks to fail within practical iteration budgets. We further show that combining RL with adversarial training (RL-adv) provides a dual-layer defense operating at two complementary levels: RL degrades gradient information available to attackers (gradient-level defense), while adversarial training strengthens decision boundaries (boundary-level defense). RL-adv achieves the highest robustness across all major attack types evaluated, including gradient-based (PGD, AutoAttack), transfer-based, and query-based attacks, outperforming SL-adv by a significant margin. These findings identify RL-induced gradient disruption as a complementary robustness mechanism and motivate future research on hybrid SL-RL training schedules that combine SL's efficiency with RL's gradient-regularization properties.

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

How Much Do Reviews Really Contribute? A Study on Text-Enriched Matrix Factorization for Recommendations

arXiv:2606.16973v1 Announce Type: cross Abstract: Incorporating textual reviews into a Recommender System has become a prominent strategy for enriching collaborative signals with semantic information. However, the actual contribution of review-derived representations remains an open question, particularly when strong collaborative baselines are employed. In this work, we systematically investigate the impact of textual information on Matrix Factorization by introducing and comparing three enrichment strategies over a common collaborative backbone. First, we propose a learnable gating mechanism that adaptively balances collaborative and textual signals during training. This mechanism is applied to two distinct review representations: (i) aggregated topic profiles extracted from user and item histories, and (ii) full text embedding representations derived from reviews. Additionally, we explore a cross-attention mechanism that identifies and emphasizes the most informative dimensions of the textual representation before fusion with collaborative factors. We evaluate six variants: pure, enriched with topic profiles and text via gating; enriched with topics and text via gating; and enhanced with cross-attention over textual features. Experiments across multiple review-based datasets reveal that although adaptive fusion mechanisms improve representation flexibility, the marginal contribution of textual signals remains limited compared to the collaborative backbone. These findings suggest that, under typical rating-prediction settings, collaborative information continues to dominate performance, raising important considerations for the effective integration of semantic review signals into recommendation models.

12.
arXiv (quant-ph) 2026-06-16

Enhancing Quantum Machine Learning with Anyons

arXiv:2606.16090v1 Announce Type: new Abstract: The power of quantum computing and quantum machine learning relies on harnessing uniquely quantum phenomena as computational resources. While superposition, coherence and entanglement have been central to this effort, the role of particle exchange statistics remains largely unexplored. Here, we introduce a quantum kernel framework that unifies bosonic, fermionic, and anyonic (fractional) exchange statistics within a single learning paradigm. We study this family of kernels from three perspectives. At the representation level, Haar-averaged effective-dimension analysis shows that fractional exchange phases access feature-space directions inaccessible to the purely symmetric or antisymmetric limits. At the level of kernel geometry, the corresponding Gram matrices show greater separation from the distinguishable-particle baseline and reduced label-dependent model complexity. Finally, on learning benchmarks, anyonic kernels consistently outperform their bosonic and fermionic counterparts, with stronger target alignment and more favorable class geometry. Together, these findings show that exchange statistics reshape the structure and geometry of quantum feature space, leading to enhanced learning performance. Our work identifies particle exchange statistics as an overlooked computational ingredient for quantum machine learning and provides the first systematic comparison of quantum learning models across exchange phases.

13.
medRxiv (Medicine) 2026-06-18

Development and Initial Validation of the Quality of life Evaluation in NF2-related Schwannomatosis Trials (QUEST) Assessment

Individuals with NF2-related schwannomatosis (NF2-SWN) experience a complex constellation of physical, emotional, and social symptoms that substantially impact quality of life (QoL). Although disease-specific patient-reported outcome measures are increasingly important for evaluating treatment benefit in clinical trials, existing NF2-SWN QoL measures have limitations in content coverage and sensitivity to change. This study describes the development and initial validation a new disease-specific QoL assessment – the Quality of Life Evaluation in NF2-related Schwannomatosis Trials (QUEST). Using a three-phase, mixed-methods approach, items were generated through concept elicitation interviews with individuals with NF2-SWN and clinicians, prioritized via patient survey data, and refined through iterative cognitive debriefing procedures. The resulting 21-item QUEST assesses the extent to which NF2-SWN has negatively impacted a persons daily life over the past seven days. Initial psychometric evaluation was conducted in an international sample of 174 individuals with NF2-SWN aged 15 years and older (117 women (67%), 158 White individuals (89%)). Exploratory factor analysis supported a four-factor structure, and the total score demonstrated excellent internal consistency and strong test-retest reliability. Evidence of construct validity was demonstrated through hypothesized associations with disease-specific, generic, and domain-specific QoL measures, as well as known-groups validity based on self-reported disease severity and number of prior surgeries. Incremental validity analyses indicated that QUEST explained unique variance beyond existing measures. Together, findings support the QUEST as a reliable and valid disease-specific QoL measure with strong content validity and feasibility for use as a clinical trial endpoint in NF2-SWN.

14.
arXiv (math.PR) 2026-06-12

Counterintuitive problems in discrete probability

arXiv:2606.07516v2 Announce Type: replace Abstract: This manuscript contains a collection of counterintuitive problems in discrete probability, together with detailed solutions. The dataset was constructed as part of a broader research project investigating the capabilities of the latest-generation Large Language Models (LLMs) in solving discrete probability problems, in order to assess whether LLMs tend to make systematic reasoning errors associated with known cognitive biases. The problems collected here are specifically designed to challenge heuristic reasoning strategies that often lead to intuitively appealing but mathematically incorrect conclusions. The dataset combines several types of problems. Some are adapted from classical probabilistic paradoxes and cognitive-bias literature, while others originate from recreational mathematics sources or were developed by ourselves following similar principles. The primary purpose of this document is to provide a transparent and publicly accessible reference for the problems used in our experimental evaluation of language models, as well as providing detailed human-made solutions. At the same time, we believe that this collection may also prove useful for future research on probabilistic reasoning, cognitive biases, and the evaluation of reasoning capabilities in artificial intelligence systems.

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

Beyond a Single Explanation of the Adam–SGD Gap

arXiv:2606.14259v1 Announce Type: new Abstract: Prior work has identified several factors that can contribute to the performance gap between Adam and SGD, spanning data aspects, architecture design, and optimization properties. Yet these explanations are often studied in isolation, leaving their relative importance unclear. In this work, we revisit these hypotheses through a controlled empirical study across vision, language, genomics, and graph tasks, spanning modern and classical architectures, and carefully designed training setups. Our results suggest that no single factor consistently explains the Adam–SGD gap. For instance, the Adam advantage can (1) persist under a uniform vocabulary distribution yet nearly disappear under a heavy-tailed one; (2) reverse in favor of SGD in softmax-attention models; and (3) become larger under soft architectural modifications, e.g., when ReLU is replaced by a GeLU nonlinearity. This suggests that the gap arises from nontrivial data and architecture interactions, rather than from a single common factor. Yet, we observe a pattern across our settings: a crossover batch size at which the relative advantage shifts from SGD to Adam as the batch size scales. These empirical results are captured by our theoretical gap model, which predicts this batch-size-dependent crossover. Our perspective helps reconcile several existing hypotheses while offering practical insights across domains.

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

Inference-Time Decision Calibration for Temporal Classification

arXiv:2606.16034v1 Announce Type: new Abstract: Temporal classification errors are often treated as representation failures, but they can also arise from how available evidence is converted into decisions. This paper proposes a representation–calibration decomposition for temporal classification. We keep a trained native classifier frozen and separate two inference-time interventions: a conservative residual multi-scale branch that adds auxiliary logits to the native prediction, and a post-hoc branch-aware calibrator that recombines native and residual evidence at decision time. This design distinguishes missing temporal evidence from underused decision-level evidence without retraining the backbone. Across FI-2010, PTB-XL, UCI-HAR, MHEALTH, and HARTH, we find that gains are strongly regime-dependent. Residual multi-scale evidence is most useful in noisy or representation-limited settings, especially short-horizon FI-2010 and weaker recurrent backbones, while branch-aware calibration helps when native and auxiliary logits contain complementary evidence not fully exploited by the raw decision rule. Near-saturated settings show limited gains from either intervention. These results suggest that temporal classification should be understood not only as representation learning, but also as the problem of trusting, combining, and calibrating evidence from multiple views.

17.
arXiv (math.PR) 2026-06-11

Hilbert space embeddings of independence tests and interaction measures of several variables

arXiv:2411.08653v2 Announce Type: replace-cross Abstract: We present a unified theoretical framework for kernel-based measures of dependence on product spaces. Building on the ideas underlying distance covariance, distance multivariance, and the Hilbert-Schmidt Independence Criterion (HSIC), we define a new family of kernels on an $n$-fold Cartesian product, termed positive definite independent of order $k$ (PDI$_{k}$ kernels). These kernels extend the concepts of positive definite and conditionally negative definite kernels to higher orders and provide the foundation for generalized independence and interaction tests, such as the generalized Lancaster interaction of order $k$ ($\Lambda_{k}^{n}$), and the Streitberg interaction ($\Sigma$). Our analysis focuses on the continuous setting, where we prove a Kernel Mean Embedding Theorem for PDI$_{k}$ kernels and establish the corresponding integrability restrictions. Based on these results, we characterize how the Kronecker products of PDI kernels behave.

18.
arXiv (CS.CV) 2026-06-12

InterleaveThinker: Reinforcing Agentic Interleaved Generation

Recent image generators have demonstrated impressive photorealism and instruction-following capabilities in single-image generation and editing. However, constrained by their architectures, they cannot achieve interleaved generation (text-image sequence), which has crucial applications in visual narratives, guidance, and embodied manipulation. Even the latest open-source Unified Multimodal Models (UMMs) exhibit limited performance in this regard. In this paper, we introduce InterleaveThinker, the first multi-agent pipeline designed to endow any existing image generator with interleaved generation capabilities. Specifically, we employ a planner agent to organize the image-text input sequence, instructing the image generator on the required execution at each step. Subsequently, we introduce a critic agent to evaluate the generator's outputs, identify samples that deviate from the planned instructions, and refine the instructions for regeneration. To implement this pipeline, we construct the Interleave-Planner-SFT-80k and Interleave-Critic-SFT-112k to perform a format cold-start. Then we develop Interleave-Critic-RL-13k to reinforce the step-wise instruction correction capability within a generation trajectory using GRPO. Since a single interleaved generation trajectory may involve over 25 generator calls, optimizing the entire trajectory is computationally impractical. Therefore, we propose accuracy reward and step-wise reward, allowing single-step RL to effectively guide the entire generation trajectory. The results show that InterleaveThinker improves performance across various image generators. On interleaved generation benchmarks, it achieves performance comparable to Nano Banana and GPT-5. Surprisingly, it also significantly enhances the base model on reasoning-based benchmarks; for example, on 4-step FLUX.2-klein, we observe substantial gains on WISE and RISE.

19.
arXiv (CS.AI) 2026-06-12

LoRA-Muon: Spectral Steepest Descent on the Low-Rank Manifold

arXiv:2606.12921v1 Announce Type: cross Abstract: Low-Rank Adaptation (LoRA) significantly reduces compute and memory costs for finetuning Deep Learning models but is often harder to tune than dense training: when using factor-wise optimizers such as AdamW, it is sensitive to initialization choices, its optimal learning rates transfer poorly across ranks, and it often fails to beat dense baselines. We derive LoRA-Muon by applying the Muon optimizer's spectral steepest-descent rule to the low-rank setting. Along with our split weight-decay rule, our main claim is that LoRA-Muon is a good low-rank proxy for full-rank Muon and Shampoo-family optimizers. Its optimal learning rates transfer across rank, width, depth, and factor-rescaling. In our compute-matched TinyShakespeare study, a rank-$2$ proxy recovers the dense best tested learning rate, and a rank-$32$ LoRA-Muon run attains lower mean validation loss than the dense baseline in the seed-averaged sweep. We further show that the Spectron optimizer depends on arbitrary factor scaling, so it would likely be a poor fit when finetuning starts from badly imbalanced factors, and that LoRA-RITE's simplified QR-coordinate core implements the same spectral update. LoRA-Muon computes that update without QR-decomposition and avoids storing second moments, making it more accelerator-friendly and memory-efficient.

20.
medRxiv (Medicine) 2026-06-22

''Circumstantial Determinants'': An Efficient Approach to Reaching People in Need of HIV Prevention?

HIV prevention and testing programmes primarily reach people who self-refer or attend routine health services. Higher-risk individuals are missed if they are healthy, under-estimate their risk of infection or under-report sexual risk-behaviours. We assess a new approach to address limitations in existing programmes by targeting HIV services on ''Circumstantial Determinants'' (CDs) of HIV risk - the social circumstances, settings, and norms associated with behaviours that increase risk of HIV acquisition. Data on potential CDs and sexual behaviour were collected in a population survey in Zimbabwe in 2018/19 (N=9141). HIV-negative individuals reporting [≥] 1 sexual risk-behaviours were defined as the 'priority population' for HIV prevention. For each sex, six circumstantial determinants were associated with being in the priority population (aOR [≥] 1.30; p [≤] 0.01). Reach and efficiency of CDs (and combinations) were calculated; ROC curve algorithms evaluated their ability to identify priority population membership; and HIV prevention condom cascades were compared between CD-defined priority population subgroups. Example findings include that targeting men at bars and beerhalls could reach 48.5% of the priority population and 25.1% of lower-risk men. These percentages increase to 77.1% and 53.7% if men with poor mental health, no religious affiliation, negative social capital, or living on agricultural estates are also targeted. Targeting women with poor mental health could reach 32.0% of the priority population and 21.3% of lower-risk women. Targeting additional circumstantial determinants increases these percentages to 54.1% and 37.5%, respectively. Cascade barriers to condom use differed between CD-defined subgroups. The Circumstantial Determinants approach demonstrates proof-of-concept potential to strengthen HIV prevention services.

21.
arXiv (math.PR) 2026-06-12

Scaling limit of additive functionals for reversible non-gradient exclusion process: critical cases

arXiv:2606.13442v1 Announce Type: new Abstract: For the reversible speed-change exclusion process $(\eta_t)_{t \geq 0}$ in $\mathbb{Z}^d$, we study the scaling limit of additive functionals ${\Gamma_t(f) = \int_0^t f(\eta_s)\, \mathrm{d} s}$. Concerning the local centered function $f$, the previous work [Commun. Math. Phys. 104, 1-19, 1986] by Kipnis and Varadhan and [Comm. Pure Appl. Math., 66: 649-677, 2013] by Gon{ç}alves and Jara respectively covered the cases $d \geq 3$ and $d=1$. The present paper completes the missing part $d=2$, and also develops the theory for functions with higher degree. The novelty is a quantitative homogenization of the resolvent, which allows to overcome the obstacle of correlation function in non-gradient models.

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

Stochastic dominations for FK percolation and sharp thinning thresholds for the Ising energy field

arXiv:2606.13648v1 Announce Type: new Abstract: At first glance, one would imagine that the energy field of the Ising model, the set of edges whose endpoints share the same spin, is stochastically monotone as a function of the coupling constants. However, this is not generally the case. In this paper, we introduce two weaker notions of stochastic domination that make this result true: $p$–weak and $p$–weak$^\dagger$ domination. Both of these notions depend on a parameter $p$ and we find the optimal values $p$ and $p^\dagger$ so that these dominations hold. One of the key ingredient to obtain some of the results is a new stochastic domination relating FK percolations with different parameters $q,\tilde{q}\geq 1$ that is of independent interest.

23.
arXiv (CS.CV) 2026-06-12

BSViT: A Burst Spiking Vision Transformer for Expressive and Efficient Visual Representation Learning

Spiking Vision Transformers (S-ViTs) offer a promising framework for energy-efficient visual learning. However, existing designs remain limited by two fundamental issues: the restricted information capacity of binary spike coding and the dense token interactions introduced by global self-attention. To address these challenges, this work proposes BSViT, a burst spiking-driven Vision Transformer featuring a Dual-Channel Burst Spiking Self-Attention (DBSSA) mechanism. DBSSA encodes queries with binary spikes and keys with burst spikes to enhance representational capacity. The value pathway adopts dual excitatory and inhibitory binary channels, enabling signed modulation and richer spike interactions. Importantly, the entire attention operation preserves addition-only computation, ensuring compatibility with energy-efficient neuromorphic hardware. To further reduce spike activity and incorporate spatial priors, a patch adjacency masking strategy is introduced to restrict attention to local neighborhoods, resulting in structure-aware sparsity and reduced computational overhead. In addition, burst spike coding is systematically integrated across the network to increase spike-level representational capacity beyond conventional binary spiking. Extensive experiments on both static and event-based vision benchmarks demonstrate that BSViT consistently outperforms existing spiking Transformers in accuracy while maintaining competitive energy efficiency.

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

ISAP-3D: Identity-Slot Aligned Part-Aware 3D Generation

Part-aware 3D generation aims to synthesize structured objects with semantically meaningful components, yet often suffers from structural ambiguity due to identity-layout entanglement. Existing methods either infer part identity and spatial layout implicitly, which can lead to unstable part allocation (e.g., slot swapping or part merging), or rely on strong layout conditions that are difficult to obtain in practice. We attribute this ambiguity to identity-slot permutation freedom: without explicit identity-slot alignment, the correspondence between semantic parts and generation slots is not identifiable during training, allowing multiple slot assignments to fit the same supervision and leading to inconsistent decomposition. Based on this insight, we argue that stable part-aware generation requires identity-aligned one-to-one slot modelling. We therefore propose an identity-slot aligned framework, ISAP-3D, which anchors each part with semantic identity tokens and performs identity-conditioned one-to-one layout prediction, followed by layout-conditioned geometry synthesis. Structured local-global conditioning maintains identity alignment across semantic, spatial, and geometric stages. We also construct a part-level dataset with a unified semantic protocol to enable learnable and consistent identity-slot alignment. Extensive experiments demonstrate improved structural stability, controllability, and robustness over state-of-the-art part-aware generation baselines.

25.
arXiv (math.PR) 2026-06-11

On the spatio-temporal increments of nonlinear parabolic SPDEs and the open KPZ equation

arXiv:2508.05032v3 Announce Type: replace Abstract: We study spatio-temporal increments of the solutions to nonlinear parabolic SPDEs on a bounded interval with Dirichlet, Neumann, or Robin boundary conditions. We identify the exact local and uniform spatio-temporal moduli of continuity for the sample functions of the solutions. These moduli of continuity results imply the existence of random points in space-time at which spatio-temporal oscillations are exceptionally large. We also establish small-ball probability estimates and Chung-type laws of the iterated logarithm for spatio-temporal increments. Our method yields extension of some of these results to the open KPZ equation on the unit interval with inhomogeneous Neumann boundary conditions. Our key ingredients include new strong local non-determinism results for linear stochastic heat equation under various types of boundary conditions, and detailed estimates for the errors in linearization of spatio-temporal increments of the solution to the nonlinear equation.