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01.
arXiv (CS.AI) 2026-06-24

Random coloured digraphs defined by a Markov logic network

Authors:
Yasmin Tousinejad↗Vera Koponen↗

arXiv:2606.23715v1 Announce Type: cross Abstract: A Markov Logic Network (MLN) is a probabilistic relational model used in Statistical Relational Artificial Intelligence for defining a probability distribution on the set of possible worlds with domain $D$ for an arbitrary finite domain $D$. An MLN consists of soft constraints with associated weights which are nonnegative real numbers. In this study we consider a language speaking about a property $P(x)$ and a relation $R(x, y)$. We consider an MLN for which every Boolean combination of $P(x)$ and $R(x, y)$ is a soft constraint (with associated weight). Let $n$ denote the size (cardinality) of the domain. We show that, for every choice of weights, if the weights are scaled by $1/n$ then, for every first-order sentence $\varphi$, the probability that $\varphi$ holds tends to either 0 or 1 as $n \to \infty$; that is, a 0-1 law for first-order logic holds. Morover, the limit probability does not depend on the weights. If we instead use the standard semantics of MLNs, in the case of which the weights are not scaled, then the limit behaviour is more complicated and depends on the weights. With unscaled weights we get 7 qualitatively different cases which depend on the weights. In some cases we have a 0-1 law for first-order logic, in some cases not, but we may still have a convergence law. The influence of the weights on the asymptotic probability of a first-order sentence may be in the form of a sudden ``phase transition'' from one of the 7 cases to another. The presence of a convergence law has positive implications for inference on large domains.

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03.
arXiv (CS.LG) 2026-06-19

Interactive Pareto navigation for deep multi-task learning

Authors:
Augustina C. Amakor↗Konstantin Sonntag↗Sebastian Peitz↗

arXiv:2606.19521v1 Announce Type: new Abstract: In multi-task learning, handling an increasing number of objectives can quickly become challenging, both in terms of the computational resources and the decision maker's capacity to choose appropriate trade-offs. A widely used approach is thus to aggregate the individual losses in a single loss function by a weighted sum. This often fails to capture either the decision maker's preferences as a result of the shape of the Pareto front, or requires multiple adjustments and computations which becomes prohibitively expensive in deep learning applications. To address these issues, we introduce a novel framework, Preference Pareto Exploration (PPE), which enforces the decision maker's preferences while accounting for the geometry of the Pareto set in an interactive exploration process. PPE is based on a predictor-corrector method that performs predictor steps tangential to the manifold of Pareto-optimal solutions, following the decision maker's preference. The subsequent corrector step results in a new trade-off reflecting this preference. To avoid explicit Hessian computations when characterizing the tangent space of the manifold, we employ a Krylov subspace method that relies solely on matrix-vector products. These products can be efficiently obtained via automatic differentiation, ensuring both efficiency and robustness throughout the optimization process. The method's functionality and performance are demonstrated using both toy problems and examples from deep learning.

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

Generating Natural and Expressive Robot Gestures through Iterative Reinforcement Learning with Human Feedback using LLMs

Authors:
Chris Lee↗Flora Salim↗Benjamin Tag↗Francisco Cruz↗

arXiv:2606.18747v1 Announce Type: cross Abstract: Expressive gestures are essential for natural and effective communication, complementing speech when verbal cues alone are insufficient (e.g., pointing). For social robots such as the humanoid Pepper, producing natural and expressive movements is critical for improving human-robot interaction (HRI) and long-term acceptance. However, generating gestures remains challenging due to reliance on expert-authored animations, resulting in rigid behaviors that are impractical for dynamic and diverse environments. Alternatively, machine learning approaches often struggle to capture perceived naturalness, becoming increasingly challenging with more degrees of freedom. Consequently, producing expressive robot gestures requires a system that can adapt to the environment while adhering to social norms and physical constraints. Recent advances in large language models (LLMs) enable dynamic code generation, offering new opportunities for runtime gesture synthesis from natural language. In this paper, we integrate ChatGPT into the humanoid robot Pepper to generate co-speech gestures aligned with conversational output. While this baseline enables flexible gesture generation, the resulting motions are often perceived as stiff and unnatural. To address this limitation, we introduce an iterative reinforcement learning with human feedback (RLHF) system that finetunes gesture generation based on user evaluations, leveraging an iterative user study to compare Pepper's generated gestures. Our results show that RLHF improved the LLM's co-speech generative capabilities, producing more expressive, relevant and fluid movements.

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05.
arXiv (CS.LG) 2026-06-15

NeST: Neuron Selective Tuning for LLM Safety

Authors:
Sasha Behrouzi↗Lichao Wu↗Mohamadreza Rostami↗Ahmad-Reza Sadeghi↗

arXiv:2602.16835v2 Announce Type: replace-cross Abstract: Safety alignment is essential for the responsible deployment of Large Language Models (LLMs). Yet, existing approaches often rely on heavyweight fine-tuning that is costly to update, audit, and maintain across model families. Full fine-tuning incurs substantial computational and storage overhead, while parameter-efficient methods, e.g., Low-Rank Adaptation (LoRA), trade efficiency for inconsistent safety gains and sensitivity to design choices. Safety intervention mechanisms reduce unsafe outputs without modifying model weights, but do not directly shape or preserve the internal representations that govern safety behavior. We present NeST, a Neuron-Selective Tuning framework for efficient post-hoc safety alignment. NeST identifies safety-relevant feed-forward neurons via activation probing on vanilla harmful and benign prompts, clusters neurons with similar activation profiles, and trains shared cluster-level updates while freezing the rest of the model. Importantly, NeST is trained only on vanilla malicious prompts, without using jailbreak-specific attack data, yet generalizes robustly to diverse jailbreaks. The learned updates are then folded into the original weights, incurring no inference-time overhead. Evaluated on 14 open-weight language and multimodal models, NeST outperforms lightweight baselines and approaches full fine-tuning robustness with significantly fewer trainable parameters. On text-only models, NeST reduces average jailbreak attack success rate from 44.5% to 1.1% while training only 0.4M parameters on average. Across multimodal settings, it reduces ASR from 55.3% to 1.1%, and for downstream fine-tuned variants, it restores safety by reducing ASR from 53.8% to 0.8%. These results show that robust, maintainable safety alignment can be achieved by concentrating adaptation on localized, functionally coherent safety structures.

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07.
arXiv (CS.AI) 2026-06-24

Catastrophic Compositional Generation: Why Vanilla Diffusion Models Fail to Extrapolate

Authors:
Duncan Soiffer↗Chandler Squires↗Yuan Guan↗Jason Hartford↗Pradeep Ravikumar↗

arXiv:2606.23920v1 Announce Type: cross Abstract: The task of compositional generation involves using a conditional generative model, trained only on a subset of the possible conditions, to produce samples from compositionally-defined target distributions such as a geometric combination of the source distributions. In this work, we argue that this task is often infeasible for vanilla conditional diffusion models: we conjecture that no inference-time technique can efficiently produce samples from the target distribution in certain well-motivated settings. This idea is supported by theory-guided generalization arguments and carefully-designed experiments on both synthetic and realistic data. In particular, while recent methods such as Feynman-Kac correction reduce inference-time approximation error, our results show that score estimation error has a more catastrophic effect on performance when the target distribution is out-of-distribution with respect to the sources, highlighting the need for a different approach to this task.

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

Training and Evaluating Diffusion Policies with Long Context Lengths

Authors:
Abhinav Agarwal↗Adam Wei↗Taylan Kargin↗Michael Zeng↗Cole Becker↗Arif Kerem Dayi↗Pablo Parrilo↗Asuman Ozdaglar↗Russ Tedrake↗

arXiv:2606.16447v1 Announce Type: cross Abstract: Imitation learning has enabled highly-dexterous robotic manipulation from RGB observations. Policies trained with these methods, however, typically condition robot actions on only a short history of observations. These policies cannot solve tasks that require memory and can get stuck repeatedly executing the same failing motions. In this work, we first benchmark policy performance as context length is incrementally increased from short to long, across a spectrum of tasks with varying local stability and memory requirements, and in multiple data regimes. To our knowledge, this is the first study to investigate context length in imitation learning at this level of detail. Our results challenge prior claims: naively scaling context length is not as brittle as advertised in literature. With an appropriate conditioning method and denoising backbone (UNet+Cross-Attention), single-task policies achieve high success rates on many tasks in the usual data regime even with naive scaling. Next, we propose a training algorithm to jointly train policies at multiple context lengths, further reducing the sample complexity of long-context learning. Finally, we apply our findings to re-evaluate some previously proposed solutions to long-context imitation learning.

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09.
arXiv (quant-ph) 2026-06-16

Synthesizing Arbitrary Non-Hermitian Hamiltonian with Stochastic Floquet Engineering

Authors:
Lingzhen Guo↗Hui Jing↗

arXiv:2606.15664v1 Announce Type: new Abstract: The conventional Floquet engineering scheme synthesizes a given target Hamiltonian with a deterministic temporal periodic driving field. In this work, we introduce the stochastic Floquet engineering scheme that can synthesize an arbitrary non-Hermitian target Hamiltonian using a time-periodic driving field with noisy amplitude. Our method is rooted in the Hermitian dynamics taking noise as a valuable quantum resource with no need for loss or gain in prior. We apply our method to engineer a cavity Hamiltonian with dissipative coupling between Fock states, and to prepare a given quantum state from a generally arbitrary quantum state. The stochastic Floqut engineering also provides a way to generate non-unitary quantum gates, which take advantage in certain tasks compared to unitary quantum computing, without the need for ancillae or state-dependent updating.

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

MFEN:Multi-Frequency Expert Network for Visible-Infrared Person Re-ID

Authors:
Xulin Li↗Yan Lu↗Bin Liu↗Qinhong Yang↗Qi Chu↗Tao Gong↗Nenghai Yu↗

Visible-infrared person re-identification (VI-ReID) is challenging due to the large modality discrepancy between visible and infrared images. We contend that this discrepancy is largely related to differing lighting conditions, including differences in light wavelength and light source type. Recently, frequency-based VI-ReID approaches have achieved notable success because frequency information can better extract identity-relevant contours and details while excluding irrelevant lighting and color. However, existing methods either do not distinguish different frequency bands or focus on only one band, which is insufficient under diverse lighting conditions. To perform comprehensive frequency domain learning, we propose a Multi-Frequency Expert Network (MFEN) that enables multi-frequency modulation and adaptively combines different bands through a mixture-of-experts design. We further introduce Random Frequency Augmentation (RFA) and Frequency Auxiliary Optimization (FAO) to better train MFEN. The three modules are complementary and jointly capture critical frequency-domain details for robust representation learning. Extensive experiments on three VI-ReID datasets demonstrate the effectiveness of our approach.

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

Mosaic: Data-Free Knowledge Distillation via Mixture-of-Experts for Heterogeneous Distributed Environments

Authors:
Junming Liu↗Yanting Gao↗Yuqi Li↗Siyuan Meng↗Yifei Sun↗Aoqi Wu↗Yirong Chen↗Ding Wang↗Shiping Wen↗

arXiv:2505.19699v2 Announce Type: replace-cross Abstract: Federated Learning (FL) is a decentralized machine learning paradigm that enables clients to collaboratively train models while preserving data privacy. However, the coexistence of model and data heterogeneity gives rise to inconsistent representations and divergent optimization dynamics across clients, ultimately hindering robust global performance. To transcend these challenges, we propose Mosaic, a novel data-free knowledge distillation framework tailored for heterogeneous distributed environments. Mosaic first trains local generative models to approximate each client's personalized distribution, enabling synthetic data generation that safeguards privacy through strict separation from real data. Subsequently, Mosaic forms a Mixture-of-Experts (MoE) from client models based on their specialized knowledge, and distills it into a global model using the generated data. To further enhance the MoE architecture, Mosaic integrates expert predictions via a lightweight meta model trained on a few representative prototypes. Extensive experiments on standard image and multimodal benchmarks demonstrate that Mosaic consistently outperforms state-of-the-art approaches under both model and data heterogeneity. The source code has been published at https://github.com/Wings-Of-Disaster/Mosaic.

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12.
arXiv (CS.AI) 2026-06-24

Reward-Centered ReST-MCTS: A Robust Decision-Making Framework for Robotic Manipulation in High Uncertainty Environments

Authors:
Xibai Wang↗

arXiv:2503.05226v2 Announce Type: replace-cross Abstract: Monte Carlo tree search is attractive for robotic manipulation because it can improve action selection through simulation without requiring a fully differentiable policy. In uncertain domains, however, sparse terminal rewards and noisy transitions can make shallow search brittle: many candidate branches remain indistinguishable until late rollouts, and small simulation budgets amplify this ambiguity. This paper presents Reward-Centered ReST-MCTS, a decision-making framework that decomposes intermediate feedback into rule, heuristic, optional neural, and value-estimation channels, centers the resulting process signal against matched task contexts, and uses it to bias or repair search while preserving terminal-task evaluation. The primary evidence is intentionally tiered. Local tasks and matched ManiSkill diagnostics isolate reward-center mechanisms and ablations; matched option-level ManiSkill sweeps test robustness under primitive failure, observation noise, and initial-pose shifts while not claiming standard benchmark superiority; and an official same-backbone OpenVLA-OFT/LIBERO bridge tests bounded VLA action repair. The OpenVLA-OFT clean reproduction reaches 10/10 LIBERO-Spatial successes both with and without RCRM-Guard. A single-suite same-backbone action-channel stress artifact over ten paired LIBERO-Spatial action-channel stress episodes records 0/10 unguarded successes and 9/10 guarded successes. Additional observation-noise, language-perturbation, and visual-distractor probes are reported as coverage and negative-result context rather than superiority evidence. The resulting claim is bounded: Reward-Centered ReST-MCTS is an inspectable test-time verifier for same-backbone high-uncertainty manipulation, not a replacement VLA policy or a broad standard-benchmark superiority claim.

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13.
arXiv (CS.CV) 2026-06-17

Test-Time Training for Robust Text-Guided Open-Vocabulary Object Counting

Authors:
Hao-Yuan Ma↗Yuda Zou↗Li Zhang↗Yongchao Xu↗

Text-guided Open-vocabulary Object Counting (TOOC) enables counting arbitrary object categories specified by text prompts, offering substantially greater flexibility than conventional closed-set counting. However, existing TOOC methods are developed and evaluated primarily on ideal images, while real-world scenes often suffer from adverse conditions such as rain, fog, darkness, and sensor noise, which severely degrade visual quality and impair vision-language alignment. To bridge this gap, we introduce Robust-TOOC, the first benchmark for evaluating TOOC under diverse corruption conditions, which covers six representative degradation types: rain, fog, darkness, Gaussian noise, salt-and-pepper noise, and mixed corruption. To improve robustness while preserving the original counting architecture, we propose Dual-TTT, a dual-architecture test-time training framework for TOOC. Specifically, during test-time training, Dual-TTT updates only the Text-guided Lightweight Denoising module (TL-Denoiser), while keeping the original counting network frozen. Inspired by diffusion models, the TL-Denoiser is optimized to remove corruption-aware noise from image representations under degraded conditions. Since only the TL-Denoiser is trained at test time, Dual-TTT is annotation-free and can be seamlessly integrated into existing TOOC models without modifying their original architecture. Extensive experiments on multiple recent TOOC baselines demonstrate the effectiveness of our method.

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

ToolSense: A Diagnostic Framework for Auditing Parametric Tool Knowledge in LLMs

Authors:
Ashutosh Hathidara↗Sai Shruthi Sistla↗Sebastian Schreiber↗Sahil Bansal↗

arXiv:2606.12451v1 Announce Type: new Abstract: Large language models deployed as agents over large tool catalogs face a critical tool-retrieval bottleneck. As embedding-based retrieval approaches rely on compact encoders that may under-capture specialized tool semantics, parametric tool retrieval addresses this by encoding each tool as a virtual token appended to the LLM vocabulary, fine-tuned in two stages (memorization then retrieval SFT) to use the LLM as a retriever, achieving strong performance on standard ToolBench retrieval benchmarks. Yet these benchmarks use verbose, fully-specified queries, and their evaluation applies constrained decoding that restricts outputs to valid token paths, neither reveals whether the model actually understands its tools. We introduce ToolSense, an open-source LLM-powered diagnostic framework that takes any tool catalog as input and automatically generates three benchmarks: a Realistic Retrieval Benchmark (RRB) with queries at three ambiguity tiers, an MCQ probing benchmark, and a QA probing benchmark. Applying ToolSense to ToolBench (~47k tools) and evaluating five parametric model training configurations reveals a knowledge-retrieval dissociation: on RRB queries, several configurations collapse by ~50-64 percentage points compared to fully-specified ToolBench benchmarks, falling below the embedding-model baseline. Additionally, despite strong retrieval performance, some models score near-random on factual probes, suggesting a knowledge-retrieval dissociation. We open-source the ToolSense framework and the ToolBench diagnostic benchmarks at https://github.com/SAP/toolsense.

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

Tacit Coordination of Large Language Models

Authors:
Ido Aharon↗Emanuele La Malfa↗Michael Wooldridge↗Sarit Kraus↗

arXiv:2601.22184v2 Announce Type: replace-cross Abstract: Large Language Models (LLMs) are increasingly deployed in multi-agent settings that require coordination without communication, from human-AI interaction to safety-critical scenarios. Humans often overcome the absence of communication through focal points: salient solutions that naturally stand out to all participants. We present the first large-scale evaluation of how, when, and why focal points emerge in LLMs, comparing their behaviour with humans across cooperative and competitive games, including realistic search and rescue scenarios, demonstrating when focal points enable effective coordination. Across more than 20 open- and closed-source models, we find that LLMs exhibit a remarkable ability to coordinate without communication, often matching or outperforming humans. However, the same models consistently fail in tasks requiring numerical common sense or culturally nuanced notions of salience. We additionally evaluate simple learning-free strategies that substantially improve coordination both among LLMs and between humans and LLMs. Our results reveal striking coordination capabilities, as well as social limitations in modern LLMs, and offer new insight into the latent notions of salience encoded within them. Our findings caution against assuming that LLMs share humans' cultural and perceptual substrate when deployed in coordination settings.

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16.
Nature (Science) 2026-06-17

Confined migration induces non-lethal DNA damage in developing neurons

Authors:
Zhejing Zhang↗

Migratory cells tend to have soft nuclei that deform and penetrate narrow spaces1,2. Extensive nuclear deformation during migration can cause nuclear-envelope rupture and DNA damage in cancer cells, which may contribute to malignant transformation during tumour progression3–6. However, the importance of DNA damage in physiological migration is less well understood. Here we demonstrate that the migration of neurons in developing cerebral and cerebellar cortices is accompanied by massive DNA double-stranded breaks (DSBs) due to mechanostress during passage through narrow interstitial spaces. In contrast to many other migratory cells, these DSBs occur without detectable nuclear envelope rupture. Confined migration increases topoisomerase-IIβ covalently bound DSBs, and these lesions are repaired through non-homologous end-joining during brain development without causing cell death. Genome sequencing revealed that DSBs tend to occur at transcriptionally inactive regions. The deletion of ligase IV at the onset of neuronal migration leads to persistent DSB accumulation in cerebellar neurons with moderate transcriptional changes in genes related to synaptic function, neuronal development and stress and immune responses. The mutant mouse develops mild motor deficits in later life, suggesting that the DNA damage generated during normal brain development poses a potential disease risk if left unrepaired. The migration of neurons in developing cerebral and cerebellar cortices is accompanied by massive DNA double-strand breaks due to mechanostress during passage through narrow interstitial spaces.

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

Retrofitters, pragmatists and activists: Public interest litigation for accountable automated decision-making

Authors:
Henry Fraser↗Zahra Stardust↗

arXiv:2511.03211v4 Announce Type: replace-cross Abstract: This paper examines the role of public interest litigation in promoting accountability for AI and automated decision-making (ADM) in Australia. Since ADM regulation faces political and geopolitical headwinds, effective governance will have to rely on the enforcement of existing laws. Drawing on interviews with Australian public interest litigators, technology policy activists, and technology law scholars, the paper positions public interest litigation as part of a larger ecosystem for transparency, accountability and justice with respect to ADM. The paper explores the tactics and strategies of what one participant described as 'retrofitting' old laws to ADM. These go beyond creative legal argumentation, to encompass practices of community-building, collaboration on theories of change, canny selection of clients and causes of action, and the alignment of the interests of stakeholders in litigation. Naturally, the paper also contends with the limits of these strategies, and of the Australian legal system. Where limits are, however, capable of being overcome, the paper presents findings on urgent needs: the enabling institutional arrangements without which effective litigation and accountability will falter. The paper is relevant to law and technology scholars; individuals and groups harmed by ADM; public interest litigators and technology lawyers; civil society and advocacy organisations; and policymakers.

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

3D-PLOT-LLM: Part-Level Object Tokens for 3D Large Language Models

Authors:
Jintang Xue↗Xinyu Wang↗Yixing Wu↗Jingwen Chen↗C. -C. Jay Kuo↗

3D multimodal large language models (3D MLLMs) describe a 3D object as a whole but cannot address, name, or reason about its parts. Prior part-aware attempts add segmentation decoders, heavier 3D encoders, or bounding-box grammars at substantial parameter cost. We take a fundamentally different path: we reorganize the input token stream so that parts become directly addressable through the LLM's own vocabulary. Our model, 3D-PLOT-LLM, partitions the frozen point encoder's patches into K locally coherent regions and inserts, before each region's patch tokens, a learnable per-region marker and a reserved vocabulary token ; a Marker-Space Refinement (MSR) module then conditions each marker on its region's spatial statistics and adjacency neighbors. The model thus cites parts in its output and follows prompts that refer to parts by token, a capability absent from prior object-level 3D MLLMs. To probe this interface, we construct PartVerse-QA, a vocabulary-level part-QA benchmark adapted from PartVerse mesh annotations (77K training pairs and 588 held-out queries on disjoint object splits), on which 3D-PLOT-LLM reaches caption-to-slots Jaccard 0.459 and Exact-match 13.78%, with a slot-to-caption GPT-4o judge of 44.68. On the 3DCoMPaT-GrIn part-aware grounded description benchmark, 3D-PLOT-LLM outperforms PointLLM, Kestrel, PARIS3D, and SegPoint on every text-output metric, and ShapeLLM on 3 of 4, with up to +3.03 GPT-4o judge over PointLLM. On Objaverse whole-object captioning, adding PartVerse-QA at Stage 2 yields +0.65 SBERT and +1.85 GPT-4o over PointLLM, and tops PointLLM-PiSA on 4 of 5 traditional metrics (SBERT, SimCSE, BLEU-1, METEOR) despite targeting a different (part-grounded) objective. All with under 1M new trainable parameters on a frozen point encoder, an order of magnitude below prior part-aware 3D MLLMs, and no segmentation decoder or bounding-box head.

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

ShearFuse-UNet: Hadamard, DCT, and Shearlet Transform Fusion for Next-Day Wildfire Spread Prediction

Authors:
Ene Meco↗Yingyi Luo↗Emadeldeen Hamdan↗Adam Watts↗Ahmet Enis Cetin↗

We propose ShearFuse-UNet, a lightweight and computationally efficient deep learning model for next-day wildfire spread prediction from multi-modal satellite data. The model integrates three complementary transform-domain branches inside each encoder block of a U-Net backbone: a 2D Fast Walsh-Hadamard Transform (WHT) branch, a 2D Discrete Cosine Transform (DCT) branch, and a cone-adapted digital Shearlet residual branch. The WHT and DCT branches establish orthogonal latent spaces with learnable spectral scaling and fixed soft-thresholding, while the Shearlet branch provides anisotropic, multi-directional feature decomposition that explicitly encodes the elongated edge structures characteristic of fire fronts. A learned SpectralFusion gate adaptively combines the WHT and DCT responses, and the Shearlet reconstruction is added as a residual. This three-branch design bears a loose structural analogy to transformer self-attention: the WHT and DCT branches provide complementary spectral representations that are adaptively fused, while the Shearlet branch contributes directional content through a residual pathway. Unlike self-attention, the proposed design relies on fixed mathematical transforms rather than learned projection operators, reducing parameter count and computational cost. Evaluated on the WildfireSpreadTS dataset, ShearFuse-UNet achieves an F1 score of 0.596 with only 267k parameters, outperforming a ResNet18-based U-Net (14M parameters, F1 = 0.589) and demonstrating a highly favorable accuracy-efficiency trade-off. Results on the Google Next-Day Wildfire Spread dataset further validate these findings across a different benchmark.

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20.
arXiv (math.PR) 2026-06-15

Real-order moments, tail representations, and logarithmic means

Authors:
Roberto Vila↗Eduardo Nakano↗

arXiv:2606.14019v1 Announce Type: cross Abstract: This paper develops a unified framework for the study of real-order moments of arbitrary random variables. General integral representations are established in terms of cumulative distribution functions and survival functions, covering continuous, discrete, and mixed distributions supported on the whole real line. These formulas extend the classical tail-integral identities for nonnegative random variables and provide a common treatment of positive, fractional, and negative moments. For discrete distributions, explicit series representations are derived in terms of cumulative probabilities, yielding simple criteria for the existence of moments. Applications are presented for the zeta and Skellam distributions, illustrating how tail behavior determines moment finiteness and how moments can be represented geometrically through cumulative distribution functions. In addition, a representation for logarithmic moments is obtained, linking logarithmic means, Laplace transforms, and the classical Frullani identity. The results provide a unified perspective on moment representations and establish useful connections between tail probabilities, distribution functions, Laplace transforms, and moment existence.

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21.
arXiv (CS.AI) 2026-06-16

Attention is Just Another Name for Coupling?: A Fast-Slow ODE Perspective on Hierarchical Pretraining

Authors:
Zhengyuan Gao↗

arXiv:2606.16730v1 Announce Type: cross Abstract: Causal self-attention is a coupling mechanism: each token's hidden state is updated by a learned mixture of preceding tokens at the same timescale. This paper asks whether a second, temporally slower coupling-a slow sub-system operating on a temporally-downsampled view of the sequence and fed back into the fast path through a zero-initialised gate-complements it. The question is framed in the language of singularly perturbed ordinary differential equations (ODEs), where the fast variable $x$ evolves at the token rate, the slow variable $y$ evolves at one update per $P$ tokens, and the timescale ratio $\varepsilon = 1/P$ is enforced structurally by causal block-mean pooling. The paper instantiates the fast-slow ODE formalism as a concrete neural network: a fast path of standard causal attention over $T$ tokens, a slow path of full attention over $T/P$ pooled tokens ($P^2 \times$ cheaper per layer), and a zero-initialised additive gate. In addition, under a linear-generator assumption on the fast dynamics, we prove that the equilibrium manifold $x = \phi(y)$ is exactly the master-equation (ME) stationary distribution $p_{\mathrm{st}}(y)$; in that regime a learned MLP $\phi_\theta(y)$ is a variational approximation of it (the trained block is not a generator, so this identity is the structured limit, not a claim about the network as trained). Empirically, at $500$k tokens the coupling is neutral – the gate stays closed and the coupled and frozen ablations are within run-to-run noise – at a wall-clock cost comparable to a dense baseline. The contribution is the precise, gap-marked mapping itself, not a performance gain.

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22.
arXiv (quant-ph) 2026-06-12

Exceptional Points as Manifestations of Analyticity Breakdown in the 't Hooft Model

Authors:
Kejun Liu↗

arXiv:2606.10141v2 Announce Type: replace-cross Abstract: We use the exactly-solvable t Hooft model of 1+1D large-N_c QCD as a rigorous laboratory for the breakdown of analyticity of a causal response function, the meson two-point function. A PT-symmetric deformation i gamma(x-1/2) of the light-cone meson operator, the analogue of an imaginary chemical potential, drives the lowest two mesons to an exceptional point (EP) at gamma_c. Recasting the resolvent as a Jacobi continued fraction yields gamma_c in closed form: 2 pi g^2 N_c at the two-pole level, converging to 7.966 g^2 N_c by depth five – an analytic, not numerical, threshold. The square-root exponent nu=1/2 is fixed by the 2x2 Jordan form and confirmed by finite-size scaling to N=1999. The breakdown has an unambiguous time-domain signature: the propagator norm is bounded for gamma < gamma_c, grows linearly at gamma_c (the Jordan secular law), and exponentially beyond – observable, since the deformed operator is a non-Hermitian Wannier-Stark ladder, in photonic and topolectrical analogues. The threshold is locked to confinement, gamma_c propto g^2 N_c, and recurs as a uniform EP cascade; a second, non-reciprocal deformation yields an exactly-exponential non-Hermitian skin effect. This is the first analytically-controlled instance of exceptional-point analyticity breakdown in a confining gauge theory.

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23.
medRxiv (Medicine) 2026-06-22

ECG-Guided Pre-Screening of Family Members for Hypertrophic Cardiomyopathy

Authors:
Lootah↗Min↗Fatah↗Hamilton↗R. M↗Mital↗

Background: Current clinical guidelines recommend serial ECG and echocardiographic surveillance for first-degree relatives of probands with Hypertrophic Cardiomyopathy (HCM). Objectives: To evaluate the accuracy and validity of ECG alone as a pre-screening tool for the diagnosis of HCM and to develop a random forest (RF) model for HCM phenotype prediction. Method: Pediatric relatives of primary HCM probands attending the cardiomyopathy screening program at The Hospital for Sick Children were included from 1993 to 2025. Subjects were followed until the last follow-up, censored at phenotype conversion. ECGs were classified as normal or abnormal based on predefined parameters. Associations between binary ECG variables and HCM phenotype were assessed using Phi ({varphi}) coefficient. A Random Forest classifier was developed using significant ECG variables (70:30 training: test split) and evaluated using precision, recall, specificity, negative predictive value, F1 score and AUROC. Feature importance was assessed using SHAP analysis. Variables with an impact of >5% were included in a simplified model, which was evaluated by repeating performance metrics and externally validated in a healthy cohort. Results: 350 screened relatives (44% female, mean follow-up 6.8 +- 4.8 years) were included. At baseline, 13% (46350) were phenotype-positive for HCM. 9 subjects converted during the surveillance. Thirteen ECG variables were significantly associated with phenotype-positive HCM and were included in the full random forest model. Four variables had >5% impact (Left ventricular hypertrophy, right ventricular hypertrophy, T-wave inversion and ST-segment depression) and were included in a simplified model, which maintained high specificity (93% vs 97%), negative predictive value (97% vs 93%) and AUROC (90% vs 96%). The simplified model classified 83% subjects as phenotype-negative, with eight being false-negative, all of whom developed an abnormal ECG in a mean of 1 year, and none had an interim adverse cardiac event. The simplified model was evaluated in an independent healthy cohort of 153 school-age subjects and correctly identified 98% as phenotype-negative with 100% NPV. Conclusion: ECG abnormalities were strongly associated with phenotype-positive status. A simplified ECG-based random forest model using four ECG variables demonstrated high specificity and negative predictive value for identifying phenotype-negative subjects. If prospectively validated, this could reduce the need for concurrent echocardiographic screening by up to 83% per encounter, lowering screening burden and cost.

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24.
arXiv (quant-ph) 2026-06-24

Logical qubits with erasure conversion using metastable neutral atoms

Authors:
Bichen Zhang↗Genyue Liu↗Guillaume Bornet↗Sebastian P. Horvath↗Pai Peng↗Shuo Ma↗Shilin Huang↗Shruti Puri↗Jeff D. Thompson↗

arXiv:2506.13724v2 Announce Type: replace Abstract: Implementing large-scale quantum algorithms with practical advantage will require fault-tolerance achieved through quantum error correction, but the associated overhead is prohibitive. This overhead can be reduced by engineering physical qubits with fewer errors, and by shaping the residual errors to be more easily correctable. In this work, we demonstrate quantum error correcting codes and logical qubit circuits in a metastable ytterbium-171 nuclear spin qubit with a noise bias towards erasure errors. These errors can be located separately from any syndrome information diagnosing the error, and we demonstrate adaptive circuit execution based on erasure information. We show that dephasing errors on the qubit during coherent transport can be strongly suppressed, and implement entangling gates that maintain a high fidelity in the presence of gate beam inhomogeneity or pointing errors. Furthermore, we demonstrate logical qubit encoding in the [[4, 2, 2]] code, with error correction during decoding based on mid-circuit erasure measurements despite the fact that the code is too small to correct any Pauli errors. Finally, we demonstrate logical qubit teleportation between multiple code blocks with conditionally selected ancillas based on mid-circuit erasure checks, a key part of leakage-robust error correction schemes using neutral atoms.

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25.
arXiv (math.PR) 2026-06-24

Exact Evaluation of Probabilistic Programs with Cylindrical Algebraic Decomposition

Authors:
Fredrik Dahlqvist↗Mohamed Hamza Bandukara↗Niki Omidvari↗

arXiv:2606.24514v1 Announce Type: cross Abstract: We present a method for computing the exact output distribution of small programs with random inputs. Specifically, we are interested in inline programs manipulating sensor data such as \eg GPS or inertial measurement sensors whose inputs have a known or well-modelled distribution. These programs typically only include relatively few variables, arithmetic operations, square roots and if-else statements. This small syntax allows us to recast the problem of computing the exact output distribution as a cylindrical algebraic decomposition problem followed by symbolic and/or numerical integration. We present this method in detail and show with two prototypes that it can successfully be applied to benchmarks from the literature on floating-point arithmetic and small programs from open-source sensor libraries.

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