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01.
arXiv (CS.CL) 2026-06-18

PragReST: Self-Reinforcing Counterfactual Reasoning for Pragmatic Language Understanding

Natural language understanding often depends on meanings that are implied rather than explicitly stated, requiring pragmatic reasoning. Despite strong performance on math and logical reasoning, large language models (LLMs) still struggle with making pragmatic inferences, often choosing literal interpretations. To improve LLM pragmatic reasoning, we introduce PragReST, a self-supervised framework that constructs pragmatic QA data, generates counterfactual reasoning traces, and trains models to internalize them through supervised fine-tuning and reinforcement learning, without human-labeled training data or distillation from a stronger teacher. Across four pragmatic benchmarks (PragMega, Ludwig, MetoQA, and AltPrag), PragReST improves over backbone models, task-specific pragmatic tuning baselines, and non-counterfactual variants of the same pipeline. On accuracy-based benchmarks, PragReST improves over the instruct backbone by 5.37 and 5.50% (absolute) for Qwen3-8B and Qwen3-14B, respectively. Our error analysis and ablations underscore the importance of counterfactual reasoning: PragReST primarily reduces errors caused by failures to contrast observed utterances with plausible alternatives, and removing counterfactual reasoning substantially reduces performance. Moreover, our training preserves out-of-domain performance on general-knowledge and mathematical reasoning benchmarks.

02.
arXiv (quant-ph) 2026-06-19

Electrical Noise Produced by Micron-Sized Particles above a Surface Paul Trap

arXiv:2606.19585v1 Announce Type: new Abstract: Electric field noise produced by the surface of ion trap electrodes reduces the fidelity of quantum computing operations. Despite decades of investigation its microscopic origins remain unclear. Here, we measure electric field noise at trapping locations along the symmetry axis of a linear surface Paul trap. We find that noise levels vary by three orders-of-magnitude in one 600$\,\mu$m section of the trap. Optical and scanning electron microscope images show micron-sized particles close to the trapping locations with the highest noise levels. We find that modeling the particles as a lossy dielectric with a effective loss tangent $\tan\theta=0.33(0.06)$ describes the magnitude of the noise, as well as its spatial and frequency dependence. Our observations may explain the large variation of reported noise levels in literature.

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

Multi-Modal Agents for Power Distribution Defect Detection: An Evaluation of Foundation Models

Authors:

arXiv:2606.12969v1 Announce Type: new Abstract: The power distribution network is critical to reliable electricity delivery, yet traditional inspection methods face limitations in semantic understanding, generalization, and closed-loop automation. To address these challenges, this paper proposes a Multi-Modal Agent framework specifically for power distribution defect detection. Central to this study is the systematic evaluation of multimodal foundation models as unified cognitive engines. We rigorously assess their integrated performance across three critical capabilities: (1) Perception, where the model must accurately identify equipment and generate expert-level descriptions of defects; (2) Reasoning, where the model interprets visual findings to diagnose causes, assess severity, and plan maintenance strategies based on domain knowledge; and (3) Tool Usage, where the model acts as an autonomous operator to execute actions – such as querying knowledge bases or generating work orders – to achieve closed-loop maintenance. To support this evaluation, a domain-specific evaluation dataset and a comprehensive benchmark are developed. Experimental results demonstrate the strengths and limitations of current foundation models in these three dimensions, providing empirical evidence for deploying autonomous agents in high-stakes industrial environments.

04.
arXiv (CS.LG) 2026-06-16

TreeGRNG: Binary Tree Gaussian Random Number Generator for Efficient Probabilistic AI Hardware

arXiv:2606.16599v1 Announce Type: cross Abstract: Bayesian Neural Networks (BNNs) offer opportunities for greatly enhancing the trustworthiness of conventional neural networks by monitoring the uncertainties in decision-making. A significant drawback for BNN inference at the extreme edge, however, is the imperative need to incorporate Gaussian Random Number Generators (GRNG) within each neuron. State-of-the-art GRNG algorithms heavily depend on multiple arithmetic operations and the use of extensive look-up tables, posing significant implementation challenges for ultra-low power hardware implementations. To overcome this, this paper presents an innovative binary tree random number generator (TreeGRNG) allowing the use of ultra-low-cost constant comparators instead of arithmetic units. We further enhance the TreeGRNG proposal with a set of hardware-aware optimizations exploiting the Gaussian properties. The optimized TreeGRNG surpasses the State-of-the-Art (SoTA) in terms of distribution accuracy while achieving a 3.7$\times$ reduction in energy per sample and boosting the throughput per unit area by 5.8$\times$. Moreover, our TreeGRNG proposal possesses a distinct advantage over the current SoTA in terms of flexibility, as it easily enables designers to adjust the shape of the sampled probability distribution, extending beyond the capabilities of traditional GRNGs, opening the horizon towards future probabilistic AI designs. The TreeGRNG design is available open-source in the link

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

Vocabulary Dropout for Curriculum Diversity in LLM Co-Evolution

Co-evolutionary self-play, where one language model generates problems and another solves them, promises autonomous curriculum learning without human supervision. In practice, the proposer quickly converges to a narrow distribution of problems that satisfy the reward function. This diversity collapse renders the curriculum uninformative for the solver, stalling the co-evolutionary loop. We introduce vocabulary dropout, a random mask applied to the proposer's output logits during both policy training and curriculum generation, as a lightweight mechanism to sustain diversity. The mask is hard and non-stationary, preventing the proposer from locking into fixed token sequences. Training Qwen3-4B and Qwen3-8B on mathematical reasoning via R-Zero, we find that vocabulary dropout sustains proposer diversity across lexical, semantic, and functional metrics throughout training. It also yields solver improvements averaging +4.4 points at 8B, with the largest gains on competition-level benchmarks. Our findings suggest that explicit action-space constraints, analogous to the structural role that game rules play in classical self-play, can help sustain productive co-evolution in language. Vocabulary dropout is one simple instantiation of this principle.

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

The Professor: Multi-Teacher Unsupervised Prompt Distillation for Vision-Language Models

arXiv:2606.23897v1 Announce Type: cross Abstract: Prompt distillation compresses large vision-language models (VLMs) such as CLIP into lightweight student models by matching teacher predictions on unlabeled domain images. PromptKD (CVPR 2024) established this paradigm with a single PromptSRC-finetuned ViT-L/14 teacher and a ViT-B/16 student. We propose TheProfessor, a multi-teacher extension that distills from a fixed two-teacher ensemble: a domain-finetuned PromptSRC ViT-L/14 teacher and a zero-shot EVA-CLIP-L/14 teacher whose logits are pre-computed per dataset. We evaluate single-teacher PromptKD, equal-probability ensembling, and confidence-weighted ensembling on four base-to-novel datasets: Caltech-101, DTD, UCF101, and EuroSAT. In a 12-run single-seed sweep, confidence-weighted ensembling improves average HM from 87.52 to 89.28 (+1.77 points), while equal averaging improves average HM to 88.88 (+1.37 points). Gains are dataset dependent: they are negligible on Caltech-101 (+0.16 HM for confidence weighting), modest on UCF101 (+0.62), and largest on domain-shifted EuroSAT (+5.78). These results update our earlier Caltech-only analysis and show that multi-teacher prompt distillation is most useful when the second teacher contributes complementary supervision under domain shift.

08.
arXiv (CS.AI) 2026-06-18

Scaling Learning-based AEB with Massive Unlabeled Data

arXiv:2606.18864v1 Announce Type: cross Abstract: This paper studies how to scale learning-based automatic emergency braking (AEB) with massive unlabeled fleet data under production constraints. Our approach is based on meta-feedback semi-supervised learning (MF-SSL), where a teacher generates pseudo labels for unlabeled driving data and is updated using a small labeled anchor set as safety-critical feedback. In production, anchor ambiguity and labeled-unlabeled mismatch can amplify systematic pseudo-label errors, leading to spurious triggers. We propose a stabilized MF-SSL framework with (i) Noise-Aware Decoupling, which removes ambiguity-prone anchors from the teacher's supervised update path, and (ii) kinematics-gated pseudo-labeling with a teacher conflict penalty to suppress mismatch-induced risk hallucinations on unlabeled data while maintaining broad coverage. Extensive experiments show consistent gains as unlabeled data scale from 1M to 1B windows, improving safety while keeping comfort stable. The 1B-trained student model is deployed to hundreds of thousands of vehicles and validated over \$10^9$ km of driving, achieving a positive-to-false activation ratio exceeding 100:1 and a 35% improvement in accident-free driving mileage over a production rule-only baseline.

09.
arXiv (CS.CV) 2026-06-24

Towards Fast and Effective Long Video Understanding of Multimodal Large Language Models via Adaptive Quasi-Gaussian Sampling

Long video understanding remains a daunting challenge for Multimodal Large Language Models (MLLMs) due to the excessive computation and memory footprint. Thus, keyframe selection is often adopted to mitigate this shortcoming, which however still suffers from low flexibility and high noise due to its hard sampling principle. In this paper, we define video frame selection as a problem of Quasi-Gaussian Sampling, and propose an adaptive and training-free approach termed AdaQ. Inspired by the $3$-$\sigma$ rule of Gaussian distribution, the objective of AdaQ is to achieve the optimal $3$-$\sigma$ interval for different examples, i.e., a smaller $3$-$\sigma$ interval for the local query and a larger one for the global query, thereby facilitating robust and adaptive frame sampling. To validate AdaQ, we apply it to four MLLMs with three embedding models. The extensive experimental results not only show its obvious performance gains over the default MLLMs and the SOTA keyframe selection methods, e.g., helping Qwen3-VL-8B outperform GPT4o by 15.8\% on average by using only 64 frames, but also confirm its superior robustness and high efficiency for long-video understanding, e.g., only 1 hyper-parameter needs to be set. Our code project is given at \href{https://github.com/Zkayovo-xmu/AdaQ}{https://github.com/Zkayovo-xmu/AdaQ}.

10.
arXiv (math.PR) 2026-06-16

Risk-averse mean field games: exploitability and non-asymptotic analysis

arXiv:2301.06930v5 Announce Type: replace-cross Abstract: In this paper, we use mean field games (MFGs) to investigate approximations of $N$-player games ($N$pGs) with uniformly symmetrically continuous heterogeneous closed-loop actions. To incorporate agents' risk aversion (beyond the classical expected utility of total costs), we use an abstract evaluation functional for their performance criteria. Centered around the notion of exploitability, we conduct non-asymptotic analysis on the approximation capability of MFGs from the perspective of state-action distributions without requiring the uniqueness of equilibria. Under suitable assumptions, we first show that scenarios in the $N$pGs with large $N$ and small average exploitabilities can be well approximated by approximate solutions of MFGs with relatively small exploitabilities. We then show that $\delta$-mean field equilibria can be used to construct $\varepsilon$-equilibria in $N$pGs. Furthermore, in this general setting, we prove the existence of mean field equilibria. This proof reveals a possible avenue for incorporating penalization for randomized action into MFGs.

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

FORT-Searcher: Synthesizing Shortcut-Resistant Search Tasks for Training Deep Search Agents

Training deep search agents requires verifiable questions whose answers remain unavailable until sufficient evidence has been acquired through search. Existing synthesis methods often increase apparent difficulty by enriching graph structures, but structural complexity alone does not guarantee realized search difficulty: the intended search process can collapse through a cheaper identifying route. We formalize this gap with a shortcut-aware difficulty framework and identify four actionable shortcut risks: evidence co-coverage, single-clue selectivity, exposed constants, and prior-knowledge binding. To diagnose their realized effects, we use trajectory signatures including solving cost, answer hit time, and prior-shortcut rate. Guided by this framework, we introduce FORT, a Framework of Shortcut-Resistant Training-Data Synthesis. FORT constructs shortcut-resistant training data by controlling shortcut risks across entity selection, evidence graph construction, question formulation, and adversarial refinement. Experiments show that FORT induces longer pre-answer search and fewer shortcut patterns than existing open-source deep search datasets. Using the resulting trajectories, we train FORT-Searcher with supervised fine-tuning (SFT) only, and it achieves the best overall performance among comparable-size open-source search agents on challenging deep search benchmarks. Relevant resources will be made available at https://github.com/RUCAIBox/FORT-Searcher.

12.
Nature (Science) 2026-06-10

A prognostic human brain network for diffuse midline glioma

Authors:

Diffuse midline gliomas (DMGs) are near-universally lethal tumours of the childhood central nervous system1,2. In animal models, DMGs form brain-wide integrated networks through neuron-to-glioma synapses3–6 and glioma-to-glioma gap junctional coupling3. This extensive connectivity robustly promotes the growth and invasion of DMG3–9 and other glial malignancies10–12 through paracrine mechanisms and direct neuron-to-glioma synapses. However, the organization and clinical implications of these connections in the living human brain remain to be elucidated. Here, we develop tumour network mapping to compute the brain-wide connectivity profile of DMG, defining a conserved brain network across pontine and thalamic DMG associated with patient short-term survival (DMG network). Tumour functional connectivity with the DMG network was independently predictive of patient overall survival across two external validation cohorts. Tumour growth mapped to DMG network-specific trajectories and peak in-network neurometabolic changes across development spatiotemporally aligned with the peak age incidence of DMG. Analyses of single-nucleus RNA sequencing data confirmed diverse synaptic gene enrichment in high-connectivity DMG. Strikingly, incidental surgical resection of high-connectivity thalamic DMG tissue conferred a significant survival advantage. Collectively, these data define a conserved and prognostically important brain network in children with DMG, consistent with the hypothesis that DMGs exploit otherwise healthy brain circuits to promote tumour growth. Tumour network mapping of diffuse midline glioma (DMG) defines a conserved and prognostically important brain network in children with DMG, consistent with the hypothesis that DMGs exploit otherwise healthy brain circuits to promote tumour growth.

13.
arXiv (CS.LG) 2026-06-16

When to use what Schatten-$p$ norm in deep learning?

arXiv:2606.15268v1 Announce Type: new Abstract: Schatten-$\infty$ based optimizers such as Muon have shown promising empirical performance, but there remains seemingly conflicting observations regarding whether they are beneficial. We resolve this conflict by showing that the conclusion is regime dependent. Even when the objective is smooth in the Schatten-$\infty$ geometry, smaller Schatten-$p$ geometries can be optimal, specifically in the low-dimensional regime, which we show includes Chinchilla scaling. This conclusion follows from a new noise-robust acceleration result for the SODA framework for $p>2$. The same analysis explains why Muon-like methods do not require warmup, why they naturally favor large batches, and yields a batch size scaling rule for arbitrary $p$.

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

NeuroSymbolic AI for Legal AI-TRISM: Trustworthy, Reliable, Interpretable, Safe Models

arXiv:2606.15646v1 Announce Type: new Abstract: Large Language Models (LLMs) have transformed natural language processing, but their lack of interpretable reasoning and tendency to hallucinate pose significant challenges for legal applications. While LLMs show promise for legal text analysis and generation, they struggle with accurate citation attribution and precedent verification. For example, in legal contexts, a single incorrect precedent can jeopardize a case. Current approaches to improve LLM reliability in legal domains suffer from two key limitations: inadequate integration of structured legal knowledge during training or fine-tuning, and insufficient verification mechanisms for generated legal content. To address these challenges, we propose the TRISM (Trustworthy, Reliable, Interpretable, Safe Models) framework, which integrates NeuroSymbolic AI principles with LLMs to leverage both neural learning capabilities and symbolic reasoning over structured legal knowledge. The TRISM approach addresses the above limitations while maintaining interpretable decision pathways. Our framework formalizes the extraction of symbolic knowledge from legal textual documents and incorporates Retrieval-Augmented Generation (RAG) as a core component for grounding LLM outputs in verified legal sources. In this position paper, we make the following contributions: (1) An analysis of the limitations of AI in law; (2) Introduce RASOR RAG which creates foundations for neurosymbolic RAG by generating explicit interpretable rationales that could be formalized into symbolic representations; (3) A formalized methodology for creating symbolic legal knowledge bases that support both interpretable reasoning and output verification in LLMs; and (4) The TRISM framework for integrating symbolic legal knowledge with LLMs.

15.
arXiv (CS.LG) 2026-06-16

LoComposition: Terrain-Adaptive Energy-Efficient Quadruped Locomotion without Gait Priors

arXiv:2606.15896v1 Announce Type: cross Abstract: Learning-based quadrupedal locomotion typically relies on complex reward formulations that entangle task specification, operational limits, gait preference, and terrain adaptation within a single optimization objective. We instead treat these functions through distinct mechanisms: rewards for task specification, constraints for operational limits, energy minimization for gait preference, and exteroceptive perception for adapting energy use to terrain difficulty. We show that these components jointly enable efficient, terrain-adaptive locomotion, and that removing each component exposes a distinct failure mode. Our formulation removes explicit gait priors (including air-time, contact-count, and foot-clearance targets) in favor of emergent behavior. Compared to a conventional complex-reward baseline, our formulation achieves comparable terrain traversal while reducing cost of transport by 56% and operational-limit violations by 96%. The resulting policies transfer zero-shot to a physical Unitree Go2 using LiDAR-based elevation mapping. Project website with videos: https://tinyurl.com/locomposition.

16.
medRxiv (Medicine) 2026-06-24

Digital exclusion and mental health in UK Armed Forces veterans: findings from the Veterans Digital Needs Study

Background: Public services are increasingly delivered through digital platforms. Although digital health may improve access and scalability, they may also widen inequalities for people who lack reliable access, confidence, skills, affordability or trust. Objective: This study examined the prevalence of self-reported digital exclusion among UK veterans and assessed its association with depression, anxiety and loneliness. Methods: A cross-sectional online survey was conducted between July 2025 and March 2026. Participants were UK Armed Forces veterans and resident in the UK. The survey collected sociodemographic, military service, digital access and health data. Self-reported digital exclusion was defined as reporting feeling excluded or disadvantaged due to lack of digital access or skills. Probable depression, anxiety and loneliness were assessed using the PHQ-2, GAD-2 and three-item UCLA Loneliness Scale, respectively. Associations between digital exclusion and each outcome were examined using adjusted multivariable logistic regression. Results: Of 1,911 responses received, 1,607 were included after data quality exclusions. Among participants with valid responses to the primary digital exclusion item, 553 (41.7%) reported digital exclusion. Digital exclusion was more common among females, younger veterans and those with lower household income. Probable depression, anxiety and loneliness were more prevalent among digitally excluded participants than among non-excluded participants. In adjusted models, self-reported digital exclusion was associated with higher odds of probable depression (AOR 1.38; 95% CI 1.04 to 1.83; p=0.028), probable anxiety (AOR 1.63, 95% CI 1.23 to 2.16; p

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

BadWorld: Adversarial Attacks on World Models

Visual world models (VWMs) synthesize interactive, action-conditioned rollouts from a single context image. However, it remains an open question how robust these models are to adversarial perturbations. Standard adversarial attacks fail to assess this vulnerability because attackers lack ground-truth future videos and cannot predict subsequent user controls. We introduce BadWorld, a label-free adversarial framework tailored for autoregressive VWMs that systematically overcomes both constraints. First, to bypass the need for future supervision, we propose a self-supervised velocity attack that directly disrupts the early denoising dynamics of the model. Second, to ensure the attack generalizes across unpredictable user actions, we formulate a trajectory-adaptive bi-level optimization that actively mines hard control sequences to forge control-agnostic perturbations. Evaluated on representative VWMs with continuous and discrete controls, BadWorld exposes severe structural fragility. Visually indistinguishable adversarial images reliably trigger catastrophic degradation in future rollouts, leading to incomplete denoising, structural collapse, and control inconsistency. These findings reveal critical risks for deploying VWMs in safety-critical systems while highlighting a practical mechanism for privacy protection.

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

Data-Driven Dynamic Assortment in Online Platforms: Learning about Two Sides

arXiv:2606.11118v2 Announce Type: replace Abstract: We study a dynamic assortment problem on a two-sided service platform with incomplete information and heterogeneous customers in a discrete-time setting. In each period, a customer arrives seeking service, and the platform chooses an assortment of sellers to display. The customer then proposes a transaction to at most one seller in the assortment according to a multinomial logit choice model. After a fixed number of periods, sellers review the proposals they have received and each chooses at most one customer according to another multinomial logit choice model, after which the cycle repeats. A key challenge is that the platform does not know the choice-model parameters of either customers or sellers in advance. To our knowledge, this is the first study of a dynamic assortment problem in which both sides' choice parameters are unknown. We develop a data-driven algorithm that learns these parameters while optimizing the platform's objective over time. We evaluate performance using regret, which measures revenue loss relative to a clairvoyant benchmark that knows all parameters and customer arrivals in advance. We show that the algorithm's worst-case regret grows polylogarithmically over time, and we derive a matching lower bound, establishing its rate optimality.

19.
arXiv (CS.CL) 2026-06-17

Rift: A Conflict Signature for Deception in Language Models

Authors:

A model that lies while knowing the truth is the central case ELK cannot handle with behavioral evaluation alone. We ask whether such deception leaves an internal signature distinguishing it from honest error. Our key move is a control for wrongness: we contrast a sleeper agent (knows the truth, lies on trigger) against a naive liar (fine-tuned to emit the same wrong answers with no honest training). Both produce identical wrong outputs; any difference is about knowledge conflict, not incorrectness. We find deceptive forward passes carry a conflict signature - 2.1-2.3x higher residual rank than naive-liar passes on the same wrong answer - strong enough to identify which of two responses is the lie with 100% accuracy and no labels, across GPT-2 small/medium (three seeds) and three instruct models. Across Qwen2.5-1.5B/7B and Phi-3-mini, instructed deception raises residual rank on every tested fact (18/18, 40/40, 34/34); on Phi-3, lies separate perfectly from both honest answers and hallucinations (AUC 1.0, Wilcoxon p~6e-11). The signature survives strategic self-constructed deception (model invents its own lie, AUC 1.0), active concealment attempts (AUC 1.0), and length-controlled replication (20/20, AUC 1.0, p~1e-6). Using basis-free relative representations, a probe trained on one model family detects deception in two other families zero-shot (mean AUC 0.933), surviving simultaneous architecture and format change (AUC 0.821), and transfers across five languages (AUC 1.000, length-controlled). The signature is read-only: detectable but not injectable (0/8 both directions). Honest limitations and six negative experiments are documented in full.

20.
arXiv (CS.CV) 2026-06-17

OpenTie: Open-vocabulary Sequential Rebar Tying System

Robotic practices on the construction site emerge as an attention-attracting manner owing to their capability of tackling complex challenges, especially in the rebar-involved scenarios. Most of existing products and research are mainly focused on the collection of large amounts of data with model training demands. To fulfill this gap, we propose OpenTie, a 3D training-free rebar tying framework utilizing a RGB-to-point-cloud generation and an open-vocabulary rebar detection on the real-world test. We implement the OpenTie via a robotic arm with a binocular camera and guarantee a high accuracy by applying the prompt-based object detection method on the image filtered by our proposed post-processing procedure for the image-to-point-cloud generation framework. Our pipeline requires no training efforts and outperforms the training-based object detection, i.e., YOLO-based method, with the verification on the real-world sequential rebar tying test. The system is flexible for horizontal and vertical rebar tying tasks and holds the potential application to the real construction site with possibility of commercialization.

21.
arXiv (quant-ph) 2026-06-17

Universal Design and Physical Applications of Non-Uniform Cellular Automata on Translationally Invariant Lattices

arXiv:2605.13379v2 Announce Type: replace Abstract: Motivated by recent theoretical and experimental advances, hyperbolic lattices have emerged as a paradigmatic setting in which geometry becomes an active organizing principle of quantum systems. Their negative curvature, exponential volume growth, and non-Abelian translation symmetry make them fundamentally distinct from Euclidean lattices and give rise to rich geometry-dependent physics, but also hinder the direct application of well-established analytical and computational approaches originally developed for physical systems defined on Euclidean lattices. To establish a unified framework for geometry-dependent physics on Euclidean and hyperbolic lattices, we develop higher-order non-uniform cellular automata (NUCA) as a local-to-global construction for translationally invariant regular lattices. This construction derives geometry-dependent update rules through a lattice-deforming procedure that embeds hyperbolic lattices into a Euclidean square lattice, thereby encoding hyperbolic geometry while preserving physical locality. It thus provides a systematic route toward quantum and classical physics on hyperbolic lattices. We demonstrate the framework in three applications ranging from quantum many-body physics to non-equilibrium statistical physics. First, on the hyperbolic $\{5,4\}$ lattice, a linear NUCA generates exactly solvable subsystem symmetry-protected topological (SSPT) models and spontaneous subsystem symmetry-breaking models. Second, as a quantum generalization, we construct non-uniform Clifford quantum cellular automata (CQCA) for the hyperbolic cluster state. Third, we formulate a probabilistic NUCA for directed percolation (DP) on the hyperbolic lattice.

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

Manifold GCN: Diffusion-based Convolutional Neural Network for Manifold-valued Graphs

arXiv:2401.14381v3 Announce Type: replace Abstract: We propose two graph neural network layers for graphs with features in a Riemannian manifold. First, based on a manifold-valued graph diffusion equation, we construct a diffusion layer that can be applied to an arbitrary number of nodes and graph connectivity patterns. Second, we model a tangent multilayer perceptron by transferring ideas from the vector neuron framework to our general setting. Both layers are equivariant under node permutations and the feature manifold's isometries. These properties have led to a beneficial inductive bias in many deep-learning tasks. Furthermore, they enable novel, more flexible feature designs. Numerical examples on synthetic data and an Alzheimer's classification application on triangle meshes of the right hippocampus demonstrate the usefulness of our new layers: While they apply to a much broader class of problems, they outperform task-specific state-of-the-art networks.

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

Learning-Infused Formal Reasoning: From Contract Synthesis to Artifact Reuse and Formal Semantics

arXiv:2602.02881v2 Announce Type: replace-cross Abstract: This paper articulates a long-term research vision for formal methods at the intersection with artificial intelligence, outlining multiple conceptual and technical dimensions and reporting on our ongoing work toward realising this vision. It advances a forward-looking perspective on the next generation of formal methods based on the integration of automated contract synthesis, semantic artifact reuse, and refinement-based theory. We argue that future verification systems must builds towards individual correctness proofs toward a cumulative, knowledge-driven paradigm in which specifications, contracts, and proofs are continuously synthesised and transferred across systems. To support this shift, we outline a hybrid framework combining large language models with graph-based representations to enable scalable semantic matching and principled reuse of verification artifacts. Learning-based components provide semantic guidance across heterogeneous notations and abstraction levels, while symbolic matching ensures formal soundness. Grounded in compositional reasoning, this vision points toward verification ecosystems that evolve systematically, leveraging past verification efforts to accelerate future assurance.

25.
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.