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

Societal Alignment Frameworks Can Improve LLM Alignment

Recent progress in large language models (LLMs) has focused on producing responses that meet human expectations and align with shared values - a process coined alignment. However, aligning LLMs remains challenging due to the inherent disconnect between the complexity of human values and the narrow nature of the technological approaches designed to address them. Current alignment methods often lead to misspecified objectives, reflecting the broader issue of incomplete contracts, the impracticality of specifying a contract between a model developer, and the model that accounts for every scenario in LLM alignment. In this paper, we argue that improving LLM alignment requires incorporating insights from societal alignment frameworks, including social, economic, and contractual alignment, and discuss potential solutions drawn from these domains. Given the role of uncertainty within societal alignment frameworks, we then investigate how it manifests in LLM alignment. We end our discussion by offering an alternative view on LLM alignment, framing the underspecified nature of its objectives as an opportunity rather than perfect their specification. Beyond technical improvements in LLM alignment, we discuss the need for participatory alignment interface designs.

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

Infinitesimal Causality

arXiv:2606.24621v1 Announce Type: cross Abstract: This paper introduces a categorical account of infinitesimal causality in Frobenius Markov categories equipped with tangent-bundle semantics. IDC captures the infinitesimal layer in which interventions act as tangent deformations of copy/discard structure. Two distinct Frobenius structures interact: (1) the categorical Frobenius algebra on classical variables encoding copying, comparing, and discarding; and (2) the geometric Frobenius integrability condition, namely involutive closure of the intervention distribution, distinct from the algebraic Frobenius structure. Categorical causal sufficiency is defined as the compatibility of these two notions. A key observation is that, for structural causal models, infinitesimal causality is most naturally formulated in the slice of deterministic mechanisms over exogenous variables, with visible stochastic kernels obtained only after pushforward. Interventions are tangent vectors that deform the Frobenius copy/discard operations; their Lie brackets measure whether this deformation preserves classical information-flow structure. Pearl's do-calculus is used as a guiding example of intervention identities: ignoring irrelevant interventions corresponds to counit invariance, action/observation exchange to coproduct compatibility with pushforward, and independence to involutive bracket closure of the visible intervention distribution.

03.
arXiv (CS.CV) 2026-06-17

CIAN: Multi-Stage Framework for Event-Enriched Image Captioning via Retrieval-Augmented Generation

Event-enriched image captioning describes not only visible content but also the broader context of events, including timing, location, and participants, capabilities missing in most pixel-bound models. We propose the Contextual Image-Article Narrator (CIAN), a multi-stage framework that enriches captions with external narratives. CIAN retrieves relevant articles using SigLIP, summarizes them to guide a Narrative Generation stage with a LoRA-fine-tuned Qwen model, and applies N-Gram-based Refinement for fluency and coherence. On the OpenEvents-V1 benchmark, CIAN achieves high retrieval performance (mAP 0.979) and improves caption quality, increasing CIDEr from 0.030 to 0.094. These results highlight the effectiveness of retrieval-augmented reasoning combined with linguistic refinement for generating context-aware, human-like captions.

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

Agentra: A Supervisable Multi-Agent Framework for Enterprise Intrusion Response

arXiv:2606.18325v1 Announce Type: cross Abstract: Enterprise intrusion response still depends on static playbooks and analyst-driven triage, creating delay between alert generation and containment. We present Agentra, a supervisable multi-agent Intrusion Response System (IRS) framework that converts alerts from IDS, EDR, and XDR platforms into structured incident response plans grounded in MITRE ATT&CK, MITRE D3FEND, and NIST CSF 2.0. Agentra decomposes response reasoning across role-scoped agents, validates proposed plans through a bounded Planner–Validator review loop, screens retrieved threat intelligence through a Moderator security gateway, gates actions through an Action Catalog and risk score, and records decisions in an append-only audit log. We evaluate Agentra against a static OASIS CACAO v2.0 cyber-playbook baseline on a 120-event corpus drawn from ThreatHunter-Playbook, Splunk BOTSv3, and DARPA OpTC. The strongest configuration improves FP-aware IRS F1 from 0.61 to 0.84 and restores the projected harmful-action rate to the static baseline level of 0.0% after Planner-only configurations introduce unsafe overreaction. These results indicate that multi-agent response planning can improve ontology-grounded IRS coverage while preserving analyst approval and auditability.

05.
arXiv (quant-ph) 2026-06-11

Exact Entanglement Dynamics Beyond Nearest-Neighbor Dual-Unitary Floquet Systems

Authors:

arXiv:2606.11311v1 Announce Type: new Abstract: Exact results using dual-unitarity largely rely on nearest-neighbor structures, while finite-range interactions typically lead to complications. Going beyond the usual nearest-neighbor setting, we introduce an analytically tractable family of finite-range kicked Ising models that admit exact closed-form entanglement dynamics. The construction is based on a staggered structure in which dual-unitarity is present on sublattices that are then coupled to each other. The central observation is that these inter-sublattice couplings do not obstruct the dual-unitarity of the resulting model. For the minimal interaction range of $r= 2$, we derive exact expressions for all the $n-$Rényi entanglement entropies at all times and show that the result is the sum of the two coupled sublattice contributions. Our framework extends naturally to larger finite interaction ranges and to systems with heterogeneous local Hilbert spaces, without additional assumptions. It thus provides a controlled setting for studying exact entanglement growth beyond strictly nearest-neighbor dual-unitary models.

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

Monotonic Kolmogorov-Arnold Networks: A Theoretical and Empirical Study of Monotonicity as an Inductive Bias

arXiv:2606.17886v1 Announce Type: new Abstract: Monotonicity has been a long-running architectural inductive bias for neural networks, motivated by tabular, scientific, and economic settings where outputs are known to respond monotonically to certain inputs. Existing approaches are MLP- or flow-based and lack per-edge functional transparency; the only Kolmogorov–Arnold Network (KAN) variant with monotonicity, MonoKAN, enforces the constraint only on a restricted parameter subset and requires a projection-style training procedure. We close this gap with MKAN, a KAN with hard monotonicity guaranteed for all parameter values via exponential reparameterization of B-spline coefficients, positive edge weights, and a monotone base activation. Training reduces to standard unconstrained gradient descent. Our headline theoretical contribution is a representation-cost theorem: any $C^K, K >0$ feature extractor inducing a ball-shaped semantic-neighborhood partition admits a monotone realization of the equivalent neighborhood structure at $N' = N^* + k \le 2N^*$, where $k$ is the number of non-monotone coordinates of the original. The bound is architecture-agnostic and gives a principled sizing rule for monotone encoders. Empirically, MKAN is competitive with state-of-the-art monotone NNs on the SMM/ICML-2024 benchmark while being the only method that combines hard unconstrained monotonicity with KAN's per-edge functional transparency; the $2N^*$ prediction is validated in a self-supervised feature-size sweep on four real datasets, and on a controlled monotone-generative dataset MKAN recovers ground-truth factors with substantially higher Spearman alignment than KAN, MLP, and linear baselines.

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

Feature-Aligned Speech Watermarking for Robustness to Reconstruction Distortions

arXiv:2606.11828v1 Announce Type: cross Abstract: Audio watermarking aims to embed identifiable information into audio while remaining imperceptible. Existing methods adopt high-fidelity, low-energy designs to preserve perceptual quality, but the resulting watermarks lack robustness under suppression by speech reconstruction models. Improving robustness is challenging due to the inherent robustness-fidelity trade-off in existing designs, where increasing watermark energy improves robustness but reduces fidelity. To address this problem, we propose a feature-aligned watermarking method that aligns the watermark with the original speech feature distribution, allowing higher watermark energy to improve robustness while preserving imperceptibility. We use a pretrained speech codec to generate a pseudo-speech watermark and fuse it into the spectrogram of the input audio, with VAD loss and perceptual losses guiding embedding within voiced regions. Experiments show that our method maintains imperceptibility comparable to existing approaches while substantially improving robustness under both seen and unseen speech reconstruction models.

08.
medRxiv (Medicine) 2026-06-16

Care Delivery Gap framework: a proof-of-concept patient-reported measure of guideline-referenced care-process omissions in sickle cell disease

Abstract Background:Sickle cell disease (SCD) is concentrated in sub-Saharan Africa, where delivery of guideline-referenced care remains challenging. Current evaluation approaches rely largely on access indicators and clinical outcomes, which do not directly measure care delivery. We developed the Care Delivery Gap (CDG) framework, a patient-reported approach for identifying care-process omissions, and conducted a proof-of-concept study to assess feasibility and explore variation across income strata. Methods: We conducted a cross-sectional framework-development study involving a proof-of-concept sample of 52 individuals with SCD or caregivers recruited through clinics and moderated SCD communities across Africa, North America, and Europe between June 2025 and March 2026. The CDG framework assessed patient-reported omissions in specialist involvement, follow-up continuity, cardiovascular screening, and biochemical surveillance. Analyses were descriptive. Results: Substantial multi-domain care-process omissions were identified despite high reported healthcare engagement. Across geographic income strata, cardiovascular screening was reported by 4/35 (11%) LMIC versus 16/17 (94%) HIC participants, and regular follow-up within the preceding 12 months by 14/35 (40%) versus 16/17 (94%), respectively. High CDG scores, representing 1 omissions across three or four domains, occurred in 20/35 (57%) LMIC compared with 1/17 (6%) HIC participants. Similar disparities were observed across specialist review and vitamin B12 surveillance domains. Conclusion: A structured patient-reported framework identified multi-domain omissions in guideline-referenced SCD care, including among individuals reporting healthcare access. The divergence between access indicators and reported care delivery suggests that service contact alone may not reflect care quality. The framework provides a feasible foundation for future process-level quality measurement in high-burden settings.

09.
arXiv (CS.LG) 2026-06-12

Generalized Schrödinger Bridge on Graphs

arXiv:2602.04675v2 Announce Type: replace Abstract: Transportation on graphs is a fundamental challenge across many domains, where decisions must respect topological and operational constraints. Despite the need for actionable policies, existing graph-transport methods lack this expressivity. They rely on restrictive assumptions, fail to generalize across sparse topologies, and scale poorly with graph size and time horizon. To address these issues, we introduce Generalized Schrödinger Bridge on Graphs (GSBoG), a novel scalable data-driven framework for learning executable controlled continuous-time Markov chain (CTMC) policies on arbitrary graphs under state cost augmented dynamics. Notably, GSBoG learns trajectory-level policies, avoiding dense global solvers and thereby enhancing scalability. This is achieved via a likelihood optimization approach, satisfying the endpoint marginals, while simultaneously optimizing intermediate behavior under state-dependent running costs. Extensive experimentation on challenging real-world graph topologies shows that GSBoG reliably learns accurate, topology-respecting policies while optimizing application-specific intermediate state costs, highlighting its broad applicability and paving new avenues for cost-aware dynamical transport on general graphs.

10.
arXiv (CS.LG) 2026-06-15

Conformal calibration and look-elsewhere effect in anomaly detection for new-physics searches

arXiv:2606.13780v1 Announce Type: cross Abstract: Machine-learned anomaly detection is reshaping searches for new physics, but it has outrun the statistics used to interpret it. A raw anomaly score has no calibrated meaning, a model that scans many regions inflates the look-elsewhere effect, and the asymptotic significances the field relies on are blind to the background mismodelling that anomaly detectors are especially prone to. We propose a calibration layer, built on conformal prediction, that turns any anomaly score into a defensible significance with distribution-free, finite-sample guarantees. Conformal prediction converts scores into valid local p-values, weighted and Mondrian variants repair the sideband-to-signal-region exchangeability failures that resonant searches suffer, and a Gross-Vitells step carries the result through to a look-elsewhere-aware global significance. The layer does two things at once. It exposes miscalibration that the standard pipeline cannot see, and it corrects it without retraining the detector. On public LHC Olympics data, a classifier develops a substructure-mass correlation that makes sideband-calibrated background p-values anti-conservative. Taken at face value, this manufactures a $\sim 46\sigma$ excess from background sculpting alone, which the label-free weighted correction removes, restoring an honest null. When run as a blind wide-mass bump hunt, the standard asymptotic and unweighted procedures fabricate $\gtrsim10\sigma$ excesses and $\approx5\sigma$ excesses even in signal-free windows, while the conformal layer raises no false alarms and its global false-positive rate is verified on background-only pseudoexperiments. The result is an auditable, detector-agnostic path from an uncalibrated score to a trials-factor-aware significance, ready to be folded into experimental anomaly searches.

11.
arXiv (math.PR) 2026-06-12

The Lov\'{a}sz Local Lemma: Foundations and Applications

Authors:

arXiv:2603.07245v5 Announce Type: replace-cross Abstract: The Lov\'{a}sz Local Lemma (LLL) is a central tool in probabilistic combinatorics, providing a sufficient condition under which a finite collection of undesirable events with limited dependencies can be simultaneously avoided with positive probability. This paper offers a self-contained expository treatment of the lemma and its strengthened versions, emphasizing mathematical foundations, conceptual clarity, and applications. We begin with a pedagogically motivated proof of the LLL based entirely on unconditional probability inequalities. Particular attention is given to the symmetric form of the lemma and several subsequent strengthenings. The paper also discusses a variety of classical applications of both the symmetric and asymmetric forms of the LLL in combinatorics and graph theory, including bounds for the edge-disjoint paths problem, satisfiability of Boolean formulas in conjunctive normal form, lower bounds on diagonal and off-diagonal Ramsey numbers, hypergraph coloring results, structural properties of directed graphs, and acyclic graph colorings. Additional observations and refinements are provided throughout. We also introduce the algorithmic framework of Moser and Tardos, highlighting its constructive counterpart to the LLL, together with an introduction to the entropy-compression principle. The lopsided LLL, a refinement of the LLL, is presented along with an application to the Latin transversal problem. We further discuss the cluster-expansion lemma and its relation to the LLL, and present an alternative treatment of the Latin transversal problem from the cluster-expansion perspective that yields an improved result. The paper concludes with a high-level overview of the iterated LLL, also known as the semi-random method.

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

MMed-Bench-IR: A Heterogeneous Benchmark for Multilingual Medical Information Retrieval

Retrieval-augmented generation (RAG) in clinical settings increasingly requires multilingual retrieval against predominantly English evidence corpora. Multilingual medical retrieval demands three capabilities: cross-lingual alignment, concept discrimination, and evidence retrieval. However, existing benchmarks evaluate these only in isolation, leaving the interaction between biomedical expertise and multilingual coverage unmeasured. We introduce MMed-Bench-IR, a benchmark designed to disentangle these axes across 6 languages and three structurally heterogeneous tasks: (1) cross-lingual medical QA retrieval with 6,127 queries grounded in the Unified Medical Language System (UMLS), (2) concept discrimination over 4,975 confusion sets at three difficulty tiers, and (3) multilingual evidence retrieval for RAG with 2,040 quality-assured queries. The three tasks share zero concept and query overlap by design, ensuring that aggregate scores reflect genuine capability breadth. Evaluation of ten systems across six paradigm families reveals severe cross-lingual failure: biomedical encoders that score 0.818 nDCG@10 in English drop to 0.056 in Japanese, a gap that English-only benchmarks cannot detect.

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

Mojo: A Promising Tool for Scalable Financial AI Efficiency

Authors:

arXiv:2606.16059v1 Announce Type: cross Abstract: For thirty years, quantitative finance has paid a costly two-language tax: models researched in Python are rewritten in C++ for production, often introducing numerical discrepancies. GPU-accelerated deep learning exacerbates this problem, as nondeterministic floating-point reductions can produce drift in long backtests, challenging regulatory reproducibility and auditability expectations. This article surveys Mojo, Modular's 2026 Python-like systems language, as a structural response for capital markets engineering. While closing the Python-to-C++ performance gap, Mojo uniquely combines native interoperability with the low-level systems control required to construct bit-exact deterministic kernels. Its MLIR compilation infrastructure further allows a single codebase to target scalar, SIMD, multicore, and GPU execution, reducing the translation bottleneck between research and production. We benchmark four core financial AI workloads: Monte Carlo option pricing, LLM sentiment inference, multi-asset backtesting, and portfolio Value at Risk. On Apple Silicon, Mojo demonstrates 20x to 180x speedups over pure Python on directly measured kernels; larger-scale GPU workload results are projections calibrated from published benchmarks. Alongside transparent performance data, we introduce mojo-deterministic, an open-source library of reproducible reduction kernels, and provide a candid assessment of the problems Mojo does and does not yet solve.

14.
arXiv (CS.AI) 2026-06-11

Improving Detection of Rare Nodes in Hierarchical Multi-Label Learning

arXiv:2602.08986v2 Announce Type: replace-cross Abstract: In hierarchical multi-label classification, a persistent challenge is enabling model predictions to reach deeper levels of the hierarchy for more detailed or fine-grained classifications. This difficulty partly arises from the natural rarity of certain classes (or hierarchical nodes) and the hierarchical constraint that ensures child nodes are almost always less frequent than their parents. To address this, we propose a weighted loss objective for neural networks that combines node-wise imbalance weighting with focal weighting components, the latter leveraging modern quantification of ensemble uncertainties. By emphasizing rare nodes rather than rare observations (data points), and focusing on uncertain nodes for each model output distribution during training, we observe improvements in recall by up to a factor of five on benchmark datasets, along with statistically significant gains in $F_{1}$ score. We also show our approach aids convolutional networks on challenging tasks, as in situations with suboptimal encoders or limited data.

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

Residual-Space Evolutionary Optimization via Flow-based Generative Models

arXiv:2606.20084v1 Announce Type: new Abstract: Data editing with generative methods typically requires differentiable objectives and gradient-based search. However, these assumptions break down in flow-based settings, where edits are performed through forward and backward integration and often involve non-differentiable or black-box objectives. We introduce residual-space evolutionary optimization, a model-agnostic framework that addresses this gap by combining flow-based generative editing with evolutionary algorithms. Building on the observation that conditional flow matching (CFM) can disentangle condition-controlled factors from instance-specific residuals, our framework directly operates in residual space and separates two complementary search regimes: self-pollination performs local exploitation through feature-preserving residual refinement, and cross-pollination promotes broader exploration by recombining residuals across heterogeneous samples. As a proof of concept, we validate on MorphoMNIST, a benchmark dataset for counterfactual generation, and on crystal data, demonstrating that this exploration–exploitation decomposition provides a useful mechanism for balancing target alignment, instance preservation, and diversity, and extends beyond images to real-world scientific domains.

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

Learned Image Compression for Vision-Language-Action Models

Vision-language-action (VLA) models increasingly rely on high-frequency multi-camera observations, making visual communication a major bottleneck for real-time robotic control in bandwidth-constrained or distributed deployment settings. Existing image and video codecs, however, are designed to preserve generic visual fidelity rather than the control performance of downstream VLA policies. In this work, we introduce SPARC (SPatially Adaptive Rate Control), a learned image compression framework tailored for VLA-driven robots. Our key observation is that the importance of visual information varies substantially across both camera views and spatial regions within an image. Based on this observation, SPARC employs a lightweight temporal mask selector that adaptively allocates bitrate over latent representations according to task relevance while leveraging temporal context. We further introduce a tilted rate loss that stabilizes training by reducing the tendency of entropy-based objectives to over-suppress rare yet task-critical visual patterns. Experiments on diverse robotic benchmarks, including RoboCasa365, VLABench, and LIBERO, show that SPARC consistently achieves stronger control performance than conventional image/video codecs and recent learned compression methods under the same bitrate budget. We additionally demonstrate real-world deployment benefits in remote-control settings, where our method substantially improves the bitrate-success tradeoff.

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

Spectral recovery of a planted triangle-dense subgraph

arXiv:2606.17604v1 Announce Type: cross Abstract: Given a simple graph on $n$ vertices and a parameter $k$, the triangle-densest-$k$-subgraph problem is known to be computationally hard in the worst case. To circumvent the computational hardness, we study an average-case model where a triangle-dense subgraph on $k$ vertices is planted in an Erdős-Rényi random graph on $n$ vertices. For the recovery of the planted subgraph, we propose a simple spectral algorithm and a semidefinite program, both of which use a graph matrix whose entries are local signed triangle counts. Theoretical guarantees for these algorithms are established through spectral analysis of the graph matrix. Finally, we provide evidence showing a statistical-to-computational gap analogous to that for the planted clique problem. The computational threshold in terms of the subgraph size $k$ is at least $\sqrt{n}$ in the framework of low-degree polynomial algorithms, while the information-theoretic threshold is at most logarithmic in $n$.

18.
arXiv (CS.LG) 2026-06-16

Structured Nonparametric Variational Inference for Dependent Latent Modeling

arXiv:2606.15458v1 Announce Type: cross Abstract: Variational inference (VI) is a core engine of modern AI, enabling scalable approximate Bayesian learning and uncertainty-aware training of large probabilistic and generative models. In this paper, we propose Structured Nonparametric Variational Inference (SN-VI), a novel framework for modeling complex dependencies among latent variables in posterior approximation, leveraging multivariate spline techniques. Unlike traditional methods that rely on the mean-field assumption, SN-VI preserves intricate latent variable dependencies, providing a flexible and accurate approximation of posteriors with arbitrary shapes. We establish rigorous theoretical guarantees, including the derivation of the lower bound for the variational objective and proof of asymptotic consistency in posterior estimation. To facilitate practical implementation, we develop an algorithm that automatically identifies dependent latent variables and their underlying dependence structure, without requiring manual specification. Simulation studies validate the effectiveness of SN-VI in approximating posterior distributions with bounded support and complex dependencies. The proposed method has been successfully applied to high-dimensional structured data, including computer vision datasets and spatial transcriptomics. In these applications, SN-VI demonstrates improved generative model performance and effectively uncovers coupled biological signals through the learned dependency structure.

19.
arXiv (CS.AI) 2026-06-16

Safe Exploration via Policy Priors

arXiv:2601.19612v3 Announce Type: replace-cross Abstract: Safe exploration is a key requirement for reinforcement learning (RL) agents to learn and adapt online, beyond controlled (e.g. simulated) environments. In this work, we tackle this challenge by utilizing suboptimal yet conservative policies (e.g., obtained from offline data or simulators) as priors. Our approach, SOOPER, uses probabilistic dynamics models to optimistically explore, yet pessimistically fall back to the conservative policy prior if needed. We prove that SOOPER guarantees safety throughout learning, and establish convergence to an optimal policy by bounding its cumulative regret. Extensive experiments on key safe RL benchmarks and real-world hardware demonstrate that SOOPER is scalable, outperforms the state-of-the-art and validate our theoretical guarantees in practice.

20.
arXiv (CS.CV) 2026-06-16

Facial Affect Analysis for Service-Oriented Systems: Advances, Challenges, and Future Visions

Facial Affect Analysis (FAA) is evolving from a stand-alone recognition task into a reusable perception capability for Service-Oriented Software Ecosystems (SoSE). This paper preserves the FAA methodological core while reframing recent advances through systems-engineering requirements for composable and dependable services. We review representative progress in static and dynamic expression analysis, action-unit and micro-expression modeling, and modern CNN, Transformer, graph, and hybrid architectures, then interpret these advances by their operational fit in edge, cloud, and hybrid service pipelines. The synthesis emphasizes SoSE concerns that determine deployability: service contracts for uncertainty-aware outputs, latency and availability envelopes, lifecycle monitoring and recalibration, governance-aware integration, and interoperability across independently evolving components. Our analysis shows that benchmark gains alone are insufficient for SoSE readiness; robustness under shift, intervention stability, fairness, privacy posture, and runtime guarantees are equally critical. We conclude with a roadmap for treating FAA as an operational service component with explicit interfaces, measurable quality attributes, and accountable lifecycle management.

21.
arXiv (quant-ph) 2026-06-15

Quantum codes and optimal pure quantum $(r,\delta)$-LRCs via the MP construction

arXiv:2606.14253v1 Announce Type: new Abstract: In this paper, we employ MP codes whose defining matrices are $\tau$-optimal defining ($\tau$-OD) matrices to construct new quantum codes and quantum $(r,\delta)$-LRCs. Specifically, we report the following results: We establish a unified $\tau$-monomial decomposition theorem for invertible self-adjoint matrices over finite fields of arbitrary characteristic, which generalizes the result in "Quantum codes using the $\tau$-OD MP construction" where the characteristic was required to be odd. Based on this theorem, we prove the existence of $\tau$-OD matrices over $\mathbb{F}_{q^2}$ for any characteristic and demonstrate that there exist several new infinite families of $\tau$-OD matrices over $\mathbb{F}_{q^2}$ of characteristic $2$. As an application of MP codes involving $\tau$-OD matrices, we construct several infinite families of quantum codes with flexible parameters. Within this framework, we present $222$ record-breaking quantum codes that surpass the best-known records maintained in Grassl's database. We propose two effective schemes for constructing optimal pure quantum $(r,\delta)$-LRCs via MP codes. Accordingly, we construct four new infinite families of optimal pure quantum $(r,\delta)$-LRCs with flexible parameters. Notably, we report an interesting phenomenon by exhibiting $30$ optimal pure quantum $(r,\delta)$-LRCs derived from our framework; that is, there exist quantum codes that are not only optimal pure quantum $(r,\delta)$-LRCs but also, according to Grassl's database, best-known, optimal, or record-breaking quantum codes. To the best of our knowledge, the new discovery that quantum codes are simultaneously optimal pure quantum $(r,\delta)$-LRCs and record-breaking quantum codes has not been previously reported in the literature.

22.
arXiv (CS.LG) 2026-06-18

GrapNet: A Programmable Dynamic-Architecture Neural Graph Substrate

Authors:

arXiv:2606.18923v1 Announce Type: new Abstract: Programmability is a missing first-class interface in fixed-tensor neural networks: editing a relation, freezing a subgraph, auditing a local function, or changing the execution backend should be an operation on the neural program rather than ad-hoc parameter surgery. GrapNet studies this graph-as-network setting. The graph is the architecture and executable program, not an input data graph. Each compute node owns its next-layer child references and a trainable allocation vector aligned with those references; deleting a relation physically removes both the child reference and the corresponding allocation coordinate. Structural rules and execution policies live outside the node core, so the same child-owned graph can be grown, frozen, structurally edited, grouped into trainable family blocks, routed by attention over active relations, or lowered to dense snapshots after topology stabilizes. GrapNet composes with conventional modules through a vector-valued parent interface: dense layers, CNN encoders, ResNet feature extractors, attention blocks, and transformer representations can all feed one sensory GrapNode per coordinate. The evaluation is organized as a programmability stress suite rather than as a new replay benchmark. In a matched ten-seed Split Fashion-MNIST study, a plastic GrapNet+ER head reaches 63.16 percent seen-class accuracy versus 51.08 percent for a parameter-larger dense MLP+ER under the same seen-class loss and replay memory, with paired delta 12.08 points and p=1.3e-5. On Split CIFAR-10 with a frozen ImageNet ResNet-18 encoder, the same substrate improves the online head over MLP-256 by 3.81 points, with p=0.0026. These results support GrapNet as an editable neural graph substrate whose core value is structural programmability with faithful execution views.

23.
arXiv (math.PR) 2026-06-11

Numerical simulations of the spread from the mean of the SLE and Multiple SLE dynamics

arXiv:2606.11254v1 Announce Type: cross Abstract: The Schramm-Loewner Evolution (SLE) describes a family of fractal curves that arise in the study of the scaling limits of many planar Statistical Physics models. These curves are modeled using the Loewner Differential Equation for the conformal maps $g_t(z)$ with a Brownian motion driver. Using Euler's Method, in the current work we performed numerical experiments to study at a fixed time the quantities $|g_t(z) - \overline{g_t(z)}|$ and $Re(g_t(z)) - Re(\overline{g_t(z)})$, where $Re$ denotes the real part and $\overline{g_t(z)}$ refers to the sample average. These random variables measure the 'spread' of the dynamics from the average behavior at fixed time. One of the scopes of this work is to give numerical predictions for future theoretical investigations on these quantities. When investigating these quantities in the SLE case our experiments predict that the distribution is bimodal when the dynamics started close to the origin, and it can become bell-shaped if the dynamics is started further from the origin. In the second part, we performed experiments for a Multiple SLE model whose driver is Dyson Brownian Motion. Due to singularity in the dynamics of the drivers and the many data points needed, this part is challenging from a computational perspective. In the multiple SLE case, our experiments predict that the distribution is bell-shaped in all cases. In addition, we check the changes in the distributions as we vary the parameter $\kappa$ in the SLE case and $\beta$ in the Multiple SLE case.

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

What Does ODRL Mean? A Cross-Level Ontological Grounding of Permissions, Prohibitions, and Duties in UFO-L

arXiv:2606.24344v1 Announce Type: cross Abstract: ODRL policy evaluators produce verdicts, but say nothing about the normative positions a policy brings into existence, the authority structures those positions presuppose, or who holds the power to declare a norm violated. We formulate the Cross-Level Design Principle: any normative language with violable, consequential norms requires both conduct-level positions (Permission, Duty, Right, No right) and competence-level positions (Power, Subjection, Immunity, Disability). Applying this to ODRL, we establish that prohibition is sanctioned (violation possible and consequential), that permission is underspecified across its behaviour parameter (open vs. closed world), and that the formal semantics covers achievement obligations only. We ground ODRL in UFO-L, mapping each activated rule to a simple legal relator and extending coverage from two to eight legal positions; violation-declaration authority, implicit in every existing evaluator, becomes an explicit Power-Subjection pair. All axioms are mechanically verified in Isabelle/HOL and across a 39-problem benchmark under Vampire, E, and Z3.

25.
arXiv (CS.AI) 2026-06-24

When CQs Go Wrong: Challenges in CQ Verification with OE-Assist

arXiv:2606.24619v1 Announce Type: new Abstract: Competency Questions (CQs) are the central component of CQ-verification, an established process in which an ontology is evaluated against a set of natural language questions to determine whether the intended purpose of the ontology has been properly modelled. However, CQ-verification is often time-consuming and error-prone, as it requires careful interpretation of linguistic nuances and precise alignment with formal ontology constructs. Ambiguities and complexity in CQs can further complicate this process, leading to inconsistent modelling decisions and verification outcomes. In this paper, we investigate what makes a CQ challenging and possible solutions to enhance the users' performance in the CQ-verification process. We experimented with the data of 19 participants who performed CQ-verification on 20 tasks using an LLM assistant to support ontology evaluation. The results show the necessity of a tool to refine CQs before publishing them to avoid ambiguity or excessive complexity in later phases of the ontology engineering process.