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01.
arXiv (CS.AI) 2026-06-17

Learning Red Agent Policy from Observations for Neurosymbolic Autonomous Cyber Agents

arXiv:2606.18223v1 Announce Type: cross Abstract: With sophisticated cyber-attacks becoming increasingly prevalent, modern networks require intelligent autonomous cyber-defense agents trained via Reinforcement Learning (RL). These agents employ neurosymbolic approaches such as behavior trees with learning-enabled components (LECs) to learn, reason, adapt, and implement security rules while maintaining critical operations. However, these autonomous networks are partially observable systems, i.e., the cyber-attacker's (red agent's) actions are not observable, making it difficult for the defender to predict red actions, learn red policies, or assess the attacker's intrusion levels. To address this, we propose a Policy Learning Technique using imitation learning to learn policies for partially observable RL agents with discrete states and discrete actions. We apply this technique in an autonomous cyber environment to predict red agent's actions from network observations and defender actions. Integrated with a neurosymbolic cyber-defense agent, our method effectively handles different red policies and achieves high prediction accuracy across diverse simulated scenarios.

02.
arXiv (CS.CV) 2026-06-16

Federated Medical Image Segmentation under Real-World Label Noise: A Benchmark Suite for Noisy Label Learning Method Selection

While federated learning (FL) enables collaborative medical image segmentation without centralizing sensitive data, real-world deployment is frequently complicated by cross-site label imperfections such as contour disagreement, missing or additional structures, and confused labels. Federated noisy label learning (FNLL) aims to mitigate these effects, yet remains underused in practice as existing evidence is largely based on synthetic noise, simplified settings, and limited real-world noisy evaluation. We address this gap by introducing a benchmark suite that combines diverse real-world noisy datasets, deployment-relevant client-noise scenarios, and label-noise-targeted evaluation to support systematic FNLL assessment and informed method selection. The suite combines curated real-world noisy medical image segmentation datasets from diverse sources with a comprehensive federated segmentation framework including various client-noise scenarios and noise-targeted evaluation. The presented suite provides a realistic and discriminative basis for FNLL evaluation in medical image segmentation and establishes a reusable foundation for fair benchmarking, dataset-specific label-noise characterization, and future method development under realistic federated settings. Code is available at https://github.com/MIC-DKFZ/FedSegNoiseBench.

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

Skill-Constrained Model Predictive Control for Resilient Manufacturing Supply Chains

arXiv:2606.17269v1 Announce Type: new Abstract: In skill-constrained production-inventory systems, the qualified human capacity available tomorrow depends on training decisions made today: production requires certified workers, certifications decay unless maintained, and training consumes the same scarce worker hours that production needs now. We study a closed-loop skill-constrained model predictive controller that, at every shift, solves a finite-horizon mixed-integer program over production, inventory, backlog, and training, with binary predicted certification, hard production eligibility, and an interpretable terminal value that prices certified-capacity gaps at the horizon boundary; only the first-period action is applied before replanning. On synthetic, seed-controlled SkillChain-Gym scenarios - announced and surprise new-skill shocks, demand shocks, absenteeism, forecast- and availability-quality modes, capacity-boundary and training-rate sweeps, and negative controls - we evaluate the controller against production-only and maintenance-only ablations, static cross-training insurance plans, and a strong reactive heuristic, under an ex-ante locked configuration and paired statistics. The result is regime dependence, not superiority: no policy class dominates. Predictive control helps when skill or labor bottlenecks are forecastable early enough for training to complete; lean static insurance remains hard to beat under surprise shocks, near the demand-capacity boundary, and wherever pre-shock slack makes insurance cheap. Attribution ablations separate certification maintenance, re-acquisition of lapsed certifications, and greenfield skill acquisition. Forecastability, not adaptivity per se, decides when predictive control pays.

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

MCompassRAG: Topic Metadata as a Semantic Compass for Paragraph-Level Retrieval

Retrieval-augmented generation (RAG) systems depend critically on how documents are chunked and searched. Fine-grained chunks can improve retrieval precision but expand the search space, increasing latency and cost; larger chunks reduce the number of candidates but make dense similarity less reliable, as the representation for each chunk mixes multiple topics and introduces more semantic noise. This trade-off becomes especially limiting in deep research tasks, where retrieval must be both fast and precise across large, heterogeneous corpora. We introduce MCompassRAG, a metadata-guided retrieval framework that uses topic-level signals as a semantic compass for selecting relevant evidence. Instead of relying only on cosine similarity between queries and noisy chunk embeddings, MCompassRAG enriches chunk representations with topic metadata in the same embedding space and trains a lightweight retriever through LLM-teacher distillation. At inference time, MCompassRAG performs topic-aware retrieval without additional LLM calls, improving both efficiency and evidence quality. Across six complex retrieval benchmarks, MCompassRAG improves information efficiency (IE) by 8.24% on average with over 5 times lower latency than the strongest efficient RAG baselines. Code is available on https://github.com/AmirAbaskohi/MCompassRAG.

05.
arXiv (CS.AI) 2026-06-24

Coordinate-Queryable Neural Field Reconstruction for EEG Spatial Super-Resolution with Unseen-Electrode Generation

arXiv:2606.23707v1 Announce Type: cross Abstract: EEG spatial super-resolution (EEGSR) in real deployments is challenged by random channel missingness, unstable electrode quality, and changing visible-channel patterns caused by bad contacts or device variability. Most existing EEGSR methods learn a fixed low-to-high channel mapping under pre-defined input-output layouts, which makes them brittle when missing channels vary at test time. In this paper, we reformulate EEGSR as learning a shared conditional scalp field from partially observed support channels. Specifically, a position-guided encoder summarizes the observed EEG channels and their coordinates into a latent condition, and a conditional implicit neural representation decoder reconstructs target EEG signals by querying this condition at desired electrode coordinates. During inference, the model directly reconstructs unseen electrode signals from the available EEG support and the queried coordinates. To strengthen the constraint of the encoded latent representation on the decoder and thereby construct a more stable scalp field consistent with the observed channels, we further introduce a fidelity-preserving channel corruption training strategy under mixed electrode states. Extensive experiments across multiple EEG datasets demonstrate the effectiveness of our framework for both random missing-channel reconstruction and strict unseen-electrode signal generation. Notably, under the strict held-out-electrode setting on AAD, our method reduces NMSE by 37.5\% and improves SNR by 2.12 dB over the strongest baseline, showing its ability to synthesize signals at electrode locations never exposed during training.

06.
medRxiv (Medicine) 2026-06-24

TMPRSS2-Coagulation Nexus: A Novel Molecular Link Revealed by Pairwise Correlation Analysis Following AstraZeneca (ChAdOx1 nCoV-19) Vaccination in a Nigerian Cohort

Background: While haematological and coagulation changes following AstraZeneca vaccination have been described, the molecular mechanisms linking TMPRSS2 expression to coagulation remain underexplored, particularly in African populations. Methods: In this case-control study, 102 adults (51 vaccinated with AstraZeneca >=6 months prior, 51 unvaccinated controls) aged 18-65 years in Port Harcourt, Nigeria, were evaluated. Full blood count (Sysmex XN-1000), PT/aPTT (Erba Mannheim), RNA concentration, and qRT-PCR for ACE2/TMPRSS2 (normalized to GAPDH) were performed. Pearson correlations and t-tests were conducted (SPSS v26, p

07.
Nature Medicine 2026-06-08

Post-adjuvant chemotherapy in ctDNA-positive patients with resected colorectal cancer: a randomized phase 3 trial

Tumor-informed circulating tumor DNA (ctDNA) enables detection of molecular residual disease (MRD) after curative resection of colorectal cancer (CRC), but whether early intervention improves outcomes remains uncertain. ALTAIR was a randomized, double-blind, phase 3 trial embedded in the CIRCULATE-Japan platform evaluating a post-adjuvant ctDNA surveillance strategy with treatment initiation upon molecular recurrence. Patients with resected stage 0–IV CRC who became ctDNA positive after completion of standard-of-care therapy and had no radiological evidence of disease were randomly assigned (1:1) to receive trifluridine/tipiracil (FTD/TPI) or placebo for 6 months. The primary endpoint was investigator-assessed disease-free survival (DFS). Between July 2020 and June 2023, 243 patients were randomized to FTD/TPI (n = 122) or placebo (n = 121). Median DFS was 9.30 months with FTD/TPI and 5.55 months with placebo (hazard ratio = 0.79, 95% confidence interval: 0.60–1.05, P = 0.107), and the primary endpoint was not met. FTD/TPI increased grade 3 or higher hematologic adverse events (73.0% versus 3.3%) without new safety signals. These findings indicate that post-adjuvant intervention with FTD/TPI did not significantly improve DFS in ctDNA-positive patients without radiological disease. ClinicalTrials.gov identifier: NCT04457297 . In the randomized, double-blind phase 3 ALTAIR trial, patients with resected colorectal cancer who became positive for circulating tumor DNA during post-adjuvant surveillance received trifluridine/tipiracil hydrochloride therapy, which did not significantly prolong disease-free survival compared with placebo.

08.
arXiv (CS.CV) 2026-06-11

FOCUS on Contamination: Hydrology-Informed Noise-Aware Learning for Geospatial PFAS Mapping

Per- and polyfluoroalkyl substances (PFAS) are persistent environmental contaminants with significant public health impacts, yet large-scale monitoring remains severely limited due to the high cost and logistical challenges of field sampling. The lack of samples leads to difficulty simulating their spread with physical models and limited scientific understanding of PFAS transport in surface waters. Yet, rich geospatial and satellite-derived data describing land cover, hydrology, and industrial activity are widely available. We introduce FOCUS, a geospatial deep learning framework for PFAS contamination mapping that integrates sparse PFAS observations with large-scale environmental context, including priors derived from hydrological connectivity, land cover, source proximity, and sampling distance. These priors are integrated into a principled, noise-aware loss, yielding a robust training objective under sparse labels. Across extensive ablations, robustness analyses, and real-world validation, FOCUS consistently outperforms baselines including sparse segmentation, Kriging, and pollutant transport simulations, while preserving spatial coherence and scalability over large regions. Our results demonstrate how AI can support environmental science by providing screening-level risk maps that prioritize follow-up sampling and help connect potential sources to surface-water contamination patterns in the absence of complete physical models.

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

Scalable Physics-Inspired Transformers for Spin Glasses

arXiv:2606.22984v2 Announce Type: replace-cross Abstract: Efficient sampling of the Boltzmann distribution in frustrated spin glasses is central to statistical mechanics and combinatorial optimization. Despite advances in machine-learning-based approaches, two issues persist: limited understanding of why variational models fail to benefit from increased scale, unlike the monotonic scaling law of large language models; and high computational cost on large systems that negates advantages over classical sampling methods. Here, we develop a physics-inspired transformer with interpretable sparse attention and spin-tailored positional embeddings to address these challenges. By further leveraging FlashAttention for parallel ancestral sampling, it achieves up to two orders of magnitude speedup over vanilla variational autoregressive networks, enabling neural-network simulations of spin-glass systems to unprecedented sizes on a single GPU. It can resolve full probability distributions, free energies, and overlap statistics across temperatures, for Sherrington-Kirkpatrick and 2D or 3D Edwards-Anderson models, where existing machine-learning methods encounter limitations at certain temperatures. This framework thus establishes a scalable paradigm for frustrated spin-glass systems.

10.
arXiv (CS.CL) 2026-06-12

Quickest Detection of Hallucination Onset: Delay Bounds and Learned CUSUM Statistics

作者:

Token-level hallucination detectors are evaluated as classifiers, by AUC over all tokens, yet a streaming monitor is judged by its reaction time: the number of tokens that pass between the onset of a hallucination and the alarm. We formulate hallucination onset detection as a quickest change detection problem. A first-order Markov model of the latent faithful/hallucinated state, validated on RAGTruth, places the task inside classical change-point theory and yields Lorden's lower bound on detection delay: about 1.3 tokens at a false-alarm rate of 0.01. We then show that a causal recurrent labeler acts as a CUSUM with a learned increment; at a matched false-alarm rate it detects in 11-13 tokens, against 31 for a linear per-token baseline, and a controlled decomposition attributes most of this advantage to a better per-token score rather than to temporal accumulation. An information-rate optimality theorem of Donsker-Varadhan type explains the remaining order-of-magnitude gap: the learned score realizes only 1/4.5 of the divergence the features carry, a deficit that recalibration cannot remove, with the remainder a finite-horizon effect. Classification metrics conceal this delay structure; sequential analysis makes it measurable

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

RAIL: Rethinking Auditory Intelligence in Large Audio-Language Models with a CHC-Grounded Benchmark

arXiv:2606.11260v1 Announce Type: cross Abstract: Humans process rich auditory environments through tightly integrated cognitive capabilities such as audio perception, audio reasoning, and memory. Despite recent progress in large audio-language models (LALMs) across speech understanding and multimodal audio reasoning, current evaluation paradigms remain largely task- or modality-centric, focusing on end performance while overlooking underlying auditory cognitive behaviours. This reveals a fundamental gap between how auditory cognition is understood in humans and how it is evaluated in LALMs, particularly in the lack of frameworks that operationalise cognitive principles beyond task-level metrics to systematically capture model behaviour. In this work, we introduce RAIL, a human-centric evaluation paradigm grounded in the Cattell-Horn-Carroll (CHC) cognitive framework. RAIL formalises auditory cognition into five core capabilities and develop them into structured evaluation tasks that probe how models process, retain, and integrate auditory information. We further construct a cognitively grounded benchmark with principled data curation and human-aligned evaluation protocols. Evaluating 26 state-of-the-art LALMs, we find that current models exhibit highly uneven performance across cognitive abilities. RAIL establishes a new evaluation paradigm that moves beyond task-centric benchmarking toward cognitively grounded assessment of auditory intelligence.

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

EPEdit: Redefining Image Editing with Generative AI and User-Centric Design

The demand for image manipulation has seen a significant increase recently. Traditional tools like Photoshop and Capture One, while powerful, require considerable expertise to use effectively. Generative AI has introduced alternative platforms, such as Luminar Neo, Pixlr X, and Canva. However, many of these solutions, including resource-heavy models like Stable Diffusion, often require substantial retraining and fine-tuning, leading to high costs for users. To address these challenges, we introduce Efficient Photo Editor (EPEdit), an application that integrates a robust backend framework with a user-friendly front-end interface. EPEdit supports a wide range of creative image editing tasks, including image generation, object replacement, object removal, background modification, changes in object pose or perspective, region-specific editing, and thematic collection design, all guided by masks and prompts. Users can interact with the system through simple text commands or by marking areas for precise adjustments, making it accessible even to those without technical expertise. At its core, EPEdit leverages zero-shot image editing algorithms based on Stable Diffusion model, removing the need for additional fine-tuning. This approach enables efficient image manipulation and thematic collection creation. User evaluations for tasks of image editing, thematic design, and overall system performance demonstrate that EPEdit outperforms existing solutions, offering a user-friendly, cost-effective solution for comprehensive image editing.

13.
arXiv (CS.AI) 2026-06-19

KG-SoftMAP: Soft Knowledge-Graph Priors for Bayesian Network Structure Learning from Sparse Discrete Data

arXiv:2606.10358v2 Announce Type: replace-cross Abstract: Learning Bayesian network (BN) structure from sparse discrete data is hard: when each instance records only a few variables, most variable pairs lack the joint observations needed for reliable scoring, and data-only methods recover little structure. However, imperfect domain knowledge, expressible as a weighted directed knowledge graph (KG), is often available. We propose KG-SoftMAP, which encodes such a KG as a finite-strength, confidence-weighted edge prior and maximizes a MAP objective combining the BDeu score with a logit-form prior; the KG may be expert-curated or LLM-extracted. On synthetic benchmarks with known DAGs, KG-SoftMAP reaches Directed-F1 (DF1) $0.19$–$0.32$ at observation rate $\rho=0.05$ and DF1 $0.44$–$0.97$ at $\rho\geq0.2$, while every data-only learner tested stays near zero under the same sparse masks. Recovery tracks KG quality: controlled corruption degrades it smoothly, a zero-signal KG yields DF1 $0.00$, and a blindly LLM-extracted KG with imperfect precision and recall still drives substantial recovery. On three real sparse educational datasets, the learned BN acts as a concept-level posterior model: on SAF it matches logistic regression (LR) within $0.03$ F1_FAIL while providing an inspectable concept graph, calibrated Fail probabilities, and tractable posterior queries from partial observations.

14.
arXiv (CS.CV) 2026-06-15

FBSDiff++: Improved Frequency Band Substitution of Diffusion Features for Efficient and Highly Controllable Text-Driven Image-to-Image Translation

With large-scale text-to-image (T2I) diffusion models achieving significant advancements in open-domain image creation, increasing attention has been focused on their natural extension to the realm of text-driven image-to-image (I2I) translation, where a source image acts as visual guidance to the generated image in addition to the textual guidance provided by the text prompt. We propose FBSDiff, a novel framework adapting off-the-shelf T2I diffusion model into the I2I paradigm from a fresh frequency-domain perspective. Through dynamic frequency band substitution of diffusion features, FBSDiff realizes versatile and highly controllable text-driven I2I in a plug-and-play manner (without need for model training, fine-tuning, or online optimization), allowing appearance-guided, layout-guided, and contour-guided I2I translation by progressively substituting low-frequency band, mid-frequency band, and high-frequency band of latent diffusion features, respectively. In addition, FBSDiff flexibly enables continuous control over I2I correlation intensity simply by tuning the bandwidth of the substituted frequency band. To further promote image translation efficiency, flexibility, and functionality, we propose FBSDiff++ which improves upon FBSDiff mainly in three aspects: (1) accelerate inference speed by a large margin (8.9$\times$ speedup in inference) with refined model architecture; (2) improve the Frequency Band Substitution module to allow for input source images of arbitrary resolution and aspect ratio; (3) extend model functionality to enable localized image manipulation and style-specific content creation with only subtle adjustments to the core method. Extensive qualitative and quantitative experiments verify superiority of FBSDiff++ in I2I translation visual quality, efficiency, versatility, and controllability compared to related advanced approaches.

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

Beyond Reasoning Gains: Mitigating General-Capability Forgetting in Large Reasoning Models

arXiv:2510.21978v2 Announce Type: replace-cross Abstract: Reinforcement learning with verifiable rewards (RLVR) has delivered impressive gains in mathematical and multimodal reasoning and has become a standard post-training paradigm for contemporary language and vision-language models. However, the RLVR recipe introduces a significant risk of capability regression, in which models forget foundational skills after prolonged training without employing regularization strategies. We empirically confirm this concern, observing that open-source reasoning models suffer performance degradation on core capabilities such as perception and faithfulness. While imposing regularization terms like KL divergence can help prevent deviation from the base model, these terms are computed on the current task and therefore do not guarantee preservation of broader knowledge. Meanwhile, commonly used experience replay across heterogeneous domains makes it nontrivial to decide how much training emphasis each objective should receive. To address this, we propose RECAP-a replay strategy with dynamic objective reweighting for general knowledge preservation. Our reweighting mechanism adapts online using short-horizon signals of convergence and instability, shifting the post-training focus away from saturated objectives and toward underperforming or volatile ones. Our method is end-to-end and readily applicable to existing RLVR pipelines without training additional models or heavy tuning. Extensive experiments on benchmarks using Qwen2.5-VL-3B and Qwen2.5-VL-7B demonstrate the effectiveness of our method, which not only preserves general capabilities but also improves reasoning by enabling more flexible trade-offs among in-task rewards.

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

CASR: A Robust Cyclic Framework for Arbitrary Large-Scale Super-Resolution with Distribution Alignment and Self-Similarity Awareness

Arbitrary-Scale SR (ASISR) remains fundamentally limited by cross-scale distribution shift: once the inference scale leaves the training range, noise, blur, and artifacts accumulate sharply. We revisit this challenge from a cross-scale distribution transition perspective and propose CASR, a simple yet highly efficient cyclic SR framework that reformulates ultra-magnification as a sequence of in-distribution scale transitions. This design ensures stable inference at arbitrary scales while requiring only a single model. CASR tackles two major bottlenecks: distribution drift across iterations and patch-wise diffusion inconsistencies. The proposed SSAM module aligns structural distributions via superpixel aggregation, preventing error accumulation, while SARM module restores high-frequency textures by enforcing correlation-guided consistency and preserving self-similarity structure through correlation alignment. Despite using only a single model, our approach significantly reduces distribution drift, preserves long-range texture consistency, and achieves superior generalization even at extreme magnification.

18.
arXiv (quant-ph) 2026-06-17

On the entanglement induced by the deformation of phase-space

arXiv:2606.17587v1 Announce Type: new Abstract: Most quantum gravity theories propose that the fundamental concept of space-time is mostly compatible with quantum theory in noncommutative (NC) space. In the present paper, we revisit the notion of entanglement induced by NC deformations of phase space. The positive partial transpose (PPT) criterion for separability of bipartite Gaussian states is extended to a general class of Bopp's shift. In particular, we have considered both the position-position and momentum-momentum noncommutativity, with deformation parameters $\theta$ and $\eta$, respectively. It turns out that $\theta$ and $\eta$ induce the entanglement. We have directly applied the formalism for an anisotropic two-dimensional harmonic oscillator. Peres-Horodecki separability condition leads to a constraint equation for the parameter values of the oscillator in NC space. It turns out that the bipartite Gaussian state is almost always entangled in deformed space. To implement the theoretical idea, we provide an outline for a gedankenexperiment to identify the signature of phase-space noncommutativity, i.e., quantum gravity. In particular, the gedankenexperiment is devised to test the separability of supposedly separable Gaussian states in the usual commutative space, through the covariance matrix, which is constructed via measured output photocurrents after interaction of input Gaussian states and reference states. If the experiment shows that the supposedly separable states are actually entangled, then the entanglement is created through the intermediate background noncommutative space, which is a signature of the quantum nature of gravity.

19.
medRxiv (Medicine) 2026-06-18

Human Intuition vs. Computational Precision: Neurologists, Feature-based Models, and Deep Learning for Stroke Prognosis

Background: Prognostication in large vessel occlusion (LVO) stroke remains challenging. Although several prognostic models exist, their comparison to clinician performance, human-model interaction, and specific sources of human bias remain poorly understood. Methods: Using pre-treatment clinical and CT data from the MR CLEAN trial (n=500), six neurologists predicted three-month modified Rankin Scale (mRS) scores for 40 patients, both unaided and assisted by a validated feature-based model (MR PREDICTS). Human performance was benchmarked against MR PREDICTS and a multimodal, interpretable deep learning (DL) approach using raw imaging data. We explicitly assessed neurologists? ability to estimate model-required imaging features and identified systematic human biases. Models were additionally validated in a larger MR CLEAN trial cohort (n=404). Results: For predicting the full mRS distribution, standalone models achieved good ordinal agreement (MR PREDICTS quadratic weighted kappa (QWK) 0.51 [0.24 to 0.70]; DL model 0.49 [0.25 to 0.67]), significantly outperforming unaided neurologists (QWK 0.27 [0.10, 0.42]). Neurologists showed systematic overoptimism, predicting lower mRS scores than observed. Furthermore, there was poor accuracy in extracting imaging features. Raters? ASPECTS predictions deviated by 3.4 points from the confirmed scores, and collateral score accuracy was 44.6%. However, for predicting binary mRS (0-2 vs. 3-6), accuracy was comparable between unaided neurologists (64.17% [55.42% to 72.92%]) and models (MR PREDICTS 67.50% [52.50% to 82.50%]; DL model 63.16% [47.37% to 78.95%]). Model-assistance modestly improved and harmonized neurologists? predictions (QWK 0.41 [0.22 to 0.55]; binary accuracy 68.75% [58.33% to 78.34%]. Model performance remained robust in the larger cohort. Conclusions: Multimodal prognostic models outperform clinicians in predicting the full range of mRS outcomes, while human error in imaging assessment and systematic optimism bias are primary drivers of prognostic inaccuracy. End-to-end DL models eliminate human-input variability and hold strong potential as an automated second opinion to support prognostication and decision-making in acute LVO stroke.

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

The Information-Theoretic Benefit of Shared Representations under Orthogonality Constraints

arXiv:2606.16028v1 Announce Type: new Abstract: Modern deep learning architectures are increasingly multi-task and multi-modal, using a pretrained foundation model combined with task-specific, fine-tuned models. Empirically, exploiting similarity across different problems, instead of solving them individually, can significantly improve overall performance. While the generalization and sample complexity properties of multitask learning have been widely studied, the parametric complexity of joint approximation in comparison to separate approximation remains less well understood. The question is particularly relevant in modern deep learning, where models are increasingly required to satisfy structural constraints such as equivariance, conservation laws, or orthogonality. We prove lower and upper bounds on the description-length for separate and joint approximation classes, respectively, in uniform norm. We build a class of orthogonal functions by composing a shared hard feature, realized by a Rademacher-Haar wavelet series, with Sawtooth-Walsh readouts to enforce orthogonality of output coordinates. The dyadic tree structure of the Rademacher-Haar wavelet concentrates the approximation hardness in the common feature component, while the readouts act as task-specific heads. Using an information-theoretic framework, we obtain a sharp gap between the optimal approximation rates achievable by joint and separate coding. Finally, we realize this separation in a neural network model using Heaviside activations via reduction to triangle-wave approximation. Our results show that even under an orthogonality constraint joint approximation requires strictly fewer bits in compositional architectures, provided the tasks share a latent hard feature. This provides theoretical insight into the description-length-efficiency of compositional multi-output architectures and clarifies how neural networks can retain expressivity under geometric constraints.

21.
arXiv (quant-ph) 2026-06-11

Bound State Solutions of the Relativistic Finite-difference Equation for the Ring-shaped Quesne Oscillator Potential

arXiv:2606.12082v1 Announce Type: new Abstract: We solve exactly the relativistic finite-difference equation for the quantum three-dimensional ring-shaped Quesne oscillator potential. Our investigation is based on a finite-difference version of relativistic quantum mechanics. So-called relativistic configurational r-space is a key concept here. We show that the radial wavefunctions and angular wavefunctions are expressed through the continuous dual Hahn polynomials and Jacobi polynomials, respectively. A discrete energy spectrum has been found. The radial wave functions and energy spectrum have the correct nonrelativistic limit. We also build a dynamical symmetry group SU (1, 1) for the radial part of the equation of motion, which allows us to find the energy spectrum purely algebraically.

22.
arXiv (CS.AI) 2026-06-24

Graph Alignment for Benchmarking Graph Neural Networks and Learning Positional Encodings

arXiv:2505.13087v2 Announce Type: replace-cross Abstract: We propose a novel benchmarking methodology for graph neural networks (GNNs) based on the graph alignment problem, a combinatorial optimization task that generalizes graph isomorphism by aligning two unlabeled graphs to maximize overlapping edges. We frame this problem as a self-supervised learning task and present several methods to generate graph alignment datasets using synthetic random graphs and real-world graph datasets from multiple domains. For a given graph dataset, we generate a family of graph alignment datasets with increasing difficulty, allowing us to rank the performance of various architectures. Our experiments prove that there is an optimal task difficulty for having a statistically relevant ranking of different models and that, even on a structure-only task, anisotropic models perform better compared to isotropic ones. To further prove that our synthetic task capture meaningful information, we show its effectiveness for self-supervised GNN pre-training: the learned node embeddings can be leveraged as positional encodings by transformers for graph regression or can be used to reconstruct the full structure of the graph with $98\%$ accuracy. To support reproducibility and further research, we provide an open-source Python package to generate graph alignment datasets and benchmark new GNN architectures. The source code is available at https://github.com/adrien-lagesse/graph-alignment-benchmark.

23.
arXiv (CS.LG) 2026-06-18

Everywhere Valid Bounds on False Discovery Proportions in Conformal Inference

arXiv:2605.20726v2 Announce Type: replace-cross Abstract: Modern applications of conformal inference to multiple testing problems, such as outlier detection and candidate selection, often involve selecting test samples whose conformal p-values fall below a threshold. The quality of such methods is often measured by the false discovery proportion (FDP), defined as the fraction of incorrect selections. Existing approaches typically control the expected value of the FDP, using methods such as the Benjamini-Hochberg procedure. This approach fails to provide high-probability bounds on the realized false discovery proportion and invalidates statistical guarantees if the rejection threshold is selected after inspecting the data. This paper establishes finite-sample, distribution-free upper bounds on the FDP that hold simultaneously over all possible rejection thresholds, enabling arbitrary post hoc selection of the threshold. Simultaneous validity is achieved by constructing a high-probability envelope for the empirical distribution function of null conformal p-values by sampling from their joint distribution. Furthermore, our framework allows practitioners to modulate the envelope's shape, thereby producing tight bounds in rejection regions of primary interest. We use this flexible approach to derive simultaneous FDP upper bounds for both outlier detection and conformal selection. We demonstrate through synthetic and real-data experiments that the resulting bounds are both valid and substantially less conservative than those derived from existing approaches.

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

SciR: A Controllable Benchmark for Scientific Reasoning in LLMs

arXiv:2606.13020v1 Announce Type: new Abstract: Three paradigmatic forms of inference recur across scientific reasoning: deduction, induction, and causal abduction. Reliably evaluating LLMs on these in scientific settings is currently out of reach: scientific benchmarks built on human annotations are costly and lack mechanistic ground truth, while synthetic logical-reasoning benchmarks do not resemble real scientific documents. We introduce SciR, a benchmark that combines multi-paradigm reasoning with controllable scientific rendering, anchored on three paradigmatic scientific problems. Tasks are generated from formal objects (deduction tree, inductive rule hypothesis, causal graph) to guarantee verifiable answers, then rendered into multi-document scientific discourse via per-track domain-tuned genres. The construction lets us independently vary two difficulty axes: how hard it is to extract the key information needed for inference, and how hard the principled inference itself is. We test six models. Both axes hurt every model, and their effects compound. The rendering even hurts neurosymbolic pipelines, which hand inference to a verified solver. The two axes yield a per-model extraction-vs-inference profile: for instance, reasoning models like deepseek-r1 mostly surpass non-reasoning instruct models on the inference axis. To our knowledge, SciR is the first multi-paradigm scientific-reasoning benchmark with parametric control on both extraction and inference difficulty.

25.
arXiv (math.PR) 2026-06-17

Critical spectral behavior and large deviations for geometric $\alpha$-stable processes

arXiv:2606.17501v1 Announce Type: new Abstract: In this paper, we study the Schrödinger-type operator associated with geometric stable processes on $\mathbb{R}^{d}$, especially the differentiability of spectral function. Let $\mathcal{H}$ be the generator of the geometric stable process and $\mu$ a smooth measure on $\mathbb{R}^{d}$. Then the spectral function $C(\theta)$ is defined as $C(\theta) = -\inf \sigma(-\mathcal{H} - \theta \mu)$, where $\sigma(\mathcal{A})$ denotes the spectrum of $\mathcal{A}$ and $\theta$ is a real parameter. Since the geometric stable process exhibits severe local singularities in its Lévy measure, its transition semigroup lacks ultracontractivity, which invalidates classical methods for proving the differentiability. To overcome this obstacle, we use the compact embedding of the extended Dirichlet space into $L^2(\mu)$. As a primary application of this differentiability, we establish a large deviation principle for a positive continuous additive functional associated with the smooth measure $\mu$.