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01.
medRxiv (Medicine) 2026-06-15

Evaluation of AI-Generated Synthetic Data for Clinical Research in Secondary Cardiovascular Prevention among Dyslipidemia Patients

Background: Access to high-quality clinical data is essential for advancing medical research and developing effective medical statistical and Artificial Intelligence models. However, privacy regulations and logistical barriers often hinder timely access to real-world data. Synthetic data offer a promising solution, preserving the statistical characteristics of original datasets while protecting patient privacy. Objectives: This study investigates the use of synthetic data for secondary cardiovascular prevention in patients with dyslipidemia, using two real-world datasets from Centro Cardiologico Monzino. Methods: Given the high dimensionality and limited sample size of the datasets, we employed a custom generative framework based on Large Language Models (LLMs). Pre-trained LLMs were fine-tuned on original clinical records to synthesize tabular data replicating source-data distributions. Fine-tuning was performed within the Centro Cardiologico Monzino's secure infrastructure to ensure data sovereignty. We evaluate clinical utility and privacy using fidelity and privacy metrics, identifying the optimal generative model and benchmarking against traditional anonymization methods. Results: Synthetic data achieved a superior trade-off than classically anonymized datasets. Real and synthetic datasets showed strong agreement, with significant distributional differences limited to few variables. Models trained on synthetic data replicated key associations from the original dataset, including therapy modification and creatine phosphokinase as predictors of SAMS, and pharmacological intensity as the main driver of LDL-C reduction. Conclusions: Results support the feasibility of using synthetic data as a proxy for real-world datasets in exploratory analyses and model development. Despite slight attenuation of some effect sizes, preserved clinical relationships reinforce the validity of synthetic data in medical research.

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

GradPower: Powering Gradients for Faster Language Model Pre-Training

arXiv:2505.24275v4 Announce Type: replace Abstract: We propose GradPower, a lightweight gradient-transformation technique for accelerating language model pre-training. Given a gradient vector $g=(g_i)_i$, GradPower first applies the elementwise sign-power transformation: $\varphi_p(g)=(sign(g_i)|g_i|^p)_{i}$ for a fixed $p>0$, and then feeds the transformed gradient into a base optimizer. Notably, GradPower requires only a single-line code change and no modifications to the base optimizer's internal logic, including the hyperparameters. When applied to Adam (termed AdamPower), GradPower consistently achieves lower terminal loss across diverse architectures (LLaMA, Qwen2MoE), parameter scales (66M to 2B), datasets (C4, OpenWebText), and learning-rate schedules (cosine, warmup-stable-decay). The most pronounced gains are observed when training modern mixture-of-experts models with warmup-stable-decay schedules. GradPower also integrates seamlessly with other state-of-the-art optimizers, such as Muon, yielding further improvements. Finally, we provide theoretical analyses that reveal the underlying mechanism of GradPower and highlight the influence of gradient noise.

03.
medRxiv (Medicine) 2026-06-16

MRMU: A New Paradigm for Mendelian Randomization by Accounting for Measured Covariates and Unmeasured Confounders

Mendelian randomization (MR) is a powerful approach for causal inference, however, its reliability is frequently compromised by unadjusted covariates and unmeasured confounders, such as unmeasured pleiotropy and sample structure. To address these challenges, we introduce MRMU, a novel paradigm for the MR framework. Unlike traditional single-variable or multivariable MR methods, MRMU selects instrumental variables only from the exposure of interest and estimates one exposure effect at a time, while jointly accounting for measured covariates and unmeasured confounders. This design improves the reliability of MR analyses. In simulations and real data, MRMU achieved better type I error control, higher statistical power, and more accurate effect estimation than existing MR methods. Applying to coronary artery disease (CAD), MRMU identified robust cardiometabolic risk factors, including LDL-C, APOB, systolic blood pressure, body mass index, and smoking initiation, with consistent evidence across multiple CAD datasets. In contrast, traits such as HDL-C, height, and educational attainment, which were found to be significant by existing MR methods, were no longer supported by MRMU. MRMU further supported blood pressure-related traits, rather than lipid traits, as the more relevant pathway linking urate to CAD. Finally, by integrating large-scale plasma proteomics data, MRMU identified candidate CAD drug targets beyond established HMGCR- and PCSK9-related pathways, highlighting its utility for therapeutic target prioritization.

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

Dual-Network PINNs for Optimal Control: A Reproducible Benchmark on the Mass-Spring-Damper System

arXiv:2606.15271v1 Announce Type: cross Abstract: This work presents a transparent and reproducible benchmark study of a direct dual-network Physics-Informed Neural Network (PINN) formulation for the optimal control of a mass-spring-damper system. The classical linear-quadratic optimal control problem is solved by two independent classical methods – Pontryagin's Minimum Principle with single shooting, and direct transcription through trapezoidal collocation – and recast as a constrained optimization problem solved by two feedforward neural networks: a state network whose boundary conditions are enforced exactly through a composite cubic-and-mask ansatz, and an unconstrained control network. The composite loss combines the physics residual at the collocation points with a trapezoidal approximation of the cost functional, weighted by a single scalar hyperparameter. On the benchmark considered, the PINN reproduces the classical optimal cost to four significant digits, satisfies the terminal state constraints exactly by construction, and produces pointwise state and control errors that fall within the spread of the two classical references. Training is approximately two orders of magnitude slower than classical shooting on this benchmark, which is honestly reported. The contribution is methodological clarity rather than methodological novelty: the formulation and the accompanying Google Colab implementation are intended to lower the barrier to entry for practitioners exploring PINN-based optimal control without prior exposure to adjoint methods or two-point boundary value problems.

05.
bioRxiv (Bioinfo) 2026-06-12

Deciphering cross-omics complexity of tissues via diagonal integration of unpaired spatial multi-omics data

Recent spatial multi-omics technologies enable the simultaneous in situ profiling of multiple omics modalities on the same tissue section; however, they face challenges in experimental complexity and high costs. This technical limitation can be circumvented by diagonal integration methods, which integrate omics data from different modalities. However, existing single-cell diagonal integration approaches overlook spatial information, causing unreliable anchoring across omics layers. Here, we introduce STAMO, a graph attention neural network model for spatially aware integration of unpaired spatial slices from different omics. Systematic benchmarking on spatial epigenome-transcriptome slices proves that STAMO outperforms the state-of-the-art methods in generating aligned embeddings and identifying consensus spatial domains across omics. We apply STAMO to integrate unpaired data from diverse spatial omics types (transcripts, epigenetics, DNA, and proteins), including slices from spatial RNA and four different epigenomic modalities, spatial ATAC and RNA slices across embryonic stages, spatial protein and RNA slices, and spatial DNA and RNA slices. In addition, the integration capability of STAMO can be further used to achieve cross-omics generation, offering a solution for exploring spatial region-specific gene regulatory mechanisms.

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

Design and Scheduling of an AI-based Queueing System

arXiv:2406.06855v3 Announce Type: replace-cross Abstract: To leverage prediction models to make optimal scheduling decisions in service systems, we must understand how predictive errors impact congestion due to externalities on the delay of other jobs. Motivated by applications where prediction models interact with human servers (e.g., content moderation), we consider a large queueing system comprising of many single server queues where the class of a job is estimated using a prediction model. By characterizing the impact of mispredictions on congestion cost in heavy traffic, we design an index-based policy that incorporates the predicted class information in a near-optimal manner. Our theoretical results guide the design of predictive models by providing a simple model selection procedure with downstream queueing performance as a central concern, and offer novel insights on how to design queueing systems with AI-based triage. We illustrate our framework on a content moderation task based on real online comments, where we construct toxicity classifiers by finetuning large language models.

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

The Algorithm Is Not the Behavior: Learned Priors Override Look-Ahead in a Chess-Playing Neural Network

arXiv:2508.21380v3 Announce Type: replace-cross Abstract: Recent mechanistic work has uncovered learned algorithms within neural networks, from modular arithmetic to search and planning in game-playing agents. But does algorithmic structure guarantee algorithmic behavior? We investigate this in Leela Chess Zero, the strongest neural chess engine, where prior work identified learned look-ahead. By extending the logit lens to its move-selecting policy network, we discover that correct puzzle solutions-including immediate checkmates-often appear in intermediate layers but are systematically overridden in the final output, a phenomenon we term "forgotten puzzles". Replicating prior analyses on these positions, we find that look-ahead operates normally-future moves of the correct continuation are represented, causally important, and linearly decodable-ruling out a failure of the algorithm itself. Instead, late layers increasingly shift toward prioritizing safe play over aggression. To test whether this shift drives the override, we steer the model against these preferences and recover 61.7% of forgotten puzzles, providing causal evidence that safety priors override algorithmically computed solutions. These findings demonstrate that algorithmic structure does not guarantee algorithmic behavior: a model can internally solve a problem and still output the wrong answer.

09.
medRxiv (Medicine) 2026-06-11

Neighborhood socioeconomic status associated with post-stroke cognitive impairment: a retrospective cohort study

Background: Late complications after stroke (LCAS), including cognitive symptoms, impact quality of life and recovery. It is not known if neighborhood-level measures of socioeconomic status (SES) influence LCAS. This study assessed associations between SES measures, including neighborhood income inequality (Gini) and area deprivation index (ADI), and cognitive symptoms after acute ischemic stroke (AIS) in a hospital leveraging active surveillance of LCAS. Methods: This retrospective cohort study included 512 patients hospitalized with AIS at Tufts Medical Center with subsequent follow-up (between zero and three months or between three and twelve months) in the Stroke Clinic from 1/1/2018 - 12/31/2022. Using ZIP code data, patients were characterized as low Gini (low inequality) and high ADI (high deprivation) (Gini = 5) by state medians. These variables were combined, indicating patients who were living in both a low Gini and high ADI neighborhood to evaluate the effects of living in a homogeneously deprived area. There were 206 and 281 patients in the low Gini and high ADI groups respectively. 140 patients lived in a low Gini and high ADI neighborhood. The multivariable logistic analysis assessed the likelihood of cognitive symptoms, adjusting for age, race, ethnicity, sex, NIH Stroke Scale (NIHSS), thrombolysis, active LCAS surveillance, poverty, and ADI-Gini combination. Results: There were no associations between high ADI (OR: 1.03, 95% CI: 0.67 ? 1.57) or low Gini (OR: 1.74, 95% CI: 0.98 ? 3.07) alone and cognitive symptoms after AIS. However, the combined variable demonstrated increased likelihood of cognitive symptoms in the high ADI-low Gini group (OR: 1.82, 95% CI: 1.08 ? 3.06). Conclusions: This study suggests that individuals living in homogeneously deprived neighborhoods report higher likelihood of cognitive symptoms after AIS. Further studies with increased power are needed to investigate the underlying causes of these disparities and to develop interventions to reduce these complications.

10.
arXiv (CS.AI) 2026-06-19

See-and-Reach: Precise Vision-Language Navigation for UAVs within the Field of View

arXiv:2606.20045v1 Announce Type: cross Abstract: UAV Vision-Language Navigation (UAV-VLN) is typically formulated as a holistic search-and-reach problem, where long-range target discovery and final target approach are optimized and evaluated jointly. This formulation makes it difficult to assess a critical capability of aerial embodied agents, namely whether a UAV can accurately ground a visible target and translate vision-language evidence into precise 3D motion once the target enters its field of view. To address this limitation, we introduce UAV-VLN-FOV, a target-visible navigation task that isolates the see-and-reach stage and enables a more diagnostic evaluation of terminal reaching ability. We further propose 3DG-VLN, a vision-language waypoint prediction framework guided by dynamic 3D direction cues to enhance fine-grained visual grounding and spatial direction alignment for precise target reaching. Specifically, 3DG-VLN adaptively processes high-resolution front-view and downward-view observations to preserve fine-grained visual and geometric details for target grounding. It also updates the target-relative direction online during closed-loop navigation, allowing the agent to maintain spatial alignment with the target and reduce accumulated direction drift. To support this task, we construct a dedicated high-resolution benchmark which contains 2,717 trajectories with target-oriented high-level instructions, high-resolution front-view and downward-view egocentric observations, and continuous 3D waypoint annotations. Experiments show that 3DG-VLN outperforms competitive UAV-VLN baselines, achieving a 13.82\% improvement in success rate. Real-world trials further demonstrate the potential of 3DG-VLN for practical see-and-reach navigation. The source code and benchmark are available at https://github.com/xuefanfu/3DG-VLN.

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

CheXGenBench: A Unified Benchmark For Fidelity, Privacy and Utility of Synthetic Chest Radiographs

Structured benchmarks have advanced text-conditional image generation for real-world imagery, however, no such benchmark exists for synthetic radiograph generation. Despite being a highly active area of research, existing studies continue adopting inconsistent evaluation protocols and lack a unified assessment of the three most critical criteria: generative fidelity, privacy risk, and downstream utility. To address these limitations, we introduce CheXGenBench, the first unified evaluation framework for synthetic chest radiograph generation that simultaneously assesses fidelity, privacy risks, and downstream utility across frontier text-to-image (T2I) generative models. Our evaluation protocol, comprising over 20 quantitative metrics, covers 11 leading T2I architectures with plug-and-play integration for newer models. Through a rigorous and fair evaluation protocol, we establish comprehensive baseline state-of-the-art (SoTA) performances across all dimensions to guide future research. Furthermore, our results uncover several limitations of current generative models, which include first, even SoTA models struggle with long-tailed medical distributions; second, models pose high privacy risks regardless of fidelity quality; and third, while synthetic data already benefits downstream classification, it is of limited utility for downstream multimodal tasks. Drawing from these results, we propose concrete research directions to advance the field. The code is available at https://github.com/Raman1121/CheXGenBench

12.
arXiv (CS.CV) 2026-06-17

GOT-JEPA: Generic Object Tracking with Model Adaptation and Occlusion Handling using Joint-Embedding Predictive Architecture

The human visual system tracks objects by integrating current observations with previously observed information, adapting to target and scene changes, and reasoning about occlusion at fine granularity. In contrast, recent generic object trackers are often optimized for training targets, which limits robustness and generalization in unseen scenarios, and their occlusion reasoning remains coarse, lacking detailed modeling of occlusion patterns. To address these limitations in generalization and occlusion perception, we propose GOT-JEPA, a model-predictive pretraining framework that extends JEPA from predicting image features to predicting tracking models. Given identical historical information, a teacher predictor generates pseudo-tracking models from a clean current frame, and a student predictor learns to predict the same pseudo-tracking models from a corrupted version of the current frame. This design provides stable pseudo supervision and explicitly trains the predictor to produce reliable tracking models under occlusions, distractors, and other adverse observations, improving generalization to dynamic environments. Building on GOT-JEPA, we further propose OccuSolver to enhance occlusion perception for object tracking. OccuSolver adapts a point-centric point tracker for object-aware visibility estimation and detailed occlusion-pattern capture. Conditioned on object priors iteratively generated by the tracker, OccuSolver incrementally refines visibility states, strengthens occlusion handling, and produces higher-quality reference labels that progressively improve subsequent model predictions. Extensive evaluations on seven benchmarks show that our method effectively enhances tracker generalization and robustness.

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

Ensemble RL through Classifier Models: Enhancing Risk-Return Trade-offs in Trading Strategies

Authors:

arXiv:2502.17518v3 Announce Type: replace-cross Abstract: This paper presents a comprehensive study on the use of ensemble Reinforcement Learning (RL) models in financial trading strategies, leveraging classifier models to enhance performance. By combining RL algorithms such as A2C, PPO, and SAC with traditional classifiers like Support Vector Machines (SVM), Decision Trees, and Logistic Regression, we investigate how different classifier groups can be integrated to improve risk-return trade-offs. The study evaluates the effectiveness of various ensemble methods, comparing them with individual RL models across key financial metrics, including Cumulative Returns, Sharpe Ratios (SR), Calmar Ratios, and Maximum Drawdown (MDD). Our original experimental results demonstrate that ensemble methods often outperform base models in terms of risk-adjusted returns, providing better management of drawdowns and overall stability. However, both the original analysis and the additional reproduction reported in this version show that ensemble performance is sensitive to the choice of variance threshold \(\tau\), classifier group, RL-agent pair, and market universe. The reproduction evidence strengthens the conclusion that classifier-assisted ensemble selection can improve robustness, while also clarifying that the advantage is conditional rather than automatic across all datasets. This study emphasizes the value of combining RL with classifiers for adaptive decision-making, with implications for financial trading, robotics, and other dynamic environments.

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

MineExplorer: Evaluating Open-World Exploration of MLLM Agents in Minecraft

Multimodal large language models (MLLMs) have shown strong capabilities in perception, reasoning, and action generation. However, their ability to sustain exploration in dynamic open worlds remains unclear. Existing embodied and game-based benchmarks often compress interaction into short-horizon tasks or entangle success with domain-specific game mechanics. In this paper, we introduce MineExplorer benchmark for evaluating open-world exploration capabilities of MLLM agents in Minecraft. We first filter atomic tasks whose solutions rely heavily on Minecraft-specific knowledge to better reflect general open-world reasoning. Then we organize the benchmark around a ReAct-style capability formulation and compose atomic tasks into implicit multi-hop tasks. To further construct reliable instances, MineExplorer uses a multi-agent synthesis workflow that jointly designs task graphs, sandbox scenes, and rule-based milestone evaluators. Human evaluation shows that the multi-agent synthesis workflow produces significantly more reliable instances than a single-agent baseline. Experiments with advanced MLLM agents show that open-world exploration remains challenging, as strong models can handle many single-hop tasks but degrade sharply when hidden prerequisites must be coordinated over longer trajectories. Further analysis finds that task difficulty tracks agent completion, and larger models or thinking modes do not consistently translate into better performance. Code and dataset are available at https://github.com/Jometeorie/MineExplorer.

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

Near-Optimal Regret for Distributed Adversarial Bandits: A Black-Box Approach

arXiv:2602.06404v2 Announce Type: replace Abstract: We study distributed adversarial bandits, where $N$ agents cooperate to minimize the global average loss while observing only their own local losses. We show that the minimax regret for this problem is $\tilde{\Theta}(\sqrt{(\rho^{-1/2}+K/N)T})$, where $T$ is the horizon, $K$ is the number of actions, and $\rho$ is the spectral gap of the communication matrix. Our algorithm, based on a novel black-box reduction to bandits with delayed feedback, requires agents to communicate only through gossip. It achieves an upper bound that significantly improves over the previous best bound $\tilde{O}(\rho^{-1/3}(KT)^{2/3})$ of Yi and Vojnovic (2023). We complement this result with a matching lower bound, showing that the problem's difficulty decomposes into a communication cost $\rho^{-1/4}\sqrt{T}$ and a bandit cost $\sqrt{KT/N}$. We further demonstrate the versatility of our approach by deriving first-order and best-of-both-worlds bounds in the distributed adversarial setting. Finally, we extend our framework to distributed linear bandits in $R^d$, obtaining a regret bound of $\tilde{O}(\sqrt{(\rho^{-1/2}+1/N)dT})$, achieved with only $O(d)$ communication cost per agent and per round via a volumetric spanner.

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

MVEB: Massive Video Embedding Benchmark

We introduce the Massive Video Embedding Benchmark (MVEB), a 23-task benchmark for video embeddings spanning classification, zero-shot classification, clustering, pair classification, retrieval, and video-centric question answering. We evaluate 33 models and find that no single model dominates: MLLM-based embeddings lead on classification, clustering, pair classification, and QA; multimodal binding leads on retrieval and zero-shot classification; generative MLLMs without contrastive adaptation collapse on cross-modal tasks. Paired video-only vs. audio+video evaluations show that audio's contribution depends on dataset annotation provenance: audio helps when labels were produced from both modalities and hurts when they were produced from visuals alone, a six-point gap consistent across model families. MVEB is derived from MVEB+, a 184-task pool, and is designed to maintain task diversity while reducing evaluation cost. It integrates into the MTEB ecosystem for unified evaluation across text, image, audio, and video. We release MVEB and all 184 tasks along with code and a leaderboard at https://github.com/embeddings-benchmark/mteb.

17.
arXiv (quant-ph) 2026-06-12

Theoretical Study for Generating Optical GKP State via a Single-Photon-Added Squeezed Vacuum

arXiv:2606.12467v1 Announce Type: new Abstract: A theoretical framework is developed to analyze the generation of the optical GKP state using a single-photon-added squeezed vacuum. This state, defined by the squeezing parameter $r$, is injected into a 50:50 beam splitter, and the optical GKP state is obtained through conditional measurement at one output port. The single-photon-added squeezed vacuum is especially prominent in this context because it provides a simpler and more experimentally accessible ingredient than Schrodinger cat states, while conditional measurement ensures projection onto a state that closely approximates the finite-energy GKP form. Fidelity is employed to quantify this closeness, and the analysis demonstrates that the scheme achieves a maximum fidelity of 85% at a squeezing level of $3.76 \ dB$. This performance surpasses approaches based on squeezed optical odd Schrodinger cat states, underscoring the single-photon-added squeezed vacuum as a practical and effective pathway toward fault-tolerant photonic quantum computing.

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

Decoding the Multimodal Maze: A Systematic Review on the Adoption of Explainability in Multimodal Attention-based Models

arXiv:2508.04427v2 Announce Type: replace-cross Abstract: Multimodal learning has witnessed remarkable advancements in recent years, particularly with the integration of attention-based models, leading to significant performance gains across a variety of tasks. Parallel to this progress, the demand for explainable artificial intelligence (XAI) has spurred a growing body of research aimed at interpreting the complex decision-making processes of these models. This systematic literature review analyzes research published between January 2020 and early 2024 that focuses on the explainability of multimodal models. Framed within the broader goals of XAI, we examine the literature across multiple dimensions, including model architecture, modalities involved, explanation algorithms and evaluation methodologies. Our analysis reveals that most studies are concentrated on vision-language and language-only models, with attention-based techniques being the most commonly employed for explanation. However, these methods often fall short in capturing the full spectrum of interactions between modalities, a challenge further compounded by the architectural heterogeneity across domains. Importantly, we find that evaluation methods for XAI in multimodal settings are largely non-systematic, lacking consistency, robustness, and consideration for modality-specific cognitive and contextual factors. To address these gaps, we not only synthesize findings from the surveyed works but also incorporate a complementary analysis that integrates recent and emerging advances driving multimodal explainability. Based on these insights, we provide a comprehensive set of recommendations aimed at promoting rigorous, transparent, and standardized evaluation and reporting practices in multimodal XAI research. Our goal is to support future research in more interpretable, accountable, and responsible multimodal AI systems, with explainability at their core.

19.
arXiv (math.PR) 2026-06-15

Ergodicity for stochastic 2D Boussinesq equations with a highly degenerate pure jump Levy noise

arXiv:2503.18045v2 Announce Type: replace Abstract: This study aims to analyze the ergodicity for stochastic 2D Boussinesq equations and explore the impact of a highly degenerate pure jump L\'{e}vy noise acting only in the temperature equation, where this noise could appear on only a few Fourier modes. By leveraging the equi-continuity of the semigroup established through Malliavin calculus and an analysis of stochastic calculus, together with the weak irreducibility of the solution process, we prove the existence and uniqueness of the invariant measure. Moreover, we overcome the main challenge of establishing time asymptotic smoothing properties of the Markovian dynamics corresponding to this system by conducting spectral analysis of the Malliavin covariance matrix.

20.
bioRxiv (Bioinfo) 2026-06-18

Deciphering shared and divergent tissue architectures from cross-species spatial transcriptomics

Authors:

The integration of spatial transcriptomics (ST) data across species is essential for cross-species and translational studies, but remains challenging due to molecular divergence and anatomical differences between organisms. We present STACAME, a graph attention autoencoder-based framework to decipher shared and divergent tissue architectures from cross-species ST data by explicitly modeling both orthologous and species-specific genes. STACAME aligns ST slices in a spatially aware manner, identifies homologous and species-specific domains, and enables a suite of downstream comparative analyses. We demonstrate its utility by integrating ST datasets from diverse tissues, including hippocampus, isocortex, embryo, breast, liver, and cerebellum, across multiple species such as human, macaque, marmoset, mouse, and zebrafish. STACAME supports cross-species spatial domain alignment, the detection of shared and divergent spatially variable genes, development alignment and comparison, and the 3D integration of tissue architecture. This flexible approach facilitates the translation of findings from model organisms to humans, providing a unified computational platform for cross-species spatial transcriptomics.

21.
arXiv (CS.LG) 2026-06-11

Reliable Error Estimation for PINNs: Lower and Upper A Posteriori Bounds

arXiv:2606.12050v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) combine machine learning with physical laws to solve differential equations. While existing results provide rigorous a posteriori upper bounds for PINN prediction errors, complete certification also requires complementary lower information in order to obtain computable two-sided error enclosures. In this paper, we derive computable a posteriori lower bounds for PINN errors in ordinary differential equations on suitable certified state-space domains under a localized strong monotonicity condition. We combine these estimates with complementary localized upper bounds under a one-sided Lipschitz condition, which is weaker than the global Lipschitz assumption used in previous work and can yield sharper upper error bands. The resulting bounds depend only on the neural-network approximation, the ODE residual, and local monotonicity and growth constants, and therefore do not require access to the exact solution. For linear time-invariant and time-varying systems, we further derive explicit formulas in terms of the minimal and maximal eigenvalues of the symmetric part of the system matrix. We also discuss the distinction between soft and hard enforcement of initial conditions in PINNs and explain why exact enforcement can make the scalar lower certificate uninformative. To recover nontrivial lower information in the linear setting, we use a signed-residual finite-probe certificate based on coordinate unit vectors. We also formulate a certificate-informed training strategy in which the propagated upper certificate is used as an auxiliary regularizer, while lower certificates remain post-training diagnostics. Altogether, the proposed framework provides rigorous and practically computable error certificates for PINN approximations of ODEs, while making explicit the domains and model classes for which the assumptions can be verified.

22.
arXiv (CS.CL) 2026-06-15

OmniOPD: Logit-Free On-Policy Distillation via Speculative Verification

On-Policy Distillation (OPD) trains a student model on its own generative trajectories under dense token-level feedback from a stronger teacher, mitigating both the off-policy distribution shift of Supervised Fine-Tuning (SFT) and the sparse credit assignment of Reinforcement Learning (RL). However, standard OPD faces two coupled limitations. First, it requires direct access to the teacher's token-level logits, excluding a broad class of capable proprietary models from serving as teachers. Second, the token-level logit signal itself is brittle, depending on a narrow overlap of plausible next tokens between teacher and student, and prone to amplifying degenerate patterns such as repetition loops. In this paper, we introduce OmniOPD, a novel framework that addresses both limitations through a logit-free, chunk-level supervision signal. OmniOPD replaces deterministic logit matching with Monte Carlo rollouts that approximate the teacher's local preferences through a continuous semantic similarity metric over multi-token chunks, and concentrates this supervision via a peak-entropy scheduler that audits the student only at its high-uncertainty reasoning forks. A Dirichlet-Multinomial Bayesian prior and a base-model KL anchor further bound the variance of discrete sampling and prevent policy collapse across unaudited tokens. Across competitive benchmarks, OmniOPD surpasses the standard OPD approach by up to +28.64% on math, confirming that chunk-level semantic verification extracts a more reliable learning signal than token-level logit matching, whose high information density is offset by significant noise and brittleness. Furthermore, when paired with stronger black-box teachers such as Claude-4.5-Haiku and Gemini-2.5-Flash, OmniOPD achieves an additional +9.54% relative on math over its open-weight teacher counterpart, advancing the student past the performance of self-exploratory RL.

23.
arXiv (quant-ph) 2026-06-16

Quantum optimal control of steady orbits

arXiv:2606.15383v1 Announce Type: new Abstract: Periodically driven dissipative systems can settle into steady orbits - fixed loops on their dynamical manifolds. In quantum mechanics, steady orbits occur in cooling engines (used to initialise quantum devices), coherent oscillators (such as lasers and masers), precision metrology devices (atomic clocks, optical and spin magnetometers), and magnetic resonance (steady state free precession, dynamic nuclear polarisation). Steady orbits and stroboscopic steady states are a promising target for quantum optimal control, but the numerical complexity is prohibitive: the infinite loop defeats gradient ascent pulse engineering (GRAPE) which relies on explicit numerical propagation in the time domain. Here we propose an efficient quantum control strategy for stroboscopic steady states and limit cycles that are approached asymptotically when a control sequence is repeated infinitely many times. The formalism is different from Floquet-Lindblad state engineering and effective Hamiltonian theories: it finds control sequences that drive a dissipative quantum system towards a steady orbit passing through user-specified waypoints. The software implementation (same numerical complexity scaling as GRAPE) is done for the Spinach library.

24.
arXiv (quant-ph) 2026-06-12

Influence-solvability: a systematic theory of $(1+1)D$ solvability and its application to brickwork circuits

arXiv:2606.12538v1 Announce Type: cross Abstract: `Solvable' circuits, such as dual unitaries and its generalisations, have arisen as paradigmatic examples of tractable chaotic non-equilibrium dynamics, both in classical and quantum systems. However, while increasingly more complicated sufficient conditions have been proposed, a systematic theory classifying and understanding general features of solvable circuits is missing. We develop such a theory by introducing influence-solvable circuits, a class of $(1+1)D$ circuits whose influence matrix, which represents the `bath' generated by its own evolution, is given by a uniform MPS with finite bond-dimension $\chi$. This property allows for efficient computation of subsystem dynamics and essentially contains all known examples of solvable circuits. We derive a set of necessary and sufficient local conditions by using a version of the fundamental theorem of MPS for open boundary conditions. Next we apply our theory to brickwork circuits with $\chi=1$ influence-solvability and perform a systematic classification of classical brickwork circuits with local dimension up to $d=3$ and quantum brickwork circuits with $d=2$. Our search reveals new solvable circuits that are not captured by known solvability conditions.

25.
arXiv (CS.CL) 2026-06-12

HKVM-RAG: Key-Value-Separated Hypergraph Evidence Organization for Multi-Hop RAG

Multi-hop RAG poses a data-engineering problem beyond passage matching: under fixed retrieval budgets, a system must organize retrieved text into evidence units that expose answer chains. Dense retrievers score passages independently, while graph-based memories make associations explicit but often rely on pairwise or entity-centered keys that fragment multi-hop evidence. We present HKVM-RAG, a key-value-separated evidence-organization layer. It assembles answer-path hyperedges from cached passage-level LLM evidence tuples and uses them as retrieval keys, while retaining passage text as answer values. To isolate key-space design, our fixed-substrate protocol holds the tuple cache, candidate passages, reader, and evaluation budget constant across pairwise graph and hypergraph variants. Weighted hypergraph key-value retrieval improves over KG-PPR by +3.426 F1 on 2WikiMultiHopQA and +3.592 F1 on MuSiQue; HotpotQA shows that higher structured support coverage need not yield standalone answer-F1 gains. We therefore study WHG-KV as an evidence-control signal rather than a dense-retrieval replacement. Oracle and train-to-dev analyses identify support selection as repairable, and a dense-aware controller combines frozen ColBERTv2 and HKVM rank/score features using out-of-fold HKVM predictions. It reaches 88.846, 65.073, and 85.810 F1 on the three benchmarks, improving over ColBERTv2 by +11.084, +6.763, and +5.966 F1. Source-level ablations show that matched non-WHG structured signals do not match the WHG-KV gains. These results provide bounded evidence that key-value-separated hypergraph organization can serve as a reusable evidence-control mechanism for multi-hop RAG.