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01.
arXiv (math.PR) 2026-06-18

On a class of reflected McKean-Vlasov Stochastic Differential Equations with jumps

arXiv:2606.18433v1 Announce Type: new Abstract: This paper investigates a class of reflected McKean-Vlasov Stochastic Differential Equations driven by both Brownian motion and a compensated Poisson random measure. We establish the existence and uniqueness of solutions and provide moments estimates for the state processes.

02.
arXiv (quant-ph) 2026-06-12

Beyond-Third-Order Quantum Coherence in Two-Dimensional Spectroscopy via Order-Selective Isolation

arXiv:2606.12794v1 Announce Type: new Abstract: A central challenge in nonlinear spectroscopy is the order-selective readout of weak higher-order responses that spectrally overlap with dominant lower-order signals. This bottleneck is particularly severe in two-dimensional (2D) spectroscopy, where extending conventional phase-cycling schemes to higher orders rapidly increases measurement and analysis complexity. Here we introduce a computation-assisted strategy that combines rotating-frame acquisition with a frame-shift tracking algorithm to separate signals by their frame-dependent spectral shifts. In a rubidium vapor experiment, we use this approach to isolate a 7th-order nonlinear contribution from coexisting 3rd-order components, enabling direct access to higher-order quantum-coherence dynamics without sacrificing operation at comparatively high pulse intensities. The method is broadly compatible with multidimensional spectroscopy platforms and provides a practical route to probing many-body and collective ultrafast dynamics beyond third order.

03.
arXiv (math.PR) 2026-06-18

On a class of unbalanced step-reinforced random walks

arXiv:2504.14767v4 Announce Type: replace Abstract: A step-reinforced random walk is a discrete-time stochastic process with long-range dependence. At each step, with a fixed probability $\alpha$, the so-called positively step-reinforced random walk repeats one of its previous steps, chosen randomly and uniformly from its entire history. Alternatively, with probability $1-\alpha$, it makes an independent move. For the so-called negatively step-reinforced random walk, the process is similar, but any repeated step is taken with its direction reversed. These random walks have been introduced respectively by Simon (1955) and Bertoin (2024) and are sometimes refered to the self-confident step-reinforced random walk and the counterbalanced step-reinforced random walk respectively. In this work, we introduce a new class of unbalanced step-reinforced random walks for which we prove the strong law of large numbers and the central limit theorem. In particular, our work provides a unified treatment of the elephant random walk introduced by Schutz and Trimper (2004) and the positively and negatively step-reinforced random walks.

04.
arXiv (quant-ph) 2026-06-16

Systematic Construction of Time-Dependent Hamiltonians for Microwave-Driven Josephson Circuits

arXiv:2512.20743v4 Announce Type: replace Abstract: Time-dependent electromagnetic drives are fundamental for controlling complex quantum systems, including superconducting Josephson circuits. In these devices, accurate time-dependent Hamiltonian models are imperative for predicting their dynamics and designing high-fidelity quantum operations. Existing numerical methods, such as black-box quantization (BBQ) and energy-participation ratio (EPR), excel at modeling the static Hamiltonians of Josephson circuits. However, these techniques do not fully capture the behavior of driven circuits stimulated by external microwave drives, nor do they include a generalized approach to account for the inevitable noise and dissipation that enter through microwave ports. Here, we introduce numerical techniques that leverage classical microwave simulations, efficiently executable in finite-element solvers, to obtain the time-dependent Hamiltonian of microwave-driven superconducting circuits with arbitrary geometries under charge, flux, or mixed electromagnetic modulation. Importantly, our techniques do not rely on a lumped-element description of the superconducting circuit, in contrast to previous approaches to tackling this problem. We demonstrate the versatility of our approach by characterizing the driven properties of realistic circuit devices in complex electromagnetic environments, including coherent dynamics due to charge and flux modulation, as well as drive-induced relaxation and dephasing. Our techniques offer a powerful toolbox for optimizing circuit designs and advancing practical applications in superconducting quantum computing.

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

Shadow Engineering of Quantum Processes

arXiv:2606.12035v1 Announce Type: new Abstract: Characterizing quantum processes is essential for hardware benchmarking, error diagnosis, and algorithm verification. While recent work [PRX QUANTUM 4, 040337 (2023)] extended classical shadows from quantum state to quantum process, enabling efficient single-channel $\mathcal{E}$ property prediction, its applicability to composite processes $f(\mathcal{E}_1, \mathcal{E}_2,\cdots, \mathcal{E}_k)$ remains unexplored. We introduce shadow engineering, a framework encoding the classical shadows of processes into sparse transfer matrices to predict $f(\mathcal{E}_1, \mathcal{E}_2,\cdots, \mathcal{E}_k)$ properties with proven polynomial sample complexity, matching single-channel efficiency while exponentially lower than quantum process tomography. Crucially, this approach repurposes existing $\mathcal{E}_m$-shadow data without physical execution of $f(\mathcal{E}_1, \mathcal{E}_2,\cdots, \mathcal{E}_k)$, enabling flexible quantum process characterization with minimal hardware overhead. We demonstrate the framework's effectiveness and practicality on a superconducting quantum processor for typical applications such as error mitigation and Hamiltonian dynamical simulation. This framework unlocks new capabilities for predicting complex quantum behaviors without physical re-execution, with immediate applications in near-term device calibration and quantum simulation.

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

MASK: Multi-Agent Semantic K-Scheduling for Risk-Sensitive 6G Robotics

arXiv:2606.11249v1 Announce Type: cross Abstract: Realizing the vision of 6G connected robotics requires reconciling high-performance collaborative control with the rigid spectral limitations of physical wireless channels. In realistic collaborative sensing scenarios, spectral resources are quantized into finite physical resource blocks or orthogonal subcarriers, rendering simultaneous transmission by all agents infeasible. To address this, we propose Multi-Agent Semantic K-Scheduling (MASK), a control architecture designed to sustain robust, risk-aware coordination under strict instantaneous bandwidth caps. We introduce Arbiter-Assisted Semantic Information Gating (A-SIG), a lightweight coordination mechanism that enforces hard access constraints by scheduling only the top-K agents based on locally computed semantic importance scores. By aggregating these prioritized observations into a compact latent state, a self-supervised global encoder enables a distributional policy to mitigate tail risks despite data sparsity. We evaluate MASK across diverse benchmarks, demonstrating that it matches the performance of communication-unconstrained baselines even when channel access is restricted to a small fraction of the swarm size. Furthermore, the framework exhibits inherent resilience to packet erasures, validating semantic scheduling as a critical enabler for resource-constrained 6G systems.

07.
arXiv (CS.CV) 2026-06-12

Augmentation techniques for video surveillance in the visible and thermal spectral range

In intelligent video surveillance, cameras record image sequences during day and night. Commonly, this demands different sensors. To achieve a better performance it is not unusual to combine them. We focus on the case that a long-wave infrared camera records continuously and in addition to this, another camera records in the visible spectral range during daytime and an intelligent algorithm supervises the picked up imagery. More accurate, our task is multispectral CNN-based object detection. At first glance, images originating from the visible spectral range differ between thermal infrared ones in the presence of color and distinct texture information on the one hand and in not containing information about thermal radiation that emits from objects on the other hand. Although color can provide valuable information for classification tasks, effects such as varying illumination and specialties of different sensors still represent significant problems. Anyway, obtaining sufficient and practical thermal infrared datasets for training a deep neural network poses still a challenge. That is the reason why training with the help of data from the visible spectral range could be advantageous, particularly if the data, which has to be evaluated contains both visible and infrared data. However, there is no clear evidence of how strongly variations in thermal radiation, shape, or color information influence classification accuracy. To gain deeper insight into how Convolutional Neural Networks make decisions and what they learn from different sensor input data, we investigate the suitability and robustness of different augmentation techniques...

08.
arXiv (CS.AI) 2026-06-19

Multi-Head Attention-Based Feature Extractor Integration with Soft Actor-Critic for Porosity Prediction and Process Parameter Optimization in Additive Manufacturing

arXiv:2606.20087v1 Announce Type: new Abstract: Additive manufacturing process optimization requires precise parameter control to minimize defects such as porosity. Traditional reinforcement learning (RL) approaches using discrete action spaces suffer from slow convergence and susceptibility to local optima, limiting their effectiveness for high-precision manufacturing tasks. This study addresses these limitations by employing a continuous action space combined with a novel architecture that integrates a multi-head attention mechanism with the Soft Actor-Critic (SAC) algorithm. The attention-based feature extractor enhances the agent's ability to capture subtle variations in low-dimensional input features, enabling more effective exploration-exploitation balance for navigating value spaces with local minima. We validate our approach on porosity prediction and process parameter optimization in laser powder bed fusion, demonstrating faster convergence and higher final reward values compared to standard RL methods including DQN, PPO, TD3, and vanilla SAC. The proposed methodology achieves a convergence value of 322.79 within 14 episodes, outperforming existing approaches while maintaining stability throughout training.

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

On Approximating the Dynamic Response of Synchronous Generators via Operator Learning: A Step Towards Building Deep Operator-based Power Grid Simulators

arXiv:2301.12538v2 Announce Type: replace-cross Abstract: This paper develops an Operator Learning framework for approximating the dynamic response of synchronous generators. The framework can be used to (i) build a neural network-based generator model that interacts with a power grid simulator or (ii) shadow the true generator's transient response. First, we develop a data-driven Deep Operator Network (DeepONet) to approximate the infinite-dimensional solution operator of the generators. Then, we design a numerical scheme based on DeepONet that simulates the generator's response over a given time horizon. The proposed scheme recursively employs the trained DeepONet to simulate the response for a given multi-dimensional input that describes the interaction between the generator and the power grid. In addition, we design a residual DeepONet numerical scheme that can incorporate information from existing mathematical models. We accompany this residual DeepONet scheme with an estimate for the prediction's cumulative error. Finally, we build a data aggregation (DAgger) strategy that allows fine-tuning of DeepONets using aggregated training data that the DeepONets will likely encounter during interactive simulations with other grid components. As a proof of concept, we demonstrate that the proposed frameworks can effectively approximate the transient model of a synchronous generator.

10.
arXiv (CS.AI) 2026-06-16

The Missing Knowledge Layer in Cognitive Architectures for AI Agents

arXiv:2604.11364v2 Announce Type: replace Abstract: The two most influential cognitive architecture frameworks for AI agents, CoALA [21] and JEPA [12], both lack an explicit Knowledge layer with its own persistence semantics. This gap produces a category error: systems apply cognitive decay to factual claims, or treat facts and experiences with identical update mechanics. We survey persistence semantics across existing memory systems and identify eight convergence points, from Karpathy's LLM Knowledge Base [10] to the BEAM benchmark's near-zero contradiction-resolution scores [22], all pointing to related architectural gaps. We propose a four-layer decom position (Knowledge, Memory, Wisdom, Intelligence) where each layer has fundamentally different persistence semantics: indefinite supersession, Ebbinghaus decay, evidence-gated revision, and ephemeral inference respectively. Companion implementations in Python and Rust demonstrate the architectural separation is feasible. We borrow terminology from cognitive science as a useful analogy (the Knowledge/Memory distinction echoes Tulving's trichotomy), but our layers are engineering constructs justified by persistence-semantics requirements, not by neural architecture. We argue that these distinctions demand distinct persistence semantics in engineering implementations, and that no current framework or system provides this.

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

PhysGuard: Fisher-Guided Gradient Projection for Sim-to-Real Neural PDE Surrogates

arXiv:2606.16602v1 Announce Type: new Abstract: Neural operator models trained on simulation data often lose accuracy when applied to experimental measurements due to the sim-to-real gap. Standard fine-tuning with limited real data can reduce this gap, but it may also damage the core physics-relevant representations learned during pretraining. Although knowledge-preserving adaptation has been widely investigated in vision or language tasks, it remains unclear whether these methods are suitable for neural operators whose architectures and protected knowledge are fundamentally different. Neural operators need to preserve core-scale physical structures rather than semantic or visual features. We propose PhysGuard, a physics-preserving framework for accurate sim-to-real adaptation of neural operators. Specifically, PhysGuard uses the empirical Fisher Information Matrix computed on simulation data to identify physics-critical parameter directions, then restricts fine-tuning updates to directions that do not interfere with them. A layer-wise Gram-matrix formulation makes this efficient for models with millions of parameters, while an adaptive threshold automatically determines the protected subspace size. A spectral probe experiment shows that the dominant Fisher directions are strongly associated with low-frequency output structures. Experiments on benchmark across four neural operator architectures and different physical systems show that PhysGuard performs strongly on most evaluation metrics compared to baselines. The benefits are most evident under severe domain shift, where it reduces low-frequency error by up to 32\% compared to standard fine-tuning while maintaining adaptability. Our code is available at https://github.com/ZhouChaunge/PhysGuard.

12.
arXiv (CS.AI) 2026-06-16

LLM-as-Code Agentic Programming for Agent Harness

arXiv:2606.15874v1 Announce Type: new Abstract: Every major LLM agent framework gives the LLM the role of orchestrator; the model decides what to do next, when to call tools, and when to stop. We argue that token explosion, control-flow hallucination, and unreliable completion are not implementation bugs but architectural consequences of assigning the deterministic work of looping, branching, and sequencing to a probabilistic system. A better prompt or a stronger model cannot guarantee the reliability of the LLM agent. We therefore propose Agentic Programming, in which the program governs all control flow, and the LLM is itself part of it, an adaptive component we call LLM-as-Code and invoke only where a task calls for reasoning or generation. Within each call the model keeps full flexibility, but it cannot alter the program's execution path. With control in the program, the LLM's context is built from the execution history's call tree and forms a directed acyclic graph (DAG). Each call's context length is then determined by its call depth rather than by accumulation over steps. A case study of computer-use agents shows that the design is practical, not just a theoretical stance, substantially improving the stability of long visual operation sequences.

13.
arXiv (CS.LG) 2026-06-11

Robustness of Mixtures of Experts to Feature Noise

arXiv:2601.14792v2 Announce Type: replace Abstract: Despite their practical success, it remains unclear why Mixture of Experts (MoE) models can outperform dense networks beyond sheer parameter scaling. We study an iso-parameter regime where inputs exhibit latent modular structure but are corrupted by feature noise, a proxy for noisy internal activations. We show that sparse expert activation acts as a noise filter: compared to a dense estimator, MoEs achieve lower generalization error under feature noise, improved robustness to perturbations, and faster convergence speed. Empirical results on synthetic data and real-world language tasks corroborate the theoretical insights, demonstrating consistent robustness and efficiency gains from sparse modular computation.

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

An End-to-End Hybrid Framework for Rumour Detection in Low-Resources Algerian Dialect

The rapid growth of social media has intensified the spread of rumours. This issue is more challenging in the Algerian context due to the informal and code-switched nature of dialectal content, the scarcity of annotated resources, and the limited effectiveness of standard Arabic NLP tools on dialect text. This paper presents an end-to-end rumour detection hybrid framework for Algerian dialect social media content. We build a domain-specific annotated dataset by combining real social media posts, synthetic data, and the FASSILA corpus, with automatic labeling based on a similarity-based annotation process. A transliteration pipeline is also introduced to generate parallel datasets in Arabic script and Arabizi. We evaluate multiple approaches, including classical machine learning, deep learning, transformers, and hybrid models. Experimental results show that a hybrid approach combining transformer embeddings with a classical classifier achieves the best performance, reaching an F1-score of 0.84. We also find that domain-specific pre-training is more important than model size, with social media-trained models outperforming larger models trained on formal Arabic corpora. These results demonstrate the feasibility of rumour detection in low-resource Algerian dialect settings.

15.
Science (Express) 2026-06-04

Long-range extended chains arising from polymerization-driven spontaneous assembly | Science

作者: 未知作者

A central challenge for conjugated polymers is to achieve long-range order while remaining solution-processable, which is essential for matching the electrical performance of their counterparts of crystalline inorganic semiconductors. Here we show that n-doped poly(benzodifurandione) (n-PBDF) can undergo polymerization-driven spontaneous assembly (PSA), in which chain growth, chemical doping, and structural ordering are intrinsically coupled, yielding long-range chain extension over hundreds of nanometers. We reveal that the spontaneously formed n-PBDF nanoribbons arise from a self-initiated, convergent growth mechanism driven by cooperative monomer–polymer interactions and stabilized by proton-coupled duplex chains and the polymer’s intrinsic polyelectrolyte character. With long-range extended chains in the nanoribbons, the aligned n-PBDF thin films demonstrate metallic-level conductivity (>10 4 Siemens per centimeter).

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

LapidaryEngine: Fully Conversational Crystal Generation

arXiv:2606.14215v1 Announce Type: new Abstract: The emergence of Large Language Models (LLMs) has inspired the vision of generating bespoke crystal materials directly from natural-language instructions, enabling users to design materials through intuitive, conversational interaction. Existing text-to-crystal generative models represent important early steps toward this goal, but they suffer from two critical limitations: (i) restricted input formats that require highly structured descriptions (e.g., chemical formulas), and (ii) one-directional generation, where models can map text to crystal but cannot perform the inverse. These limitations prevent fully conversational workflows and hinder alignment with users' inherently ambiguous and evolving desiderata. We address these challenges with LapidaryEngine, the first model to support fully conversational crystal generation. LapidaryEngine accepts free-form natural-language requests and performs iterative refinement and editing in a dialogue-like manner. The key innovation is a pivot representation, a third, intermediate form that enables bidirectional translation between text and crystal structures despite the absence of direct paired datasets. Leveraging this pivot allows robust interpretation of user feedback and precise structural control. We demonstrate LapidaryEngine across diverse tasks, including insulator discovery, stability optimization, compositional modification, and structural editing, showcasing its ability to align generated materials with user intent in an interactive manner.

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

Pose6DAug: Physically Plausible Multi-view Object Swapping for Robot Data Augmentation

arXiv:2606.20118v1 Announce Type: cross Abstract: Vision-language-action (VLA) policies have shown strong potential for general-purpose manipulation, yet they often fail on novel, out-of-distribution objects whose appearance or geometry deviates from the training distribution. The standard remedy is to collect multi-view teleoperation data for every failure case, but this scales poorly in both cost and time. We introduce Pose6DAug, a failure-driven data augmentation framework that turns a policy's own successful episodes into targeted demonstrations for its failure modes, without any new data collection. Our key insight is that each successful episode already encodes a physically valid action trajectory together with calibrated multi-view observations. By swapping only the manipulated object while preserving this trajectory, we obtain new and physically grounded demonstrations. However, naive 2D video editing breaks multi-view consistency and physical plausibility, particularly under heavy occlusion and egocentric viewpoints. Our method instead operates directly in 3D, anchoring the target object with an explicit mesh driven by a temporally coherent 6D pose trajectory, ensuring geometrically consistent renderings across all camera views. Fine-tuning a VLA on data augmented by our method improves success rates by 16.5% relative to the state-of-the-art baseline on novel objects, while preserving in-distribution performance. These results show that multi-view and physically consistent augmentation is a practical path to scalable VLA generalization.

18.
arXiv (math.PR) 2026-06-18

Power Partitions and Hayman Functions

arXiv:2602.18575v3 Announce Type: replace Abstract: We prove, within the probabilistic framework of Khinchin families, that the generating function $P_k$ of partitions into $k$-th powers is strongly Gaussian in the sense of Báez-Duarte, and even further that it is a Hayman function. Thus the Hardy–Ramanujan asymptotic formula for the number $p_k(n)$ of partitions of $n$ into $k$-th powers which reads \[ p_k(n) \sim \frac{\alpha_k}{n^{(3k+1)/(2k+2)}} \exp\!\Big(\beta_k\, n^{1/(k+1)}\Big), \qquad n\to\infty, \] where $\alpha_k$ and~$\beta_k$ are explicit constants depending only on $k$, follows directly from Hayman's asymptotic formula for strongly Gaussian power series. The proof of strong Gaussianity of $P_k$ combines a Gaussianity criterion for Khinchin families with certain bounds of Tenenbaum, Wu and Li on the generating function; the asymptotic formula is recovered by computing asymptotic approximations of the mean and variance of the associated family. Analogous results are presented for the generating function $Q_k$ of partitions into distinct $k$-th powers.

19.
arXiv (CS.CL) 2026-06-12

ArogyaSutra: A Multi-Agent Framework for Multimodal Medical Reasoning in Indic Languages

Multimodal Large Language Models (MLLMs) have shown promising reasoning capabilities in general domains, yet their performance remains limited in specialized settings such as healthcare, especially in multilingual and low-resource scenarios. This gap is critical in regions like rural India, where patients often express complex medical queries in native Indic languages and rely on multimodal inputs such as medical images. Existing English-centric MLLMs struggle to support such use cases, limiting equitable access to AI-driven healthcare assistance. To address this challenge, we introduce ArogyaBodha, a large-scale multilingual multimodal medical question-answer dataset constructed from eight heterogeneous sources, covering 31 body systems, six imaging modalities, and 21 clinical domains across English and seven major Indian languages. We further propose ArogyaSutra, an actor-critic-based multi-agent framework that integrates tool grounding with dual-memory mechanisms for step-wise, reasoning-aware decision making, and uses stored actor-critic simulation trajectories for distillation. Experiments show that our dataset and framework improve multilingual medical reasoning accuracy across all Indic languages, with ablations validating the contribution of each component. The source code and dataset are available at: https://iitp-cse.github.io/ ArogyaSutra/

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

VANDERER: Map-Free Exploration using Future-Aware and Visual-Curiosity-Guided Diffusion Policy

Mobile agents require efficient exploration strategies to map unseen environments and autonomously plan tasks. Traditional methods rely on generating occupancy maps and optimizing the sequence in which unexplored regions are visited. However, in sensor-constrained settings, such as those limited to monocular cameras, generating accurate occupancy maps is challenging. To address this, we propose VANDERER, an exploration framework that leverages a Visual Curiosity Module (VCM) to guide pre-trained diffusion policies using only monocular image data. This curiosity module predicts the outcomes of proposed actions via a navigation world model and evaluates them through a curiosity cost. The cost then guides the diffusion process toward generating actions that maximize exploration. Evaluated across diverse simulated environments, VANDERER consistently outperforms established baselines, exploring an average of 13.4% more area than NoMaD. Our results reveal a direct correlation between visual and geometric curiosity in outdoor environments, demonstrating that VANDERER can effectively leverage this relationship for efficient exploration using sensor-constrained agents.

21.
arXiv (CS.CL) 2026-06-18

Continual Adaptation for Pacific Indigenous Speech Recognition

Speech foundation models struggle with low-resource Pacific Indigenous languages because of severe data scarcity. Furthermore, full fine-tuning risks catastrophic forgetting. To address this gap, we present an empirical study adapting models to real-world Pacific datasets. We investigate the impact of data volume, adaptation strategies, and representational drift on speech foundation models for various Pacific languages. Additionally, we analyze a continual learning framework for sequential language acquisition. Empirical results across three distinct Pacific Indigenous languages demonstrate that adapting to these linguistically distant languages induces severe internal representational drift. Consequently, these models face a strict plasticity and stability dilemma. While LoRA adapts well initially, it suffers from catastrophic forgetting during sequential learning. Ultimately, this study highlights the urgent need for robust adaptation strategies tailored to underrepresented languages.

22.
arXiv (CS.CV) 2026-06-17

Disentangling Perception and Reasoning in Multimodal LLMs via Reward Design

Reinforcement learning with verifiable rewards has driven major gains in LLM reasoning, and it is intuitive to assume this recipe will transfer well to multimodal models. However, multimodal models do two things: first, perceive what is in an image, then reason about what it implies. Because these stages are graded jointly, it is hard to tell how much room reasoning alone has to grow. We study this on algorithmic visual puzzles, where both components are necessary and show that perception, not reasoning, is the binding constraint. Replacing images with simple textual descriptions raises performance by over 20 points on average for Claude models. We then evaluate six reward designs aimed at inducing visual grounding during reasoning without chain-of-thought supervision. Training Qwen-2.5-VL-7B with GRPO, reward design induces long, structured reasoning with self-reflection and visual references, yielding a 5.56-point gain over the base model. These gains are, however, uneven; no single reward improves all categories, and rewards with verifiable accuracy signals trade out-of-domain transfer for in-domain accuracy. These results point to perception-aware reward design as a path forward, so that signals correct perception at its source rather than the reasoning that inherits its errors.

23.
arXiv (math.PR) 2026-06-15

Lehner's operator norm formulas, semidefinite programming, and spiked matrix models

arXiv:2606.14687v1 Announce Type: new Abstract: Lehner (1999) derived elegant formulas for the operator norm $\|\mathfrak{X}\|$ of operators of the form $\mathfrak{X} = \mathbf{A}_0 \otimes \mathfrak{1} + \sum_{i = 1}^n \mathbf{A}_i \otimes \mathfrak{m}_i$, also easily generalized to the spectral edge $\lambda_{\max}(\mathfrak{X})$, in terms of nonlinear optimization problems over positive definite matrices. Here the $\mathbf{A}_i$ are finite-dimensional Hermitian matrices, the $\mathfrak{m}_i$ are either free semicircular or free Rademacher families of operators, and $\mathfrak{1}$ is the identity operator. We first show that both of Lehner's nonlinear optimizations can be rewritten as linear semidefinite programs (SDPs), even in the Rademacher case where Lehner's optimization is not itself convex. We give the primal and dual forms of these SDPs, derive the complementary slackness relations and consequences thereof, and propose that the SDPs are more stable and accurate than the iterative numerical scheme proposed in Lehner's original work. We then apply the SDPs from the semicircular case to spiked matrix models, studied recently via Lehner's formula by Bandeira, Cipolloni, Schröder, and van Handel (2024). We give a new proof of the Baik–Ben Arous–Péché (BBP) transition they establish in models with isotropic (but possibly correlated) Gaussian noise by constructing feasible variables for the associated primal and dual SDPs. Combining our construction with a sensitivity interpretation of optimal dual variables, we study the fluctuations of leading eigenvectors of such models. We conjecture and give numerical evidence that these fluctuations are Gaussian but anisotropic and non-universal, and that their covariance may be computed in terms of the optimizer of the dual of Lehner's formula, which in turn is approximately the leading eigenmatrix of a completely positive operator associated to the covariance of the noise model.

24.
arXiv (CS.LG) 2026-06-15

Implicit Variational Rejection Sampling

arXiv:2606.14235v1 Announce Type: new Abstract: Variational Inference (VI) is a fundamental inference technique in Bayesian machine learning for approximating complex posterior distributions. Traditional VI often relies on the mean-field factorization, which can inadequately capture true posterior complexity. Recent advancements have leveraged neural networks to model implicit distributions, offering increased flexibility. However, the practical constraints of neural network architectures still produces inaccuracies. In this paper, we propose a method called Implicit Variational Rejection Sampling (IVRS), which integrates implicit distributions with rejection sampling to improve the posterior approximation. Our method uses neural networks to construct implicit proposal distributions, and rejection sampling with a discriminator network that estimates the density ratio between the implicit proposal and the true posterior for refining the approximation. Towards this end, we introduce the Implicit Resampling Evidence Lower Bound (IR-ELBO) as a metric to characterize the resampled distribution's quality and derive a tighter variational lower bound. Experimental results demonstrate that our method outperforms traditional variational inference techniques.

25.
Nature (Science) 2026-06-17

Lethal plague outbreaks in Lake Baikal hunter-gatherers 5,500 years ago

Plague is among the most devastating diseases in human history1. However, early strains of the plague-causing bacterium Yersinia pestis lacked virulence factors that are required for the bubonic form until around 3,800 years ago2,3. Consequently, the morbidity and mortality of early plague strains remain unclear. Here we describe early plague strains that are associated with two phases of outbreaks among mid-Holocene hunter-gatherers near Lake Baikal in southeast Siberia, beginning from about 5,500 years ago. These outbreaks occur across four hunter-gatherer cemeteries, with a 39% detection rate for plague infection. By reconstructing kinship pedigrees, we show that small familial groups were affected, consistent with human-to-human spread of disease, and that the first outbreak occurred within a single generation. The infections appear to have resulted in acute mortality, especially among children (aged 8 to 11 years). We further note functional differences, including in the ypm superantigen locus, which is also present in present day Yersinia pseudotuberculosis. The new strains diverge ancestrally to known Y. pestis and constrain the timing of its emergence, indicating that this happened before approximately 5,700 years ago. These findings show that plague outbreaks happened earlier than previously thought and were indeed lethal. We contend that the occurrence of outbreaks among mid-Holocene hunter-gatherer communities well outside the sphere of Late Neolithic Europe challenges the notion that higher population densities and lifestyle changes during the Neolithic agricultural transition were prerequisites for plague epidemics. Analyses of ancient DNA from hunter-gatherers near Lake Baikal in southeast Siberia around 5,500 years ago indicate that highly virulent Yersinia pestis emerged earlier than previously estimated, far from the next known cases of infection in Late Neolithic Europe.