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01.
arXiv (math.PR) 2026-06-16

Quantitative Oppenheim Conjecture for Random Quadratic Forms and Optimal Variance Bounds in Function Fields

arXiv:2606.16699v1 Announce Type: cross Abstract: We prove a quantitative version of Oppenheim's conjecture in the function field setting. In order to do so, we compute the higher moments of the Siegel transform. In particular, we find an optimal bound on the variance of the number of lattice points in a set. Moreover, we compute the exact variance of the number of lattice points in a ball, which is of independent interest.

02.
arXiv (CS.AI) 2026-06-17

Towards Distributed Inference of LLMs on a P2P Network

arXiv:2606.17059v1 Announce Type: cross Abstract: Prefix caching can reduce LLM inference latency by reusing KV caches across requests with shared prompts, but cluster-scale reuse is challenging because caches are partitioned across nodes. We propose a decentralized, prefix-cache-aware routing scheme for peer-to-peer LLM serving. Each node maintains a local radix tree of its own cached prefixes and asynchronously refreshed estimates of peer caches using periodic anti-entropy. Requests are routed to the node with the longest estimated prefix match, without centralized coordination or KV-cache transfer. Stale metadata only causes cache misses, not incorrect outputs, making weak consistency sufficient for correctness. Evaluation on simulated MMLU workloads show that decentralized routing improves latency under low communication delay and skewed prefix distributions, while high network latency and affinity-induced hotspots limit its benefits.

03.
arXiv (CS.LG) 2026-06-15

XRDiff: Crystal Structure Prediction from Powder X-Ray Diffraction Data Using Diffusion Models

arXiv:2606.14003v1 Announce Type: cross Abstract: Determining the crystal structure of a material from its powder X-ray diffraction (PXRD) pattern is a central challenge in materials science. PXRD is an accessible and widely used characterization technique, yet recovering the atomic structure from diffraction data requires solving an underdetermined inverse problem due to the loss of phase information. Generative modeling can provide a prior over atomic structure and learn the mapping from PXRD patterns to crystal structures via simulated structure-spectrum pairs. We present XRDiff, a diffusion model that recovers crystal structures from PXRD given either the stoichiometry or, in a more challenging setting, the elemental constituents and total number of atoms in the unit cell. We evaluate on datasets where each stoichiometry has multiple polymorphs and all polymorphs of a given composition are held out together, ensuring that high performance reflects genuine use of the diffraction signal. XRDiff achieves strong structure recovery rates on simulated benchmarks, indicating that the model learns a spectrum-to-structure mapping precise enough to differentiate between polymorphs. To address generalization to experimental data, we compare a full-spectrum encoding against an encoding based on peak descriptors. The peak-based encoding generalizes substantially better, outperforming even a model trained on full spectra with augmentations fitted to the experimental noise distribution. These results demonstrate that representations robust to the noise and artifacts present in real-world PXRD offer a practical and scalable path toward closing the simulation-to-experiment gap, enabling zero-shot crystal structure solution from experimental PXRD with full or partial chemical composition input.

04.
arXiv (CS.AI) 2026-06-12

EpiBench: Verifiable Evaluation of AI Agents on Epigenomics Analysis

arXiv:2606.13602v1 Announce Type: new Abstract: We introduce EpiBench, a verifiable benchmark for short-horizon epigenomics analysis. EpiBench evaluates whether agents can make well-defined analysis decisions from realistic workflow states and return deterministically gradable answers. The benchmark includes 106 evaluations across CUT\&Tag/CUT\&RUN, ATAC-seq, ChIP-seq, and DNA methylation workflows. Across 5,088 valid trajectories from 16 model-harness pairs, no system passed a majority of attempts: GPT-5.5 / Pi led at 45.0\% (143/318 attempts; 95\% confidence interval (CI), 36.3–53.7), followed by GPT-5.5 / OpenAI Codex at 39.9\% (127/318 attempts; 95\% CI, 31.6–48.3). Claude Opus 4.8 Max / Pi and GPT-5.4 / Pi each passed 39.0\% (124/318 attempts; 95\% CI, 30.2–47.8 and 31.0–47.0, respectively). Performance varies across assay types, and many failed runs still contain parts of the correct answer. Agents often found the right files and computed useful intermediate results, but failed when the task required deeper, assay-specific scientific judgment.

05.
arXiv (CS.AI) 2026-06-19

ROSE: Benchmarking the Perception-to-Action Gap in Multimodal Models

arXiv:2606.19965v1 Announce Type: cross Abstract: Multimodal large language models (MLLMs) are increasingly expected to act on visual information, yet the same scene may require different actions under different task contexts. How reliably can a model turn the same visual evidence into the action required by the current context? To answer this question, we introduce \textsc{ROSE} (Reference-conditioned Oddity and Symbolic Execution), a controlled benchmark that holds the visual scene fixed while varying region constraints and required symbolic outputs. Through coupled counting and coordinate-action tasks, \textsc{ROSE} tests whether models can infer an implicit majority reference and act on the resulting fine-grained visual evidence under changing contexts. Across nine recent MLLMs, performance drops by as much as 44.5 percentage points from counting-oriented tasks to region-conditioned action, despite 98.8\% human performance. The gap persists on paired scenes and regions for which the same model returns the correct count, while global-click and matched local controls show that coordinate grounding explains only part of the loss, revealing a distinct, model-dependent bottleneck in turning shared visual evidence into context-specific actions.

06.
medRxiv (Medicine) 2026-06-22

Histologically validated diffusion MRI signatures of neuroinflammation and neurodegeneration in Alzheimer disease

Noninvasive neuroinflammation measurement remains a major barrier for Alzheimer disease (AD) therapeutics. We present generalized diffusion basis spectrum imaging (g-DBSI), a diffusion MRI framework that decomposes the tissue signal into biologically interpretable microstructural compartments. In postmortem Knight ADRC brains, g-DBSI-derived restricted isotropic fraction (RIF) and restricted anisotropic fraction (RAF) mapped cellularity and neurofilament density, while their ratio (RIF/RAF) tracked inflammatory cell density and peri-plaque amyloid-beta with higher specificity and regional consistency than RIF alone. In 112 living Knight ADRC participants stratified by PET amyloid, g-DBSI metrics showed amyloid-dependent trajectories: in low-amyloid individuals, RIF and RAF rose together with amyloid, consistent with early neuropil expansion and glial elaboration, whereas in high-amyloid individuals, RIF/RAF increased, and RAF declined, indicating established neuroinflammatory remodeling and neurofilament loss. CSF proteomics linked RIF/RAF to glia-enriched immune and vascular pathways, supporting g-DBSI as a clinically compatible MRI biomarker of neuroinflammation and neurodegeneration in AD.

07.
arXiv (CS.LG) 2026-06-15

PepALD: Macrocyclic Peptide Generation via Autoregressive Latent Diffusion

arXiv:2606.14510v1 Announce Type: new Abstract: Macrocyclic peptides are promising therapeutic candidates for intracellular targets, but their design requires simultaneous control over non-natural monomer chemistry, ring topology, membrane permeability, and target binding. Existing SMILES- or HELM-string generative models either operate in long atom-level sequence spaces or treat monomers as symbolic tokens with limited chemical grounding. We introduce PepALD, an Autoregressive Latent Diffusion (ALD) foundation model for de novo macrocyclic peptide generation. The model represents HELM monomers with structured chemical embeddings, generates each residue through context-conditioned diffusion in chemically informed latent space, predicts R-group-aware ring closures during autoregressive generation, and aligns the denoiser to affinity rewards using winner-protected diffusion-adapted preference optimization. In silico experiments demonstrate PepALD's generation quality and reward-optimization performance against representative peptide generation baselines.

08.
arXiv (quant-ph) 2026-06-16

Adaptively secure unitary designs with constant non-Clifford cost

arXiv:2510.08129v2 Announce Type: replace Abstract: Randomness is a fundamental resource in quantum information, with crucial applications in cryptography, algorithms, and error correction. A central challenge is to construct unitary $k$-designs that closely approximate Haar-random unitaries while minimizing the costly use of non-Clifford operations. In this work, we present a protocol able to generate unitary $k$-designs on $n$ qubits, secure against any adversarial quantum measurement, with a system-size-independent number of non-Clifford gates. Our construction applies a $k$-design only to a subsystem of size $\Theta(k)$, independent of $n$. This ``seed'' design is then ``diluted'' across the entire $n$-qubit system by sandwiching it between two random Clifford operators. The resulting ensemble forms an $\varepsilon$-approximate unitary $k$-design on $n$ qubits. We prove that this construction achieves full quantum security against adaptive adversaries using only $\tilde{O}(k^2 \log\varepsilon^{-1})$ non-Clifford gates. If one requires security only against polynomial-time adaptive adversaries, the non-Clifford cost decreases to $\tilde{O}(k + \log^{1+c} \varepsilon^{-1})$. This is optimal, since we show that at least $\Omega(k)$ non-Clifford gates are required in this setting. Compared to existing approaches, our method significantly reduces non-Clifford overhead while strengthening security guarantees to adaptive security as well as removing artificial assumptions between $n$ and $k$. These results make high-order unitary designs practically attainable in near-term fault-tolerant quantum architectures.

09.
arXiv (CS.LG) 2026-06-11

MPK: A Compiler and Runtime for Mega-Kernelizing Tensor Programs

arXiv:2512.22219v2 Announce Type: replace-cross Abstract: We introduce Mirage Persistent Kernel (MPK), the first compiler and runtime system that automatically transforms multi-GPU model inference into a single high-performance mega-kernel. MPK introduces an SM-level graph representation that captures data dependencies at the granularity of individual streaming multiprocessors (SMs), enabling cross-operator software pipelining, \rev{fine-grained overlap of computation and communication, and other optimizations that are infeasible under the conventional kernel-per-operator execution model}. The MPK compiler lowers tensor programs into optimized SM-level task graphs and generates fast CUDA implementations for each task, while the MPK in-kernel parallel runtime executes these tasks within a single persistent mega-kernel using decentralized scheduling across SMs. Together, these components provide end-to-end kernel fusion with minimal developer effort, while preserving the flexibility of existing programming models. Our evaluation shows that MPK significantly outperforms existing kernel-per-operator LLM serving systems, achieving up to 1.7$\times$ lower end-to-end inference latency and pushing LLM inference performance close to the limits of the underlying hardware. MPK is publicly available at https://github.com/mirage-project/mirage.

10.
arXiv (CS.CL) 2026-06-24

Sentence-Level Contextual Entrainment in Large Language Models

Contextual entrainment, which is a newly discovered phenomenon in large language models (LLMs), refers to the tendency of a model to assign higher probabilities to tokens that appear in its context. In this work, we extend this phenomenon from the token level to the sentence level by examining the per-token mean log-probability of a sentence instead of the probabilities of individual tokens. We investigate sentence-level contextual entrainment across 26 LLMs from seven families and two datasets, which cover both subjective and objective tasks. We find that sentence-level contextual entrainment exists. This means that the sentences in the prompt (even if they are counterfactual statements) can significantly increase their probability during model inference time. As the model size increases, contextual entrainment gradually decreases. We also find that contextual entrainment is controlled by 2% to 4% of the attention heads. Turning off these attention heads can effectively mitigate contextual entrainment without hurting the model's performance.

11.
arXiv (CS.CV) 2026-06-12

From Seeing to Experiencing: Scaling Navigation Foundation Models with Reinforcement Learning

Navigation foundation models trained on massive web-scale data enable agents to generalize across diverse environments and embodiments. However, these models, which are trained solely on offline data, often lack the capacity to reason about the consequences of their actions or adapt through counterfactual understanding. They thus face significant limitations in real-world urban navigation, where interactive and safe behaviors, such as avoiding obstacles and moving pedestrians, are critical. To tackle these challenges, we introduce the Seeing-to-Experiencing (S2E) learning framework to scale the capability of navigation foundation models with reinforcement learning. S2E combines the strengths of pretraining on offline videos and post-training through reinforcement learning. It maintains the model's generalizability acquired from large-scale real-world videos while enhancing its interactivity through reinforcement learning in simulation environments. Specifically, we introduce two innovations: (1) an Anchor-Guided Distribution Matching strategy for offline pretraining, which stabilizes learning and models diverse motion patterns through anchor-based supervision; and (2) a Residual-Attention Module for reinforcement learning, which obtains reactive behaviors from simulation environments without erasing the model's pretrained knowledge. Moreover, we establish a comprehensive end-to-end evaluation benchmark, NavBench-GS, built on photorealistic 3D Gaussian Splatting reconstructions of real-world scenes that incorporate physical interactions. It can systematically assess the generalizability and safety of navigation foundation models.

12.
arXiv (CS.CV) 2026-06-15

RATS! Patches Talk Through Registers: Emergent Parts in Register Attention Transformers

When humans see a bird, they recognize far more than just "bird" – they see a head, wings, and talons, a structured assembly of reusable parts that can be identified across every bird they have ever seen. We ask whether a self-supervised visual model can discover the same compositional structure on its own. To this end, we propose RATS (Register Attention Transformers), which decomposes the classification token into N learnable register tokens that route patch information through an L->N->N->L bottleneck via a three-step compress-communicate-broadcast attention. The N registers are partitioned across the H attention heads, so that registers assigned to different heads do not interact with each other. Without auxiliary losses or part annotations, each register spontaneously specializes into a proto-semantic region whose emerging structure resembles object parts. RATS surpasses all baselines by +12 mIoU on average across five segmentation benchmarks, with consistent gains on ADE20K (+1.11 mIoU) and COCO (+0.2 AP^m). Its register dictionary further exhibits part-level consistency and semantic proximity across related categories. Our results suggest that RATS may provide a useful architectural prior for structured and interpretable visual representation learning.

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

KATANA: A Fast, Low-Power Mapping of Kalman Filters onto Edge NPUs for Real-Time Tracking

arXiv:2606.14992v1 Announce Type: cross Abstract: State estimation is the closed-loop core of every real-time tracking system, from radar surveillance and counter-UAV defense to autonomous driving and robotics. These deployments run on edge platforms, where defense systems mount on vehicles and drones, and civilian pipelines live on cars and handheld devices. Here, every additional watt of compute erodes mission duration or operational range. Two hard constraints follow: each new measurement must be fused before the next control cycle, and the total compute must fit within a strict battery and thermal power envelope. The Linear and Extended Kalman Filters (LKF, EKF) are dominant estimators on these systems, but today they execute almost exclusively on CPUs, which serialize multi-object tracking (MOT) updates, or on custom FPGA/ASIC accelerators that lengthen design cycles. Contemporary AI-PC SoCs, like the Intel Core Ultra Series 1 and 2, integrate a low-power, data-parallel Neural Processing Unit (NPU). We therefore ask whether the Kalman filter can be mapped onto this existing matrix engine to meet real-time and low-power budgets simultaneously, avoiding a dedicated accelerator and keeping the CPU and GPU free for primary workloads. We present KATANA, an NPU-aware optimization framework delivering the first end-to-end mapping of the LKF and EKF onto a commercial NPU, alongside a cross-platform characterization on shipping AI-PC silicon. KATANA applies three algebraic graph rewrites: subtract-to-add reformulation via a precomputed negative-projection matrix H_neg, static-shape tensor fusion, and block-diagonal batched parallelization, ensuring 100% of operations execute on the DPU matrix engine. On the Series 2, the optimized batched EKF reaches 223.35 FPS at 13.43 W active power, and the LKF reaches 408.73 FPS at 14.05 W, delivering up to a 97.9% reduction in dynamic energy versus the CPU implementation.

14.
arXiv (CS.AI) 2026-06-17

DecoSearch: Complexity-Aware Routing and Plan-Level Repair for Text-to-SQL

arXiv:2606.17821v1 Announce Type: new Abstract: Large Language Models (LLMs) have demonstrated remarkable capabilities in translating natural language to SQL, yet existing methods still falter on complex queries requiring multi-step, data-aware reasoning. We introduce DecoSearch, a training-free framework that addresses this by routing each query to the appropriate level of reasoning effort. A lightweight Schema Selector first prunes the full database schema to the relevant tables and columns. An LLM Judger then decides whether the question requires decomposition: straightforward questions follow a direct generation path and complex ones are escalated to a Directed Acyclic Graph (DAG) of atomic sub-questions, each solved by a targeted SQL generation step. A RAG component grounds the decomposer with semantically similar training examples, and a Topology Refiner restructures the reasoning plan when execution failures signal a flawed decomposition rather than a fixable SQL error. DecoSearch achieves 70.53% execution accuracy on BIRD and 88.31% on Spider with a DeepSeek backbone, surpassing all training-free baselines while consuming an order of magnitude fewer tokens than competing methods. It also functions as a model-agnostic wrapper, consistently improving fine-tuned SQL generation backbones without any modification to the pipeline.

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

Beyond Bayer: Task-Optimal Sensor Co-Design for Robust Autonomous-Driving Segmentation

arXiv:2606.24096v1 Announce Type: cross Abstract: Robust perception underpins autonomous driving, and most recent progress comes from scaling the model-larger backbones, foundation models, and cooperative multi-agent fusion. We pursue a complementary, upstream question: what should the camera itself measure? Using a differentiable RAW-to-task pipeline, we decompose which sensor degrees of freedom benefit dense prediction. Learning the spectral colour-filter-array (CFA) weights is the dominant lever, improving mIoU by +0.017 (KITTI-360) and +0.023 (ACDC) over a fixed camera. In contrast, point-spread-function (optics) co-design is net-negative (-0.020 mIoU on KITTI-360) - a consequence of the data-processing inequality, which also bounds the task information that any downstream model, however large or cooperative, can recover. Noise co-optimisation is marginal, and counter to intuition enlarging the CFA tile beyond 2x2 consistently hurts, as the filters are confined to the rank three sRGB input. Because the intervention is at the sensor, the gains are model-agnostic; we validate robustness on ACDC's fog, night, rain, and snow, and conclude with a simple recipe: learn the 2x2 CFA weights and keep an identity PSF.

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

Every Eval Ever: A Unifying Schema and Community Repository for AI Evaluation Results

AI evaluations are widely used for testing and understanding progress. However, the diverse evaluators bring with them inconsistencies that challenge analysis and comparison. First, results are saved in incompatible formats, scattered across leaderboards, papers, blog posts, evaluation harness logs, and custom repositories. Second, results are created by different evaluation frameworks, which produce divergent scores for nominally identical evaluations and record metadata inconsistently, hindering comparison, cross-community evaluation science, cost reduction, and reuse. We introduce Every Eval Ever, the first shared schema and community-crowdsourced repository for AI evaluation results. The schema standardizes how evaluations are represented in a unified, single JSON document. It is source-agnostic by design, ingesting results from evaluation harnesses and papers alike, and optionally stores per-instance outputs for fine-grained analysis. We contribute: (i) a community-governed metadata schema with a companion instance-level schema, the first standardization effort of its kind; (ii) automatic converters from popular formats, evaluation harnesses, and leaderboards to the unified schema; and (iii) a crowdsourced community database hosted on Hugging Face, currently spanning to date 22,235 models, 2,273 unique benchmarks, and 31 evaluation formats.

17.
medRxiv (Medicine) 2026-06-11

Effects of Resveratrol as an Adjunct to a Low-Calorie Diet in Postmenopausal Women with Obesity and Knee Osteoarthritis

Background. Obesity is a modifiable risk factor for osteoarthritis and may contribute to pain, functional impairment, inflammation, and cartilage degradation. Resveratrol has potential anti-inflammatory and chondroprotective effects, but its efficacy as an adjunct to dietary intervention remains unclear. Objective. This study evaluated whether resveratrol supplementation provides additional benefits when combined with a low-calorie diet in postmenopausal women with obesity and knee osteoarthritis. Methods. A total of 97 postmenopausal women with obesity and knee osteoarthritis were included in this randomized controlled clinical study. Participants received either a 10-day low-calorie diet alone or the same diet combined with 150 mg/day trans-resveratrol. Anthropometric parameters, body composition, biochemical markers, pain intensity, functional status, and urinary CTX-II were assessed at baseline and follow-up. Results. Both interventions were associated with reductions in body weight, BMI, waist and hip circumferences, fat mass, glucose, HOMA-IR, lipid parameters, hsCRP, VAS, WOMAC, LAI, and urinary CTX-II. Compared with diet alone, resveratrol supplementation did not provide additional benefits for anthropometric parameters, glucose metabolism, lipid profile, or WOMAC score. However, the resveratrol group showed a greater reduction in hsCRP and urinary CTX-II. The obesity class did not modify the treatment effect. Conclusion. A short-term low-calorie diet improved metabolic, inflammatory, and osteoarthritis-related parameters in postmenopausal women with obesity and knee osteoarthritis. The addition of resveratrol did not enhance weight loss or improve most metabolic outcomes but was associated with greater reductions in hsCRP and urinary CTX-II. These findings suggest a potential anti-inflammatory and cartilage-related effect of resveratrol, which requires confirmation in longer randomized trials.

18.
arXiv (CS.LG) 2026-06-17

Recursive Learning Without Collapse: A Weighting-Based Stabilization Framework

arXiv:2502.18049v5 Announce Type: replace-cross Abstract: Recent studies identified an intriguing phenomenon in recursive generative model training known as model collapse, where models trained on data generated by previous models exhibit severe performance degradation. Addressing this issue and developing more effective training strategies have become central challenges in generative model research. In this paper, we investigate this phenomenon within a novel framework, where generative models are iteratively trained on a combination of newly collected real data and synthetic data from the previous training step. To develop an optimal training strategy for integrating real and synthetic data, we evaluate the performance of a weighted training scheme in various scenarios, including Gaussian distribution estimation, generalized linear models, and nonparametric estimation. We theoretically characterize the impact of the mixing proportion and weighting scheme of synthetic data on the final model's performance. Our key finding is that, across different settings, the optimal weighting scheme under different proportions of synthetic data asymptotically follows a unified expression, revealing a fundamental trade-off between leveraging synthetic data and model performance. In some cases, the optimal weight assigned to real data corresponds to the reciprocal of the golden ratio. Finally, we validate our theoretical results on extensive simulated datasets and a real tabular dataset.

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

Ex-Omni: Enabling 3D Facial Animation Generation for Omni-modal Large Language Models

Omni-modal large language models (OLLMs) aim to unify multimodal understanding and generation, yet extending them to jointly produce speech and 3D facial animation remains largely unexplored despite its importance for natural human-computer interaction. A key challenge is the mismatch between the discrete semantic reasoning of LLMs and the dense temporal dynamics required for 3D facial motion. We propose Expressive Omni (Ex-Omni), an open-source model that augments OLLMs with native speech-accompanied 3D facial animation. Ex-Omni decouples semantic reasoning from temporal generation through a blendshape-aware speech unit generator and a blendshape decoder, where speech units provide temporal scaffolding and hidden speech representations carry facially relevant cues. We further introduce a unified token-as-query gated fusion (TQGF) mechanism for controlled semantic injection, as well as InstructS2SF-1200K, a dataset consisting of 1200K samples for pre-training. Extensive experiments show that Ex-Omni maintains competitive speech understanding and generation ability while achieving better audio-visual synchronization and lower face-generation latency than cascaded pipelines.

20.
arXiv (CS.AI) 2026-06-12

Meta-Learning Transformers to Improve In-Context Generalization

arXiv:2507.05019v2 Announce Type: replace-cross Abstract: In-context learning enables transformer models to generalize to new tasks based solely on input prompts, without any need for weight updates. However, existing training paradigms typically rely on large, unstructured datasets that are costly to store, difficult to evaluate for quality and balance, and pose privacy and ethical concerns due to the inclusion of sensitive information. Motivated by these limitations and risks, we propose an alternative training strategy where we leverage a collection of multiple, small-scale, and domain-specific datasets. We empirically demonstrate that the increased quality and diversity of such data improve the generalization abilities of in-context learners beyond their training domain, while achieving comparable performance with models trained on a single large-scale dataset. We investigate this paradigm by leveraging meta-learning to train an in-context learner on the Meta-Album collection under several settings. Firstly, we show the performance in a controlled environment, where the test domain is completely excluded from the training knowledge. Secondly, we explore the robustness of these models to forgetting in a continual scenario where the information is accessible for a limited time. Finally, we explore the more challenging unsupervised scenario. Our findings demonstrate that transformers still generalize for in-context prediction when trained on a curated dataset collection while offering advantages in modularity and replaceability.

21.
arXiv (math.PR) 2026-06-11

Patterned matrices with random walk entries

arXiv:2512.04612v3 Announce Type: replace Abstract: It is well known that the weak limit of a suitably scaled continuous-time random walk (CTRW) is the Brownian motion. We investigate the convergence of certain patterned random matrices whose entries are independent CTRWs and their time-changed versions, in a non-commutative probability framework. For the Wigner link function, the limits are free Brownian motion and its time-changed version driven by an inverse stable subordinator. For the symmetric circulant and the circulant with CTRW entries, we use their explicit eigenvalue expressions to define some empirical processes that converge weakly to a Brownian motion and a complex Brownian motion, respectively. For matrices with iid entries, and for elliptic matrices, the algebraic limits are equal in $*$-distribution to processes whose marginals are circular and elliptic variables, respectively. A random time-changed variant of these results is also established.

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

Recursive Joint Simulation in Games

arXiv:2402.08128v3 Announce Type: replace Abstract: Game-theoretic dynamics between AI agents could differ from traditional human-human interactions in various ways. One such difference is that it may be possible to accurately simulate an AI agent, for example because its source code is known. Such an agent would then be fundamentally uncertain whether it is in the real world or in a simulation. Our aim is to explore ways of leveraging this possibility to achieve more cooperative outcomes in strategic settings. In this paper, we study an interaction between AI agents where the agents run a recursive joint simulation. That is, the agents first jointly observe a simulation of the situation they face. This simulation in turn recursively includes additional simulations (with a small chance of failure, to avoid infinite recursion), and the results of all these nested simulations are observed before an action is chosen. We show that the resulting interaction is strategically equivalent to an infinitely repeated version of the original game, allowing a direct transfer of existing results such as the various folk theorems. As evidence that the equivalence is robust, we show that it holds even when we relax some of the assumptions and that it also holds ``from the inside'' – meaning, for an agent that finds itself inside the game and has self-locating uncertainty.

23.
arXiv (CS.LG) 2026-06-24

Efficient reduction of stellar contamination and noise in planetary transmission spectra using neural networks

arXiv:2602.10330v3 Announce Type: replace-cross Abstract: Context: The characterization of exoplanetary atmospheres has been transformed by the James Webb Space Telescope (JWST), whose infrared sensitivity enables transmission spectroscopy at unprecedented precision. However, stellar heterogeneities (e.g., spots and faculae) remain a dominant source of contamination that can bias atmospheric retrievals if not properly corrected. Aims: We present a methodology for reducing stellar contamination and instrument-specific noise from exoplanet transmission spectra using neural networks, in particular the so-called Denoising AutoEncoders (DAE). Our goals are to enable fast, accurate corrections that improve the reliability of atmospheric parameter retrievals and to promote the use of unsupervised algorithms for efficient data processing. Methods: We designed and trained DAE architectures using large synthetic datasets of terrestrial (TRAPPIST-1e analogues) and sub-Neptune (K2-18b analogues) planets. Atmospheric retrieval experiments were then performed on contaminated spectra in order to compare our deep-learning approach against standard correction methods in terms of accuracy and computational cost. Results: Our autoencoders successfully reconstruct uncontaminated spectra, preserving essential molecular features even in low-S/N regimes. In retrieval tests, the denoising autoencoder pre-processing reduces bias in retrieved abundance parameters compared to uncorrected observations. Notably, our method matches the accuracy of simultaneous stellar-contamination fitting while maintaining a much lower computational cost, typically one order of magnitude smaller. Conclusions: These results demonstrate that DAEs outperform conventional correction methods in computational efficiency while maintaining high accuracy, paving the way for their integration into future atmospheric characterization pipelines for both rocky and giant exoplanets.

24.
arXiv (CS.LG) 2026-06-16

{\alpha}-Fair Insurance Pricing: A Fairness Continuum

arXiv:2606.14898v1 Announce Type: new Abstract: Fairness in insurance pricing remains a long-standing and deeply debated puzzle. On one hand, insurers, driven by profitability considerations, set premiums that differentiate across individual risks to achieve actuarial fairness. On the other hand, insurance serves a critical societal function by pooling risks across a population, motivating cross-subsidization among groups to promote solidarity fairness. The tension between these two competing notions of fairness makes insurance pricing inherently complex, particularly in modern settings where granular data allow for increasingly fine risk differentiation and regulators face growing pressure to protect vulnerable groups. To address this challenge, we propose an $\alpha$-Fair Individual Solvent Premium ($\alpha$-FISP) framework for insurance pricing that explicitly captures the trade-off between actuarial and solidarity fairness while guaranteeing solvency, a fundamental requirement in insurance operations. We formulate the pricing problem as a constrained optimization task, where actuarially fair premiums are adjusted subject to budget constraints on cross-subsidization within each risk class. This formulation naturally yields a family of solutions parameterized by $\alpha$, tracing a continuum between purely actuarial and purely solidarity-based pricing and enabling decision-makers to select an operating point along this fairness spectrum. We derive theoretical guarantees for the proposed framework. Numerical experiments show that $\alpha$-FISP is computationally tractable and aligns well with the U.S. regulatory regimes featuring heterogeneous state-level fairness requirements.

25.
arXiv (quant-ph) 2026-06-16

Learning ground state observables from quantum computing experiments

arXiv:2606.15983v1 Announce Type: new Abstract: Recent theoretical progress has established conditions under which machine learning models can efficiently predict ground-state properties of gapped local Hamiltonians when trained on quantum-generated data. Previous experimental demonstrations in this paradigm, however, have largely been limited to small systems or highly structured states, due to the difficulty of preparing many-body ground states on quantum processors. In this work, we demonstrate learning from experimental quantum data generated from approximate ground states of the two-dimensional Heisenberg XXZ model with system sizes up to 115 qubits. We construct a dataset of single-site expectation values, two-point correlations, and 12-body loop correlations across the antiferromagnetic phase. We then train neural networks on this data and show that they can accurately predict spatially resolved observables for previously unseen Hamiltonian parameters, both within the training distribution and in an out-of-distribution regime approaching the phase boundary. Our results demonstrate the practical realization of learning from quantum data for an interacting two-dimensional many-body system at scale, motivating a path toward regimes where quantum processors could provide training data beyond the reach of classical approximation methods.