Probability
Walk/Zeta correspondence for quantum walks on path graphs: a pre-geometric structure implied by a generalized reflection principle
Jiro Akahori, Riki Kitano, Norio Konno et al. (+1 more)
We establish a local Konno-Sato correspondence for reflected random and Szegedy walks on a finite path graph. A generalized reflection principle, using explicit involutions rather than point reflections in the asymmetric case, yields exact
zeta factorizations into a boundary factor and local factors indexed by the infinite dihedral group. After symmetrization, the classical and
quantum local factors correspond for each group element. The identity contribution determines the normalized thermodynamic limits. In the symmetric case, diffusive and ballistic scalings recover the Gaussian Poisson summation formula and the Dirac comb identity, respectively. Under a double scaling of the asymmetry and spectral parameter, the
quantum factorization yields a massive Dirac-type limit: nonidentity even words produce the periodic-orbit factor, the identity produces the free-field factor, and odd words together with the boundary produce a finite boundary correction.
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All authors Jiro Akahori, Riki Kitano, Norio Konno, Iwao Sato
Rings and Algebras
Genus of quaternion algebras over formally real fields
Sergey V. Tikhonov
We prove the finiteness of the genus of quaternion division
algebras over some formally real fields. In particular, if $F$ is a formally real field and the second power of the fundamental ideal $I^2(F)$ is torsion-free, then the genus of any quaternion division $F$-
algebra is trivial. For instance, this immediately implies that the genus vanishes for any quaternion division
algebra over a formally real pythagorean field. The proofs are based on methods from the theory of quadratic forms.
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Probability
Stochastic PDE construction of some non-local or non-translation-invariant Anderson operators in the full subcritical regime
Léonard Ferdinand, Samaël Mackowiak and Aurélien Minguella
We construct Anderson-type operators in the full subcritical regime via a SPDE argument. Our work encompasses perturbations by a Gaussian noise of the fractional
Laplacian on the
torus or on the full space, and of the harmonic oscillator on the full space. In every case, we are able to derive an optimal estimate on the difference between the solution and the deterministic heat flow, which allows us to get a Weyl law for the fractional case on the
torus and for the harmonic oscillator case, and so in the full subcritical regime. For the non-translation-invariant operator, the main novelty is that we develop a general argument in order to prove how to renormalise the operator with some constants. The SPDE argument uses the flow approach introduced by Duch. To construct the operators, we use the Hille-Yosida
theorem for the fractional
Laplacian on the
torus and the harmonic oscillator, and the Klein-Landau
theorem for the fractional
Laplacian in the full space.
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Signal Processing
Energy Efficiency Optimization for 5G NR PDSCH: A Cross-Layer Link Abstraction Framework
Jaebum Park, Chan-Byoung Chae and Robert W. Heath Jr
Energy efficiency (EE) optimization for cellular links often assumes Shannon-capacity transmission. The 3GPP New
Radio (NR) physical downlink shared channel (PDSCH), however, delivers a transport block whose size is fixed by the modulation and coding scheme (MCS), the rank, and the resource allocation chosen by the scheduler. The transport block must also meet a target block error rate (BLER). In this paper, we optimize EE for the NR PDSCH with the standard transport block size as the throughput and the target BLER as the constraint. Exponential effective signal-to-noise ratio (SNR) mapping (EESM) turns the BLER constraint into a convex per-subcarrier power constraint. We derive a closed-form waterfilling-like power allocation and an EE-maximizing MCS selection rule. With a single calibration parameter per MCS, fitted offline over 3GPP tapped delay line C (TDL-C) channels, EESM predicts the BLER without per-realization link-level simulation. Numerical results show that a Shannon-capacity baseline overestimates the EE of equal-power transmission by 1.5 to 1.7 times at high SNR within the transmit power budget.
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Quantum Physics
On State Distinguishing Without Inverse Queries
Emma Wang, Joseph Carolan and Andrew M. Childs
In the
quantum state distinguishing problem, an
algorithm is given copies of a state $|\psi\rangle$ or $|\phi\rangle$ separated by trace distance $\varepsilon$, and tasked with deciding which is the case. It is a standard result that $\Theta(\varepsilon^{-2})$ copies are required, while having access to a
unitary state preparation oracle and its inverse improves this to $\Theta(\varepsilon^{-1})$ queries. We study the intermediate case with forward-only access, capturing scenarios where the oracle is a physical process that cannot be reversed. Tang and Wright recently showed that distinguishing a known state from an unknown close state requires $\Omega(\varepsilon^{-2})$ forward queries in high dimension; we strengthen this result by proving the same bound even when both states are known, as in the state distinguishing setting. Moreover, our lower bound uses a direct hybrid argument, avoiding advanced compressed oracle techniques used in the prior work. In contrast, we give a dimension-independent
algorithm solving a continuous-time variant of state distinguishing with only $O(\varepsilon^{-1})$ total forward
evolution time. The
algorithm uses
quantum Zeno dynamics to confine
evolution to a known two-dimensional subspace. Thus, a quadratic advantage survives without inverse access for a natural continuous-time analogue of state distinguishing.
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Statistical Methodology
Semi-Supervised Kernel Ridge Fréchet Regression
Jaehee Seo, Kwangho Kim and Jisu Kim
Fréchet regression provides a framework for predicting random object-valued responses by minimizing the conditional expected squared distances. We propose semi-supervised kernel ridge Fréchet regression (SS-KRFR) to exploit unlabeled
covariates when labeled samples are scarce. The method learns kernel spectral features from both labeled and unlabeled
covariates, then utilizes labeled responses to estimate the conditional Fréchet function by kernel ridge regression. We derive prediction error bounds that distinguish the roles of labeled and unlabeled samples, and establish
polynomial convergence rates under suitable conditions. Under additional kernel assumptions, a sharper analysis relaxes the sample size requirements for learning the features. We also develop hybrids that combine features, predictions, or both from models fitted with and without unlabeled
covariates, establishing uniform stability over mixing weights in Hadamard spaces at common tuning and a separate rate guarantee for prediction mixing. Simulations and a real-data application show semi-supervised gains and improvements over competing Fréchet regression methods in several settings.
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Machine Learning
GNN-CB: A Graph Neural Network Competition Benchmark for Human and LLM Evaluation
Murad Hossen, Tasneem Selim, Gurur Gamgam et al. (+22 more)
Large
language models (LLMs) have demonstrated strong performance on coding and
reasoning benchmarks; however, their ability to solve graph-structured machine learning problems remains largely unexplored. In particular, no
benchmark currently evaluates whether LLMs can autonomously solve end-to-end Graph Neural Network (GNN) coding tasks under realistic competition settings. To address this gap, this paper introduces GNN-CB, the first competition-based
benchmark for evaluating both humans and LLMs on GNN coding tasks. GNN-CB consists of 18 curated competitions spanning node-, edge-, and graph-level prediction across diverse graph categories, domains, and difficulty tiers. All submissions are evaluated through a unified automated pipeline with hidden test sets and standardized scoring. Human participants solve tasks under controlled competition constraints, while LLMs are evaluated using a frozen zero-shot prompting protocol based on a plan-then-code paradigm with bounded execute-and-repair loops. The
benchmark additionally supports both non-
agent and autonomous
agent-based evaluation within the same protocol. Under our evaluated protocol, LLMs rarely match Human Top performance and show less stable performance across competitions. No single model dominates: a few competitions are won by LLMs, yet humans still hold the top score on most tasks. We release GNN-CB as a living
benchmark with automated evaluation infrastructure, dynamic leaderboards, and reproducible execution pipelines. Beyond benchmarking, GNN-CB provides a practice-oriented resource for studying GNN implementation across progressively diverse graph-learning tasks. The
benchmark and evaluation framework are publicly available at https://basiralab.github.io/GNN-CB/.
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All authors Murad Hossen, Tasneem Selim, Gurur Gamgam, Tuga Yousif, Abderrahmane Kasmi, Ikram Aissiou, Mubaraq Onipede, Faran Taimoor Butt, Sanae Zrigui, Rosa Y. G. Paccotacya-Yanque, Ignatius Balayo, Ikram Elhouiti, Hadil Affes, Bijay Adhikari, Sargam Goyal, Muhammad Ibrahim Isah, Mohammad Idrees Bhat, Samuel Kangoni Matia, Peguy Kem-Meka Tiotsop Kadzue, Maha Trabelsi, Emmanuel Owusu, Vinit, Nour Majdoub, Tamiru Alemnew, Islem Rekik
High Energy Astrophysical Phenomena
Radiation Reaction in Relativistic Magnetized Shocks of Neutron Star Magnetospheres
Arno Vanthieghem and Amir Levinson
The steepening of fast magnetosonic waves in the inner magnetospheres of magnetars can produce monster shocks, whose precursor emission may account for fast
radio bursts (FRBs). For sufficiently bright bursts, particles crossing the shock radiate their energy within a single gyration period, raising the question of how radiation reaction affects the shock structure and its coherent emission. We investigate strongly cooled, relativistically magnetized shocks using a stationary multifluid model generalized to include the Landau-Lifshitz radiation-reaction force, together with particle-in-
cell simulations of monster-shock dynamics. We show that the kinetic-scale shock transition is governed by only two dimensionless parameters: the Alfvénic Mach number and a cooling parameter $\tau$ that measures radiative losses over a gyration period. Coherent precursor emission is triggered above a critical Mach number that increases with $\tau$, at which the beam dynamics becomes chaotic. Above this threshold, radiative cooling shifts the peak frequency of the precursor to higher values, scaling as $\tau^{2/7}$. Remarkably, monster shocks remain far above the emission threshold even under strong radiative cooling. Radiation reaction therefore does not quench the precursor emission; instead, it primarily shifts the spectral peak into the kinetic regime. The luminosity of the precursor wave is determined solely by the luminosity of the driving kHz wave and the conversion efficiency, $\epsilon_X\sim 10^{-3} - 10^{-2}$.
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Computational Complexity
On the Computational Complexity of Problems: Formalizing Sensitivity to Uncertainty and Parametric Complexity Classes
Yannis Tzitzikas
Worst-case analysis, the setting of the $P \stackrel{?}{=} NP$ question, measures the cost of a problem as a function of input size alone. Yet problems that are exponential in general often become
polynomial, even linear, once a checkable property of the input is known: Partition, for instance, is decidable in linear time on inputs whose elements are all equal. We develop a framework that makes such knowledge an explicit parameter $K$ of complexity statements. Costs are measured for fixed
algorithms; we distinguish the promise cost from the guarded cost that also pays for checking $K$, and introduce the residual uncertainty $\Psi(n,K)$, the number of input
cells that, together with $K$, determine the input. An Uncertainty Reduction
Theorem decomposes the guarded cost into checking $K$, locating and reading the residual information, and solving an explicit reduced problem. The classes $P_\upsilon[K]$ and $NP_\upsilon[K]$ are restrictions to
polynomial-time promises, made informative by the coverage of $K$. We show that small $\Psi$ forces sparsity but not tractability, characterize FPT as uniform membership in graded families $P_\upsilon[K_k]$, prove a free-variable threshold for SAT, and show that under the factoring assumption no checkable property of non-negligible coverage makes factoring easy. We relate the framework to promise problems, kernelization, average- and generic-case complexity and beyond-worst-case analysis, illustrate it on Partition, Graph Isomorphism, SAT, Vertex Cover and TSP, and apply it to guarded
algorithm dispatch with latency contracts and optimal guard ordering, to solver routing in agentic AI, and to the role of promises in
quantum speedups.
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Rings and Algebras
A simple construction of a simple nil ring
Vsevolod Gubarev
In 1999, A. Smoktunowicz solved a long-standing problem and constructed a simple nil ring. We present a substantial simplification of this construction found by Aristotle (Harmonic) with the assistance of ChatGPT.
Artificial Intelligence
Sibyl: An Efficient Small-large Model Collaboration Framework for Long-horizon Tasks
Zhewei Fang, Yuxin Zhang, Zhenwei Shao et al. (+8 more)
Small
language models (SLMs) offer a promising foundation for on-device
agents through low-latency, resource-efficient inference, yet limited
reasoning and planning capabilities constrain their performance on long-horizon tasks requiring multi-step interaction with the environment. Step-level collaboration between SLMs and larger cloud-hosted models can bridge this gap, but identifying states that warrant cloud assistance remains challenging: the contribution of each cloud call is entangled with subsequent actions and can be assessed only from the final task outcome. Compounding this challenge, the SLM must balance two competing objectives: maximizing task success and minimizing cloud calls. To address this, we propose Sibyl, an
algorithm that trains SLM
agents to selectively consult cloud models at the step level and internalize their guidance for subsequent decisions, achieving strong task performance with minimal cloud reliance. Sibyl follows a three-stage training pipeline that (1) builds a robust base policy through consultation-free self-evolving reinforcement learning (RL); (2) cold-starts consultation behavior via decisive-disagreement state mining; and (3) jointly optimizes consultation decisions and guidance internalization through consultation-aware RL. Experiments on ALFWorld and WebShop demonstrate that Sibyl, using only a 0.6B-parameter model, outperforms state-of-the-art baselines, including
agent training and routing methods, by 95.2% and 80.4% in success rate while averaging only 0.8 and 3.9 cloud calls per trajectory, respectively.
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All authors Zhewei Fang, Yuxin Zhang, Zhenwei Shao, Mengze Li, Zheng Lin, Long Chen, Zhou Yu, Zhe Chen, Zhiwen Chen, Zhaode Wang, chengfei lv
Computation and Language
Harness-Search: Guiding Long-Horizon Search through Multi-Agent Coordination
Shanyong Wang, Zhenwen Ji, Lei Jin et al. (+7 more)
Long-horizon search requires
agents to gather evidence across multiple steps and synthesize it into well-supported answers. The recent
agent harnesses provide a natural and promising framework to support such long-running search processes. As interaction histories grow, one single
agent in harnesses might get stuck and cause the policy to lose track of unresolved questions, overlook useful evidence, or terminate before sufficient support has been collected. One of promising way is to decouple three distinct responsibilities of proposing
retrieval actions, updating persistent state, and deciding when to stop rather than concentrating them within a single policy. Targeted at it, we introduce Harness-Search, a multi-
agent search harness to reduce the local errors propagating across subsequent exploration, evidence curation, and termination decisions. In particular, Harness-Search assigns these responsibilities to three permission-bounded authorities: a
Retrieval Policy that proposes search operations, a
Memory Operator that validates and commits persistent-state updates, and a Summary Auditor that accepts or rejects termination based on the sufficiency of the curated evidence. Together, these roles form a Propose-Commit-Audit loop in which actions are proposed, persistent evidence is selectively committed, and stopping decisions are subjected to an explicit sufficiency check. Across seven long-horizon search
benchmarks, Harness-Search improves both
retrieval and answer generation under the same policy backbone, increasing Recall by 4.60-27.92 points and Final-Answer Recall by 12.34-30.13 points over the strongest harness-based baseline on each evidence-
retrieval benchmark. Moreover, trajectory-level analyses show that Harness-Search continues to accumulate useful evidence and expand evidence coverage with less redundant
retrieval as the search history grows.
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All authors Shanyong Wang, Zhenwen Ji, Lei Jin, Yining Zhao, Yicheng Qian, Chengqiang Lu, Yi Wu, Yao Hu, Lizhen Cui, Yanyu Xu
Systems and Control
Backup Control Barrier Functions with Memory for Online Set Expansion
M. Yusuf Uzun and Ersin Das
Backup control barrier functions (bCBFs) construct implicit safe sets for nonlinear systems with bounded inputs using finite-horizon predictions under a backup controller. As in model predictive control, an invariant backup set serves as a terminal set that guarantees safe continuation beyond the prediction horizon. However, reaching a small terminal set may require long prediction horizons, increasing the cost of online prediction. In this paper, we introduce an online construction that builds a certified region from sets stored along backup trajectories while keeping the prediction horizon fixed. The method stores finite collections of balls and connects each newly certified collection to the backup set or to previously stored balls. We derive conditions that guarantee forward invariance of the union of these balls and the backup set under a fixed backup controller. These conditions also ensure that every stored state reaches the backup set in finite time. The resulting union serves as an enlarged terminal set, allowing safety to be certified with shorter prediction horizons. We formulate a feasible quadratic program for safe control and prove that safety is preserved as additional certified collections are stored online. Simulations on a quadrotor demonstrate safe task completion with a shorter prediction horizon than the standard bCBF.
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Programming Languages
VHDL-REPOBENCH: A Repository-Level Benchmark for Evaluating Large Language Models on VHDL Design Generation
Prashanth Vijayaraghavan, Akul Malhotra, Ashutosh Jadhav et al. (+2 more)
Large
Language Models (LLMs) are increasingly applied in hardware design automation, demonstrating strong potential in generating and understanding hardware description
languages. However, most existing
benchmarks focus on Verilog, with limited evaluation of VHDL, which remains widely used in industry and academia for FPGA and safety-critical systems. To address this gap, we introduce VHDL-REPOBENCH, a large-scale, cross-file, repository-level
benchmark for assessing LLM capabilities on realistic VHDL design generation and analysis tasks. VHDL-REPOBENCH curates ~100 open-source VHDL repositories, encompassing ~2.5k VHDL files and ~500 testbenches, and provides structured problem statements, module stubs, and self-verifying testbenches. The
benchmark enables comprehensive evaluation across syntax, semantic correctness, hierarchical
reasoning, cross-file dependency resolution, and functional verification. We evaluate several state-of-the-art models, including GPT-4o, Llama-3-70B, Qwen2.5-72B, CodeLlama-70B, and multi-step
reasoning approaches such as Reflexion and CoDes. Results reveal that while current LLMs achieve moderate line- and block-level accuracy, substantial challenges remain in multi-file
reasoning, hierarchical design understanding, and specification-to-module generation. VHDL-REPOBENCH represents the first large-scale VHDL-focused
benchmark and provides a valuable resource for the hardware design community to evaluate, compare, and advance LLM capabilities for practical VHDL development.
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All authors Prashanth Vijayaraghavan, Akul Malhotra, Ashutosh Jadhav, Ehsan Degan, Vandana Mukherjee
Machine Learning
Does Explainability Survive Data Drift?
Samuel Ozechi
Model performance monitoring is a standard practice in machine learning deployments. Detection performance is tracked continuously, and model decay is expected as the relationship between the feature and target variables degrades, a phenomenon known as concept drift. Explanation fidelity, however, is rarely monitored with the same discipline, even in domains such as financial systems, healthcare, and other regulated environments where explanations are required for governance purposes. This paper investigates whether explanations can decay under data drift, even when the feature-target relationship remains stable, and whether explanations produced before drift occurs remain faithful to the decisions of the model that replaces them. Using the IEEE-CIS Transaction Fraud Detection
dataset, we find statistically significant
covariate shift but no statistically significant evidence of concept drift under the implemented conditional-drift tests, thereby providing an empirical setting in which input distributional change can be studied separately from detectable changes in the feature-target relationship. Local explanations are generated with ExIFFI and evaluated at three levels: path validity, structural behaviour, and fidelity under controlled intervention. Results show that while prior explanations retain substantial decision relevance to a retrained model, they are consistently less faithful than newly generated explanations, with no evidence of a systematically widening gap across the evaluated windows. The study shows that explanation fidelity requires its own monitoring, that structural stability of explanations does not guarantee functional fidelity, and that explanations should be treated as artifacts tied to the model that produced them.
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Machine Learning
Distributed Subliminal Learning: Replacing Model Updates with Random-Carrier Outputs
Dario Fenoglio, Gabriele Dominici, Martin Gjoreski et al. (+1 more)
Collaborative learning typically exchanges model parameters:
federated clients communicate updates, while independently adapted foundation models are combined by exchanging adapters or checkpoints. This makes communication scale with model size and requires local specializations to be reconciled in weight space, where interference is common. We ask whether knowledge can instead be shared through model behavior on task-unrelated inputs. We introduce Distributed Subliminal Learning (DSL), a collaborative learning primitive in which participants adapt a common model locally, probe it with task-unrelated inputs, and transmit only the resulting carrier outputs. A coordinator pools these outputs and distills them into a shared model. The primitive supports one-shot foundation-model composition through carrier completions and iterative
federated learning through carrier logits, without transmitting model updates or requiring task-related proxy data. In LLM composition, compared with LoRA averaging, DSL achieves higher preference retention (94.56% vs. 87.76%) and a larger GSM8K gain over the base model (22.0 vs. 0.6 points), while reducing upload by 30.6-49.0$\times$. In
federated classification, DSL reaches 96.83% on MNIST with 8.9$\times$ less uplink than FedAvg and provides lower-communication operating points on CIFAR-10 and Tiny ImageNet. These results establish random-carrier outputs as a practical communication primitive for knowledge sharing across distinct collaborative learning paradigms.
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All authors Dario Fenoglio, Gabriele Dominici, Martin Gjoreski, Marc Langheinrich
High Energy Physics (Phenomenology)
Exploring Anomaly-Free Dark Photon Models Through Solar Neutrino-Electron Scattering in Ton-Scale Dark Matter Detectors
Mehmet Demirci, Gürsel Kaz{\i}l and M. Fauzi Mustamin
We study the phenomenological implications of anomaly-free dark
photon models using low-energy
solar neutrino-electron elastic scattering data from the ton-scale PandaX-4T and XENONnT experiments. Focusing on $U(1)_X$ gauge extensions that incorporate both kinetic and mass mixing, we derive novel exclusion limits across the parameter spaces of six
benchmark models. Our analysis demonstrates that the stringency of these limits is directly correlated with the theoretical leptonic charge assignments of the respective models. Additionally, we provide model-independent limits by isolating the pure kinetic and pure mass mixing scenarios. In the sub-MeV mediator mass regime, our results meaningfully improve upon existing limits from previous
neutrino-electron scattering experiments, such as CHARM-II, TEXONO, and GEMMA. Ultimately, these findings yield improved limits on low-mass dark
photon models, demonstrating their complementarity with other ventures in the global search for dark portals.
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Systems and Control
Physics-informed neural control of heat flow rate in a counter-flow heat exchanger: modeling, identification and experimental validation
Konstantinos Skantzikas, Emmanuel Witrant and Bojan Mavkov
The advanced operation of heat exchangers plays a critical role in the development of efficient and sustainable multivector energy systems. This paper proposes a hybrid physics-informed and data-driven framework for the analysis, identification, and regulation of transient heat transfer in counter-flow heat exchangers. A parameterized physical model combines classical heat-transfer relations with transport equations to capture convective propagation, transport-induced delays, and nonlinear effects associated with flow-rate variations. The heat-transfer coefficient is identified from experimental data, enabling the characterization of flow-dependent heat-transfer dynamics over a broad operating range. The identified model is then used to develop a hierarchical real-time control strategy. An inner loop regulates the volumetric flow rate using a high-order data-driven linear model, while an outer loop regulates the exchanged heat power using a machine-learning controller initially trained on the physical model and subsequently refined with experimental data. Experimental results demonstrate accurate reproduction of transient heat-transfer dynamics and effective heat-flow-rate regulation under varying thermal boundary conditions (identification fit above 94% in normalized root-mean-square error and total variation of the flow rate reduced by half compared to a proportional-integral controller). The proposed framework combines physical interpretability with data-driven adaptation for the analysis and real-time operation of dynamic heat-transfer systems.
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Artificial Intelligence
Learning Field Reconstruction from Incomplete Data by Globally Correcting Local Estimates
Renhao Zhong, Zihan Zhou, Chiyuan Ma et al. (+1 more)
Reconstructing physical fields from training samples that are always incomplete requires learning spatial structure from fragmented observations. Existing context–query work establishes how held-out observations provide valid training targets, but this does not make the complete-field distribution identifiable when every training field is incomplete. With finite data, weak evidence of sharp transitions and localized variations can further favor averaged predictions that attenuate local detail. A structural prior is therefore needed to favor plausible completions; local spatial relationships offer one grounded in the observations. We propose a locally constructed, globally revisable
estimator that explicitly learns local field estimates and subsequently corrects them using full-domain observations. A shared coordinate-conditioned predictor learns from incomplete patches, allowing relatively well-observed neighborhoods to provide direct supervision of local structure. Its overlapping predictions are reconciled into an observation-conditioned consensus field. A full-domain
estimator retains the original observations and learns a residual correction around this frozen field estimate, allowing locally constructed structure to be revised by broader evidence. The local estimate serves as both an explicit input, accompanied by its discrepancies with the observations, and a prediction starting point that the global model can revise. On three real-world ocean
datasets with authentic observation gaps, our
estimator achieves the lowest MSE and highest PSNR on withheld source-supported values, reducing MSE by 28.9%–34.5% against the strongest external baseline.
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All authors Renhao Zhong, Zihan Zhou, Chiyuan Ma, Tianshu Yu
Quantum Physics
Minimax Quantum State Tomography in a Known Trace-Distance Ball
Yonglong Li
We study
quantum state
tomography when the unknown state lies in a trace-distance ball of radius $R$ around a known reference state $\rho$. For arbitrary collective measurements, we determine the minimax expected risk and confidence radius up to universal constants, uniformly over the dimension, center spectrum, radius, and sample size. Write $\Gamma=d(\mathrm{Tr}\sqrt\rho)^2+d^2R$. For $d\ge2$, $0<R\le1$, and $n\ge1$ copies, the expected risk is $\Theta(\min\{R,\sqrt{\Gamma/n}\})$. At failure probability $0<\delta\le1/3$, the minimax confidence radius is \[ \Theta\!\left(\min\left\{R,\sqrt{\frac{\Gamma+\log(1/\delta)}{n}}\right\}\right). \] For $\varepsilon\le c_0R$ with a universal $c_0>0$, the copy complexity is $\Theta((\Gamma+\log(1/\delta))/\varepsilon^2)$. For the lower bound we use a weighted trace-norm witness to retain all spectral scales in a square-root perturbation family. For the upper bound, we give a direct spectral and concentration analysis of a modified existing purification-based procedure.
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Computation and Language
Zaiquan Yang, Fei Wei, Yong Wang et al. (+6 more)
On-policy
distillation (OPD) has emerged as an effective post-training paradigm for
language models, with recent efforts extending it to block
diffusion language models (BDLMs). However, existing studies focus almost exclusively on small block sizes, leaving
distillation into student models with larger blocks underexplored. In this work, we investigate this regime and reveal two critical optimization biases that induce severe training instability. First, mismatched block boundaries between teacher and student cause \textbf{context misalignment}, providing distorted supervisory signals that misguide student decoding. Second, even under aligned contexts, an \textbf{intrinsic optimization bias} in OPD, where the student tends to rapidly absorb high-support signals while lagging on low-support updates, drives a premature confidence surge that traps weaker students in catastrophic overconfidence collapse. To resolve these, we propose \mbox{Un-OPD}, an unbiased on-policy
distillation framework with two novelties for stabilizing BDLM training. First, Un-OPD introduces a boundary-aware step filtering strategy that eliminates context-misaligned decoding steps. Second, Un-OPD proposes moderating optimization intensity at high-support positions via a support-rebalanced confidence calibration, thereby bypassing overconfidence collapse. Beyond stability, we also introduce a rollout reuse mechanism to reduce rollout generation overhead. Extensive experiments on math
reasoning and code generation
benchmarks show that Un-OPD consistently stabilizes training and delivers superior performance while reducing wall-clock training time by approximately half.
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All authors Zaiquan Yang, Fei Wei, Yong Wang, Yudong Han, Yiyu Li, Zhuofan Zong, Gerhard Petrus Hancke, Xiangxiang Chu, Rynson WH Lau
Space Physics
What Caused the Orbital Decay of the Twin Van Allen Probes to Diverge?
Ayisha M Ashruf, Ankush Bhaskar, C Vineeth et al. (+1 more)
The Van Allen Probes were launched into nearly identical orbits and experienced the same
solar and geomagnetic environment, yet their post-mission lifetimes diverged dramatically. Probe A underwent rapidly accelerating orbital decay and reentered the atmosphere in March 2026, while Probe B remains in orbit. We investigate the cause of this divergence using reconstructed orbital trajectories, modeled thermospheric densities, and measures of low-altitude residence and atmospheric drag. We find that small differences in orbital
evolution progressively increased Probe A residence time in the lower thermosphere, where the steep density gradient made additional low-altitude exposure increasingly important. Enhanced thermospheric density during periods of geomagnetic activity further amplified this difference, leading to greater drag and accelerating orbital decay of Probe A. Our results show how small differences in orbital
evolution can be amplified through the coupled effects of thermospheric drag and space weather, producing substantially different orbital lifetimes even for twin spacecraft sharing nearly identical initial orbits.
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All authors Ayisha M Ashruf, Ankush Bhaskar, C Vineeth, Tarun Kumar Pant
Machine Learning
Robust Ensemble Guidance for Scientific Inverse Problems
Zixiang Li, Wei Wang, Yunchao Wei et al. (+2 more)
Ensemble guidance combines pretrained
diffusion priors with black-box forward models to solve inverse problems without differentiating through the physical simulator. However, observation coordinates with large predictive spread or extreme residuals can dominate the ensemble correction, degrading reconstruction accuracy. We show that two simple modifications, weighting and clipping, substantially improve this correction. Our method, Robust Ensemble Guidance (REG), uses ensemble predictive spread to balance observation scales and adaptively clips standardized residuals to limit the influence of extreme discrepancies. Both operations reuse existing particles and forward predictions, requiring no additional denoiser or forward-model evaluations. Under a local linear Gaussian model, we derive conditions for reduced one-step estimation risk, bound the influence of individual observation coordinates, and characterize when these benefits persist with finite ensembles. Experiments on Navier-Stokes inversion, black-hole imaging, and acoustic full-waveform inversion demonstrate improved reconstruction over the underlying ensemble solver. In particular, REG increases black-hole reconstruction PSNR by 6.2-8.2 dB across three observation regimes and reduces Navier-Stokes reconstruction error by 26.4% in a matched-budget comparison. These findings highlight the importance of observation heterogeneity and residual influence in designing reliable generative solvers for scientific inverse problems.
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All authors Zixiang Li, Wei Wang, Yunchao Wei, Yao Zhao, Yue Song
Artificial Intelligence
EnGRICH: Enhancing Generative Reward Modeling with Critiques from Humans
Xuancheng Li, Beining Wang, Haitao Li et al. (+7 more)
Generative reward models (GRMs) are important for LLM optimization. Unlike scalar reward models, GRMs generate natural-
language critiques alongside preference judgments, providing finer-grained evaluation signals. Their effectiveness depends heavily on critique reliability. However, existing GRM training typically uses final preference correctness as outcome supervision. Because the preference outcome space is highly constrained, unreliable critiques can still yield correct outcomes and thus be reinforced. Recent work leverages human critiques for process supervision, but such critiques are scarce and are often reduced to scalar rewards, leaving their fine-grained evaluative information underutilized. We argue that evaluative criteria learned from human critiques can be generalized to broader outcome-only preference data. To this end, we propose EnGRICH, a GRM training framework that pairs the GRM with a training-time MetaCritic learned from a small set of human critiques. MetaCritic constructs response-specific rubrics and uses them to evaluate the evidence coverage and correctness of generated critiques. The resulting signals provide both process rewards for fine-grained credit assignment and structured guidance for exploring better critiques. During GRM training, MetaCritic is further optimized to generalize human-grounded evaluative criteria to outcome-only data. At inference, the trained GRM operates independently. Experiments across seven reward-model
benchmarks show that EnGRICH consistently improves over competitive baselines, while further analyses validate the effectiveness of its core mechanisms.
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All authors Xuancheng Li, Beining Wang, Haitao Li, Heng Wang, Yujia Zhou, Qingyi Pan, Blaze Chen, Yiqun Liu, Min Zhang, Qingyao Ai
Cryptography and Security
AutoDP-LLM: Automating Data Pre-processing for Intrusion Detection Systems using Large Language Models
Bao-Phong Nguyen, Gia-Khanh Pham, Thai-Duong Do et al. (+7 more)
The increasing complexity and scale of modern cyber-attacks demand intelligent and computationally efficient Intrusion Detection Systems (IDS). However, designing effective data pre-processing pipelines traditionally involves substantial trial-and-error effort and repeated evaluation of alternative configurations. For large, high-dimensional network traffic data, this process can create a significant computational burden. In this work, we propose AutoDP-LLM, an automated pre-processing framework designed to reduce manual pipeline development and computational overhead. Specifically, AutoDP-LLM leverages Large
Language Models (LLMs) to autonomously generate and validate executable data pre-processing pipelines. The framework combines deterministic host-side planning with LLM-based specialist
agents to formulate data-processing strategies, synthesize executable code, and adaptively determine retained feature sets using semantic
reasoning and training-derived statistical evidence, without requiring a predefined feature budget. Focusing on multiclass intrusion detection, we evaluate AutoDP-LLM on the UNSW-NB15 and NSL-KDD
benchmark datasets using multiple downstream classifiers. Comparative experiments against conventional feature-selection methods show that AutoDP-LLM achieves competitive detection performance while automating the generation of compact and executable pre-processing pipelines. Component-level ablation experiments further demonstrate the complementary contributions of the semantic and statistical feature-reduction components. The repeated generation, validation, execution, and assessment of candidate pipelines are amenable to parallel execution, highlighting the potential of scalable computing environments, including high-performance computing (HPC) systems, to support automated IDS pipeline development.
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All authors Bao-Phong Nguyen, Gia-Khanh Pham, Thai-Duong Do, Mai Xuan Trang, Minh-Tuan Le, Xuan-Nam Tran, Huan Vu, Tien-Cuong Nguyen, Vu-Duc Ngo, Thien Van Luong
Machine Learning
The Effect of Missingness-Pattern Mismatch on Method Selection for Time-Series Classification: A Controlled Empirical Study
Ruiqi Zhao, Zishun Yuan, Zhentao Wang et al. (+3 more)
Classifiers for time-series classification are commonly selected on validation data, but the temporal pattern of missing observations at deployment may differ from the pattern seen during validation. We examine whether such a mismatch affects validation-based classifier selection. In a controlled $2 \times 2$ design, validation and test sets of 64 univariate UCR
datasets were masked with either random point missingness or circular block missingness at six rates from 5% to 30%, imputed by linear interpolation, and used to select among three prespecified candidates: 1NN-DTW, MiniRocket with a Ridge classifier, and a statistical-feature Random Forest. Training data remained complete, and selections made under matched and mismatched validation patterns were compared on the same masked test sets. Mismatched validation reduced the test balanced accuracy of the selected classifier by 1.14 percentage points on average (95% CI 0.79 to 1.51), with losses on 49 of the 64
datasets. The loss was negligible at 5% missingness and increased to 2.46 percentage points at 30%. It was concentrated in point-masked deployment (1.84 percentage points), where block-masked validation shifted selection away from the usually best candidate, while the effect for block-masked deployment was small and not significant. Mismatch changed the selected classifier in 35.5% of paired comparisons, but a changed selection did not always reduce performance. A supplementary analysis with non-wrapping linear blocks reproduced these findings with a larger effect (1.67 percentage points). Matching the missingness pattern of validation data to the expected deployment pattern is therefore a simple safeguard for method selection, particularly at higher missingness rates.
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All authors Ruiqi Zhao, Zishun Yuan, Zhentao Wang, Jiahao Quan, Kangzheng Li, Jianfan Deng
Logic in Computer Science
AIProver: Agentic Auto-Formalization of Mathematical Research via Certificate-Driven Evolving Harness
Prithwish Jana, Viet Bach Hoang, Logan Luna et al. (+9 more)
Proof auto-formalization translates natural-
language (NL)
theorems and proofs into a formal
language (FL) such as Lean, enabling mechanical verification. Despite rapid progress, research-level proofs often depend on concepts missing from leading proof assistant libraries (e.g., Lean's Mathlib), and successful compilation does not guarantee that a translation preserves the
theorem's meaning or the proof's
reasoning. Furthermore, aligned NL-FL training data are scarce, and leading
agents often rely on costly frontier models and manually engineered harnesses. To address the above issues, we present AIProver, an agentic framework for autonomous proof auto-formalization and proof synthesis (AFPS) that jointly post-trains a 119B open-weight
language model and evolves its agentic, tool-calling harness with HarnessEvolve. Verifiers assess type correctness, proof completeness, and semantic correctness, returning rewards and diagnostic certificates that drive model fine-tuning and alternating reinforcement learning via symbolic feedback and HarnessEvolve, a certificate-driven evolutionary search over the whole harness control flow that re-tailors the harness to the updated model. For research-level training and evaluation, we introduce LoCoBench, 58.9k instances from Mathlib, CSLib, Mizar Math Library, and a bounded-arithmetic textbook, with a 771-instance validation split whose
theorem-proof pairs have no public Lean formalization. Against 39 frameworks spanning AFPS
agents, frontier LLMs, and coding
agents, AIProver lifts pass@4 semantic correctness over its Leanstral-1.5 base from 15.7% to 36.7% and outperforms every other open-weight system and Aristotle. As a Claude Code and Codex skill, it lifts their semantic correctness from 41.9% and 34.1% to 79.8% and 62.4%, respectively. Further, it is also 24% cheaper than Numina-Lean-
Agent, pushing the accuracy-cost frontier of research-level AFPS.
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All authors Prithwish Jana, Viet Bach Hoang, Logan Luna, Viresh Pati, Akash Singirikonda, Cy Xie, Lisa Carbone, Wuyang Chen, Walter Moreira, Joe Stubbs, Sriram Vishwanath, Vijay Ganesh
Computation and Language
The ÌròyìnSpeech Text Corpus: 24,905 Curated Yorùbá Sentences for Speech and Language Technology
Kola Tubosun, Anuoluwapo Aremu, Tolulope Ogunremi et al. (+2 more)
ÌròyìnSpeech is a 42-hour, 80-speaker Yorùbá read-
speech corpus whose audio has been distributed by ELRA since 2024. This paper describes the release of its text component: 24,905 unique, hand-verified, tone-marked Yorùbá sentences (275,897
tokens; 15,687 types), curated in 2022 as recording
prompts. Roughly 11,000 sentences were adapted from openly licensed news material; the remainder were written in-house to broaden coverage beyond the religious translation that dominates existing Yorùbá corpora. Every sentence was checked by hand for tone-mark accuracy, edited for read-aloud clarity and a neutral register, and localised so that non-Yorùbá personal and place names appear in Yorùbá form. Preparing the text for release surfaced systematic Unicode normalisation failures affecting more than 60% of lines (with precomposed and decomposed forms of the same letter co-occurring within single sentences) which we document and correct. The corpus supports diacritic restoration, grapheme-to-phoneme conversion, TTS front-end development and orthographic research, and serves as a validated
prompt set for new recording.
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All authors Kola Tubosun, Anuoluwapo Aremu, Tolulope Ogunremi, Iroro Orife, David Ifeoluwa Adelani
Statistics Theory
Poisson Autoregression on a Large Network with a Stochastic Block Model Structure
Mahmoud Khabou, Joanna Marks, Joshua Corneck et al. (+1 more)
We consider multivariate Poisson autoregressive processes evolving on random networks generated by a
Stochastic Block Model. This framework extends existing network Poisson autoregressions by incorporating latent community structure and allowing for non-Markovian dependence, both excitatory and inhibitory. We establish a mean-field approximation and prove that the finite system converges to its limit at the optimal rate $N^{-1/2}$ in the quenched setting with overwhelming probability, both on average and in uniform norm. Our analysis yields quantitative error bounds that are explicit in the time horizon and, under suitable stability conditions, remain
polynomial or uniform in time, thereby avoiding the exponential growth typically associated with Grönwall-type arguments. As a consequence, the mean-field approximation is shown to hold uniformly over any time horizon. We further demonstrate how the approximation can be exploited to reduce the computational complexity of parametric inference from $\mathcal{O}(N^2T^2)$ to $\mathcal{O}(NT^2)$. The results provide a theoretical foundation for the analysis and inference of count-valued processes on large random networks with community structure.
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All authors Mahmoud Khabou, Joanna Marks, Joshua Corneck, Edward A. K. Cohen
Representation Theory
Tempered Symplectic Distinction For Quaternionic $GL_n(D)$: A Conjecture of PRASAD
Mahendra Kumar Verma
Let $F$ be a non-Archimedean local field of characteristic zero, let $D/F$ be the quaternion division
algebra, and put $G_n = GL_n(D)$ and $H_n = Sp_n(D)$. We prove Prasad's revised
conjecture on tempered representations with
symplectic period. If $\rho$ is a
unitary $H_r$-distinguished supercuspidal representation and $\delta_m(\rho)$ denotes the generalized Steinberg representation associated to $\rho$, set $B_0(\rho) = \rho, B_m(\rho) = \delta_{m+1}(\rho) \times \delta_m(\rho), m \geq 1.$ We prove that an irreducible tempered representation $\pi$ of $G_n$ is $H_n$-distinguished if and only if $\pi$ is isomorphic to the product over $i$ of $B_{m_i}(\rho_i),$ where each $\rho_i$ is a
unitary distinguished supercuspidal representation.
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