arXiv:2605.25278v1 Announce Type: cross Abstract: Understanding the statistics of level crossings in stochastic processes is crucial across many scientific disciplines. The traditional Kac-Rice formula gives the mean rate of level crossings and has found broad use. However, that mean rate captures only a coarse summary of the crossing process. It depends entirely on local properties of the stochastic process at a given instant and is therefore blind to the correlation structure of the process over time. To understand whether crossing events, such as neuronal spikes, tend to cluster in time, spread apart, or exhibit more complex temporal organization, one must go beyond the mean rate and study higher-order crossing statistics. Here we go beyond the mean by deriving the exact analytical formulae for the variance and Fano factor of arbitrary level crossings in smooth stationary Gaussian processes. Our exact solution reveals how the full temporal correlation structure dictates whether crossings cluster or become regular. In systems with oscillatory correlations, such as a stochastic damped harmonic oscillator, a recent crossing suppresses an immediate subsequent one, producing sub-Poissonian statistics. However, as damping increases and oscillations disappear, a large and slow excursion above the threshold can produce multiple closely spaced crossings, yielding super-Poissonian statistics. In purely relaxational, non-oscillatory systems, such as a mean-reverting process driven by Ornstein-Uhlenbeck noise, the competition between the timescales of the driving noise and system relaxation produces a richer landscape, including reentrant transitions between sub- and super-Poissonian statistics as the threshold level is varied. Taken together, the exact variance and Fano factor derived here complement the Kac-Rice mean rate, enabling more robust parameter estimation and model selection across any setting where Gaussian processes are used.

arXiv:2605.25422v1 Announce Type: cross Abstract: The convergence of large language models (LLMs) with 6G networks is fostering a paradigm of autonomous multi-agent cooperation, which in turn is expected to substantially increase east-west traffic. Although latent-space interaction mechanisms can enable more efficient collaboration than symbolic natural-language (NL) exchanges, prior work often abstracts away the associated communication overhead under practical wireless constraints. In embodied multi-agent settings, heterogeneous interaction media incur disparate inference and transmission costs, thereby inducing an inherent end-to-end (E2E) latency trade-off. To address this, we propose a joint design that integrates communication-media selection with wireless resource allocation. Through analytical characterization and simulation-based evaluation, we show that neither token-based transmission nor key-value (KV) cache-based transmission is uniformly optimal across operating regimes, as performance depends critically on system parameters such as available computational resources and channel conditions. Accordingly, we formulate a joint optimization problem aimed at minimizing the E2E latency of multi-agent collaboration and develop a low-complexity joint media selection and resource allocation (JMSRA) algorithm. Numerical results further confirm that, by adaptively coordinating the interaction media and bandwidth allocation over heterogeneous links, the proposed scheme achieves markedly reduced E2E latency relative to conventional NL-only and KV-cache-only baselines, enabling efficient and robust multi-agent collaboration in future wireless networks.

arXiv:2505.05371v2 Announce Type: replace-cross Abstract: Automation of sleep analysis, including both macrostructural (sleep stages) and microstructural (e.g., sleep spindles) elements, promises to enable large-scale sleep studies and to reduce variance due to inter-rater incongruencies. While individual steps, such as sleep staging and spindle detection, have been studied separately, the feasibility of automating multi-step sleep analysis remains unclear. In this case study, we evaluate whether a fully automated analysis using validated machine learning models for sleep staging (RobustSleepNet) and subsequent spindle detection (SUMOv2) can replicate findings from an expert-based study of bipolar disorder. The automated analysis qualitatively reproduced key findings from the expert-based study, including significant differences in fast spindle densities between bipolar patients and healthy controls, accomplishing in minutes what previously took months to complete manually. While the results of the automated analysis differed quantitatively from the expert-based study, possibly due to biases between expert raters or between raters and the models, the models individually performed at or above inter-rater agreement for both sleep staging and spindle detection. Our results demonstrate that fully automated approaches have the potential to facilitate large-scale sleep research. We are providing public access to the tools used in our automated analysis by sharing our code and introducing SomnoBot, a privacy-preserving sleep analysis platform.

arXiv:2505.18190v5 Announce Type: replace-cross Abstract: Physics sensing plays a central role in many scientific and engineering domains, which inherently involves two coupled tasks: reconstructing dense physical fields from sparse observations and optimizing scattered sensor placements to observe maximum information. While deep learning has made rapid advances in sparse-data reconstruction, existing methods generally omit optimization of sensor placements, leaving the mutual enhancement between reconstruction and placement on the shelf. To change this suboptimal practice, we propose PhySense, a synergistic two-stage framework that learns to jointly reconstruct physical fields and to optimize sensor placements, both aiming for accurate physics sensing. The first stage involves a flow-based generative model enhanced by cross-attention to adaptively fuse sparse observations. Leveraging the reconstruction feedback, the second stage performs sensor placement via projected gradient descent to satisfy spatial constraints. We further prove that the learning objectives of the two stages are consistent with classical variance-minimization principles, providing theoretical guarantees. Extensive experiments across three challenging benchmarks, especially a 3D geometry dataset, indicate PhySense achieves state-of-the-art physics sensing accuracy and discovers informative sensor placements previously unconsidered. Code is available at this repository: https://github.com/thuml/PhySense.

arXiv:2512.18508v3 Announce Type: replace-cross Abstract: Validation gating is a fundamental component of classical Kalman-based tracking systems. Only measurements whose normalized innovation squared (NIS) falls below a prescribed threshold are considered for state update. While this procedure is statistically motivated by the chi-square distribution, it implicitly replaces the unconditional innovation process with a conditionally observed one, restricted to the validation event. This paper shows that innovation statistics computed after gating converge to gate-conditioned rather than nominal quantities. Under classical linear--Gaussian assumptions, we derive exact expressions for the first- and second-order moments of the innovation conditioned on ellipsoidal gating, and show that gating induces a deterministic, dimension-dependent contraction of the innovation covariance. The analysis is extended to NN association, which is shown to act as an additional statistical selection operator. We prove that selecting the minimum-norm innovation among multiple in-gate measurements introduces an unavoidable energy contraction, implying that nominal innovation statistics cannot be preserved under nontrivial gating and association. Closed-form results in the two-dimensional case quantify the combined effects and illustrate their practical significance.