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arXiv2026

Grassmannian-Coded Beamforming for mmWave Channel Sensing with Unknown Complex Path Gain

This paper introduces a subspace-coding perspective to millimeter-wave channel sensing with a single RF chain when the complex channel gain is unknown. We show that in this case, candidate directions-of-arrival (DoAs) map naturally to subspaces through their beamspace responses, revealing an intrinsic Grassmannian geometry. This motivates beamspace Grassmannian codes (BGCs), designed to reduce DoA error by maximizing the minimum subspace distance of the joint beamformer-array response. We identify two regimes: one in which existing Grassmannian packings are exactly realizable as BGCs when the angular grid matches the array size, and another in which realizability for finer grids is constrained by the array geometry. Our analysis establishes the joint roles of subspace distance and beamforming gain in sensing performance and motivates two complementary beamformer designs. Without prior DoA information, we develop spatially isotropic beamformers based on algebraic Grassmannian packings and modulation-based channel codes. With a known DoA region of interest, we design convolutional beamspaces that combine directional gain with favorable subspace distance. Numerical results demonstrate robust BGC performance for both on-grid and off-grid DoAs, supporting the effectiveness of the proposed Grassmannian framework for mmWave channel sensing.

eess.SP↗

arXiv2026

How Much Training is Needed with a Digital Twin?

The following paper addresses how much pilot training is needed when a digital twin (DT) of the wireless radio channel is available to aid a wireless communication system with a channel estimation task. The DT of a wireless channel is widely expected to reduce the pilot overhead of channel estimation, following the informal rule that \emph{``the more accurate the twin, the fewer pilots are needed.''} This trade-off, however, has only ever been demonstrated empirically and never quantified. We close this gap by treating the DT as a complementary measurement of the channel that the receiver fuses with its pilot observations in the physical world. Consequently, fusing the physical and digital worlds through the best linear unbiased estimator, we derive a DT-aided Cramér-Rao bound, and from it a \emph{pilot-equivalence law} that converts DT fidelity into an equivalent number of training symbols. For a biased twin unknown to the estimator, we obtain the exact mismatch threshold beyond which trusting the DT is worse than ignoring it. We quantify how much training is needed with the DT to attain a desired mean square error on channel estimation. Particular cases are discussed to tell when training in the physical world can be completely bypassed. We finally translate these results into a block-fading achievable rate whose optimal training length is the unique root of a single equation, and identify the DT fidelity above which pilot training can be dispensed with altogether. Extensive numerical results corroborate closed-form expression and reveal that the value of a DT is largest at finite signal-to-noise ratio and vanishes in both the low- and high-SNR limits.

eess.SP↗

arXiv2026

Benchmarking External Generalization of SPD Matrix Learning for Resting-State fMRI Connectome Prediction

Resting-state functional magnetic resonance imaging (rs-fMRI) functional connectivity (FC) matrices are widely used for individual-level prediction, but strong performance within one cohort may not generalize to a new cohort. We ask whether within-dataset performance remains when the test data come from an entirely held-out rs-fMRI dataset. Each scan is represented as a regularized symmetric positive definite (SPD) correlation connectome, which allows methods to use the geometry of the SPD manifold. We introduce a reproducible age-prediction benchmark across six rs-fMRI datasets: COBRE, ADNIDOD, Cam-CAN, ABIDE, OASIS-3, and ADNI. The benchmark compares a vectorized correlation baseline, Tangent-Space Ridge, SPDNet, and split-wise Riemannian harmonization under within-dataset GroupKFold, pooled GroupKFold, and leave-one-dataset-out (LODO) evaluation. Within-dataset and pooled GroupKFold results are substantially more favorable than LODO results. When an entire dataset is held out, prediction error increases, differences among methods narrow, and performance is strongly affected by age-range mismatch and cohort heterogeneity. The benchmark provides common inputs, model settings, data splits, and analysis scripts so that future SPD matrix learning methods can be evaluated under the same external-validation protocol.

eess.SP↗

arXiv2026

A Kalman Filter-Based Tracking Loop Design for Real-Time Aerospace GNSS Applications with Minimum Pull-Out Probability

Kalman filter-based (KF-based) tracking loops are a powerful alternative to traditional phase-locked loops (PLLs) for Global Navigation Satellite Systems (GNSS) signal tracking. The primary advantage of the KF is its ability to incorporate high-fidelity models for receiver dynamics and clock errors, allowing the loop to adapt optimally to signal conditions. However, this theoretical optimality is often compromised in practice by the processing delays inherent in real-time systems with hardware correlators, which existing KF formulations typically neglect. This paper introduces a Modified Kalman filter (mKF) that overcomes this limitation specifically for hardware-based architectures. By reformulating the measurement update to be consistent with the processing delays, the proposed mKF maintains optimality in a practical implementation. We further present a systematic method for tuning both the process noise covariance matrix and the correlation time, based on an analytical expression for the pull-out probability (POP), which is validated through Monte Carlo simulation. The mKF is then validated with a GNSS signal simulator, both by post-processing baseband samples and on a real-time GPS receiver with hardware correlators. A direct equivalence between the mKF and a one-delay Digital PLL (DPLL) is established entirely in the digital domain. At equal noise bandwidth, the mKF matches the DPLL's phase error variance while achieving lower error in the higher-order states. Moreover, the mKF sustains lock at bandwidths inaccessible to the optimal one-delay DPLL under the same dynamic stress, positioning the proposed architecture as a robust and noise-efficient solution for high-dynamic aerospace GNSS applications.

eess.SP↗

arXiv2026

Operational Regimes in Non-Convex Optimization: A Multiplier-Based Taxonomy

This paper introduces a structural taxonomy for constrained non-convex optimization based on the signature of Lagrange multipliers at KKT stationary points. Leveraging a unified game-theoretic interpretation of eight classical algorithm families--including block coordinate descent, ADMM, generalized Benders decomposition, successive convex approximation, interior-point methods, mirror descent, Frank-Wolfe, and Riemannian gradient descent--we show that the normalized multiplier vector carries an algorithm-independent structural fingerprint. Four scale-free shape features of this vector partition the dual space into five operational regimes: Unconstrained, Resource-Limited, Saturation, Strongly-Coupled, and Hybrid. We establish four structural theorems characterizing the partition: invariance under natural KKT symmetries, local stability under data perturbation with explicit Lipschitz margins from Robinson's strong regularity, codimension-one regime transitions, and the topological identification of the Hybrid regime as the Lebesgue-null boundary of the core regimes. A linear-time classifier is proposed with provable guarantees on correctness, iteration stabilization, sample complexity, and online tracking under data drift. Numerical experiments on 104 mixed-integer nonlinear programs and a downlink beamforming instance validate the theoretical predictions. The framework provides a foundational tool for regime-aware algorithm design and robustness analysis in non-convex optimization.

math.OC↗

arXiv2026

Learning the Channel Gain from Anywhere to Anywhere via Cross-environment Transformer Estimators

Channel-gain maps provide the channel gain between any two locations in a geographical region. They find numerous applications, from resource allocation and interference control to path planning for autonomous vehicles. Channel-gain map estimation (CGME) is considerably more challenging than conventional radio map estimation (RME) because channel-gain maps are functions over a 6-dimensional input space. This calls for specialized methods, which currently rely on the (inaccurate) radio tomographic model or require a prohibitively large number of measurements since they do not exploit any spatial structure. This paper overcomes this issue by leveraging spatial patterns that channel-gain maps exhibit across environments, as dictated by the laws of physics and typical environmental characteristics (e.g. building materials and layouts). Adopting a metalearning perspective, a transformer-based estimator is proposed to implicitly learn this common structure from measurements collected in multiple environments. This enables CGME in new environments from significantly fewer measurements (five times less in our experiments). To maximize learning efficiency, the transformer is composed with a feature map that enforces the invariances of CGME, such as those following from reciprocity. Numerical experiments corroborate the merits of the proposed estimator relative to existing methods.

eess.SP↗

arXiv2026

Semantic Freshness Optimal Sampling and Transmission for Gossiping Receivers

We study the optimal joint sampling and transmission policy for a transmitter communicating with two gossiping receivers that share information with each other, with the objective of tracking a source under the Version Age of Information (VAoI) metric. The transmitter can observe source-version changes, but it has to pay a sampling cost to get the current source information content. Similarly, it can communicate with a receiver by paying a transmission cost. Gossiping enables local information exchange and is able to reduce costly direct transmissions. With imperfect communication links, we formulate an infinite-horizon average-cost Markov Decision Process (MDP) to jointly minimize receiver VAoI, sampling cost, and transmission cost. Using Relative Value Iteration (RVI), we evaluate the optimal policy and establish several properties of its structure. We prove that sampling has a threshold structure in the transmitter VAoI. Among direct transmissions, it is optimal to serve the older receiver. We further characterize the transmit or idle decision through the receiver VAoI difference. Our analysis shows that link reliability and receiver VAoI imbalance have a significant effect on the optimal policy structure. Numerical results verify the structural properties and demonstrate the performance gains of the optimal policy over multiple baselines.

cs.IT↗

arXiv2026

QABBA: Symbolic Time-Series Compression via Integer-Quantized Aggregation

The expansion of time-series data from sensors and monitoring systems has made compact representations increasingly important. Such representations should retain signal structure while cutting storage, transmission and computation costs. Adaptive Brownian Bridge-based Aggregation (ABBA) addresses this need by converting long numerical series into short symbolic sequences, but reductions in parameter storage and computational precision remain desirable. We propose Quantized ABBA (QABBA), a quantized version of ABBA. By quantizing the symbolic centers, QABBA reduces the parameter footprint and enables integer arithmetic while maintaining high reconstruction quality. We establish several error bounds for the additional approximation introduced by quantization: a dimension-free bound on the excess error of each segment, a time-domain reconstruction-error bound, a stability condition for symbolic assignment, and a rule for allocating bits between segment lengths and increments. The resulting symbolic strings can be passed directly to a pretrained large language model (LLM) without any extra time-series embedding layer. Experiments on the Monash regression archive, UCR Time Series Classification Archive, and UEA Multivariate Time Series Classification Archive demonstrate a practical trade-off among storage, reconstruction accuracy and downstream predictive performance. QABBA therefore provides an error-controlled, low-precision symbolic representation for time-series compression and LLM-based analysis.

cs.LG↗

arXiv2026

From Elastic to Viscoelastic: An EEMD-Enhanced Pulse Transit Time Model for Robust Blood Pressure Estimation

Cuffless blood pressure (BP) estimation based on Pulse Transit Time (PTT) has emerged as a promising solution for continuous health monitoring. However, conventional models relying on the Moens-Korteweg equation often fail during rapid hemodynamic fluctuations, as they assume arterial walls are purely elastic and neglect inherent viscoelasticity. To address this limitation, we propose a physics-informed framework introducing a viscoelastic compensation mechanism. First, raw photoplethysmogram (PPG) signals undergo high-fidelity reconstruction using Modified Akima (Makima) interpolation. Second, a robust Intersecting Tangent Method is applied for precise pulse foot localization. Crucially, we utilize Ensemble Empirical Mode Decomposition (EEMD) to isolate high-frequency Intrinsic Mode Functions (IMFs), defining a ``Viscoelastic Velocity Metric'' to quantify the vascular damping effect ($η\cdot \dotε$) typically ignored by elastic models. The framework was rigorously validated on a challenging subset of the MIMIC-II database (364 subjects, 28,525 cardiac cycles) characterized by a high prevalence of hypertension (23.4\%). Experimental results demonstrate medical-grade accuracy, yielding a Root Mean Square Error (RMSE) of 5.22 mmHg for Systolic and 3.65 mmHg for Diastolic BP, with Pearson correlation coefficients ($R > 0.97$). These findings confirm that incorporating viscoelastic features significantly enhances robustness against vascular hysteresis.

cs.HC↗

arXiv2026

BeamRMX: Radiation-Pattern-Driven Learning for Generalizable Beam Radio Map Prediction and Beam Management

The evolution toward sixth-generation (6G) wireless networks is driving larger antenna arrays and highly directional multi-beam transmission, making accurate knowledge of beam-dependent spatial coverage important for beam management and environment-aware network operation. Radio maps (RMs) provide such a representation, yet conventional RM prediction assumes omnidirectional or transmitter-level radiation. In beamformed multiple-input multiple-output (MIMO) systems, one propagation scene instead gives rise to many configuration-dependent beam radio maps (BeamRMs), creating challenges in beam representation and generalization. Existing methods either condition prediction on beam descriptors or use beam maps as auxiliary inputs to generic architectures. We propose BeamRMX, which, to the best of our knowledge, is the first dedicated framework to treat the spatial radiation pattern as the primary BeamRM query and learn how scene geometry transforms it into the received power field. XBase learns multiscale interactions between the radiation query and scene geometry, while an optional Evidence Adapter uses a few cross-configuration BeamRMs from the same scene. Matched-domain and zero-shot experiments show consistent gains over deterministic and diffusion baselines, including mean absolute error reductions of 26.1\% on unseen scenes and 47.8\% on an unseen configuration. Cross-configuration evidence further improves reconstruction and intra-sector beam refinement.

eess.SP↗

arXiv2026

Multivariable Geometric Laplace Transform and Fault Detection in Distributed-Converter Lines

Monitoring a DC line with many distributed power converters is a genuinely spatio-temporal problem: the information about a localized fault travels along the whole conductor and reaches a few measurement points mixed with the dynamics of the line itself. This paper develops a two-dimensional geometric Laplace transform (t,x) -> (s_t,s_x) over a commutative subalgebra of the geometric algebra Cl(4,0), isomorphic to Segre's bicomplex numbers, in which two bivectors B_t and B_x act as independent imaginary units for the temporal and the spatial phase. Because the two phases live in algebraically distinguishable planes, a fault at position x_f leaves a transformed residual that factorizes as F_f(s_t) e^{-s_x x_f}: its temporal nature stays in the first factor and its location can be read as a geometric argument of the second. On this representation we build a transmission-line model of the converter line and its space-time dispersion relation, a distributed control by admittance shaping, including an exact treatment of discrete converter sites (spatial sampling, aliasing, and a per-converter droop realization that is exact on the sub-Nyquist band), and a fault diagnosis chain that detects, localizes and classifies injection-loss, shunt, sensor and local-controller faults, extends to multiple simultaneous faults with automatic order selection, and distinguishes the outage of a plant from a cable defect. As an integral object the transform is known in bicomplex analysis, and with a single independent variable it reduces to the complex Laplace transform; the contribution lies in its geometric embedding and in its operational use for fault diagnosis in distributed-converter networks. All results are reproduced by an accompanying open implementation.

eess.SY↗

arXiv2026

Slow-Fast Brain-Computer Interfaces: Preventing Neuroadaptive Overfitting in AI-Mediated Neural Interfaces

Artificial intelligence (AI) is transforming brain-computer interfaces (BCIs) from task-specific neural decoders into adaptive systems that complete language, smooth movement, regulate rehabilitation support and adjust stimulation. These capabilities can increase speed, fluency, usability and clinical reach, yet conventional performance metrics may overlook losses in intent fidelity, authorship, agency, therapeutic challenge and durable clinical benefit. I define neuroadaptive overfitting as a closed-loop failure mode in which an AI-mediated BCI becomes over-optimized to short-term proxies of success, including reduced effort, rapid acceptance, lower workload or smooth task completion, while drifting from the user's durable goals. I then propose Slow-Fast BCI, a framework for pacing AI assistance according to decoder evidence, uncertainty, contextual and clinical stakes, fatigue, and user- or clinician-defined goals. The framework distinguishes fast assistance when intent is clear and stakes are low, guarded assistance under uncertainty and slow assistance when misalignment could compromise safety, agency, authorship, motor learning or therapeutic value. Across communication, motor-control, neurorehabilitation and closed-loop neuromodulation applications, I outline corresponding safeguards and evaluation measures. This Perspective argues that AI-mediated BCIs should be evaluated not only by decoding accuracy and task performance, but also by how AI assistance is deployed: when systems act autonomously, seek confirmation, preserve user effort or return control to the user.

q-bio.NC↗

arXiv2026

A Unified Particle Filter LSTM for Data-Driven Process Simulation

Data-driven process simulation aims to generate realistic case trajectories from historical event logs without requiring an explicitly specified model of the underlying dynamics. Deep sequence models can capture complex temporal dependencies through next-activity probabilities and conditional time distributions. However, event logs provide only a partial view of the underlying process state, often recording activity completions without the corresponding service-start times. Consequently, the same observed process history may be consistent with multiple plausible latent process conditions, whereas standard recurrent models compress each process prefix into a single deterministic recurrent state. We propose a Unified Particle Filter LSTM (Unified PF-LSTM) that maintains and sequentially updates a weighted set of recurrent-state hypotheses. We summarize this particle belief using its weighted mean and learned features based on the moment-generating function. The resulting representation is used to predict a categorical distribution over the next activity and conditional quantiles of the current activity's sojourn time. The framework is trained end-to-end from event-log data and evaluated on three real-world emergency department datasets. The results show that the proposed framework consistently outperforms the considered data-driven baselines in reproducing routing, duration, and system-level behavior across all datasets, with particularly strong gains in settings where complex process dynamics are only partially reflected in the available event logs.

cs.LG↗

arXiv2026

Instance Optimal Sparse Recovery from Nonlinear Observations: A Unified Framework

This paper develops a unified framework for instance optimal sparse recovery from nonlinear observations. The main ingredient is a signal-dependent restricted approximate invertibility condition (RAIC) of some gradient, which leads to the instance optimality of iterative hard thresholding. Under Gaussian designs, we apply the proposed framework to phaseless, one-bit, and ReLU measurements, which correspond to the problems of sparse phase retrieval, one-bit compressed sensing, and sparse ReLU regression, respectively. For sparse phase retrieval, we propose a variant of thresholded amplitude flow and show its instance optimality under $O(s^3)$ measurements (up to logarithmic factors), where $s$ is the sparsity level. To our best knowledge, this is the first instance optimal efficient algorithm for sparse phase retrieval and complements Gao, Wang and Xu (2016) that achieved this via a computationally intractable program. In one-bit compressed sensing, we establish the instance optimality of normalized binary iterative hard thresholding and strengthen the recent result of Matsumoto and Mazumdar (2024). In sparse ReLU regression, it is shown that a slight variant of the algorithm in Soltanolkotabi (2017) is instance optimal. Moreover, $(\ell_2,\ell_2)$ non-uniform instance optimal guarantees are obtained for these problems. The analysis is built upon a number of high-dimensional concentration bounds, including bounds on restricted eigenvalues and a novel instance-dependent hyperplane tessellation result.

cs.IT↗

arXiv2026

Leakage-Audited Benchmarking Reveals Limited Evidence for Cross-Subject Auditory-Evoked EEG Vowel Perception Decoding

We tested whether auditory-evoked EEG supports subject-independent five-vowel perception decoding when trial identity, model identity, prediction provenance, and participant-level inference are controlled within a single benchmark. We reconstructed Study 2 event tables from OpenNeuro ds006104 version 1.0.1 and analysed the consonant-vowel pair task. One-to-one marker-stimulus pairing yielded 3,840 independent trials; control-condition selection and artifact rejection retained 1,094 epochs from 16 participants and 61 EEG channels. Thirteen unique implementations were evaluated using leave-one-subject-out testing, with participant metrics reconstructed from 36,102 trial predictions across 33 complete prediction replicas. Random Forest was numerically highest at 21.474% balanced accuracy (95% participant-bootstrap interval, 19.526-23.482%; chance, 20%), but neither its participant-level tests nor any implementation survived correction across the 13-model family. Deep-model performance was close to chance, and several architectures showed substantial seed-dependent variation and low trial-label agreement. An exploratory MDM analysis comprising 9,616 genuine refits across training cohorts of 3-15 participants showed no monotonic performance gain. Within this dataset and protocol, evidence for reliable cross-subject five-vowel decoding is limited. The benchmark provides a reproducible chain from source rows to retained epochs, predictions, participant-level metrics, multiplicity-adjusted inference, and bounded diagnostic analyses.

eess.SP↗

arXiv2026

Efficient Learning of Balanced Signed Graphs via Sparse Linear Programming

Signed graphs are equipped with both positive and negative edge weights, encoding pairwise correlations as well as anti-correlations in data. A balanced signed graph is a signed graph with no cycles containing an odd number of negative edges. Laplacian of a balanced signed graph has eigenvectors that map via a simple linear transform to ones in a corresponding positive graph Laplacian, thus enabling reuse of spectral filtering tools designed for positive graphs. We propose an efficient computation method to learn a balanced signed graph Laplacian directly from data. Specifically, extending a previous linear programming (LP) based sparse inverse covariance estimation method called CLIME, we formulate a new LP problem for each Laplacian column $i$, where the linear constraints restrict weight signs of edges stemming from node $i$, so that nodes of same / different polarities are connected by positive / negative edges. We derive a feasible CLIME parameter $ρ_i$ for each sign-constrained column problem. We solve the LP problem efficiently by tailoring a sparse LP method based on ADMM. We theoretically prove that the row / column updates produce a non-increasing objective sequence, and show that the iterations are terminated in a finite number of steps. Extensive experimental results on synthetic and real-world datasets show that our balanced graph learning method outperforms competing methods and enables reuse of spectral filters, wavelets, and graph neural nets (GNN) constructed for positive graphs.

cs.LG↗

arXiv2026

A Token/KV-Cache Communication Media Selection and Resource Allocation Strategy for Multi-Agent Collaboration

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.

eess.SP↗

arXiv2026

Beyond AHI: An Interpretable Causal-Discovery-Guided Framework for Sleep Recovery in Connected Health

Objective sleep assessment relies on polysomnography (PSG), yet clinical impact is often better reflected in patient-reported outcomes (PROs) such as sleepiness and fatigue. Existing summary indices, including the Apnea-Hypopnea Index (AHI), provide limited insight into the multidomain physiology underlying functional recovery. We propose an interpretable, causal-discovery-guided framework for deriving a hierarchical Sleep Recovery Score (SRS) from multimodal PSG. Using two large population cohorts (MESA: $n=1{,}540$; MrOS: $n=825$), we apply directed acyclic graph (DAG) learning to identify candidate physiological drivers spanning respiratory burden, hypoxic burden, sleep fragmentation, sleep architecture, and autonomic regulation. Although derived from clinical PSG, these domains map naturally to sensing streams increasingly available in connected health technologies, including wearable ECG, oximetry, and sleep-stage estimation devices. To preserve mechanistic plausibility, we introduce a two-stage screening process that combines physiology-based constraints with constrained LLM-assisted auditing to identify and remove structural confounders and construct-overlapping variables. Across cohorts, these five domains emerge as recurrent physiological domains associated with recovery, and the resulting SRS shows up to $3.4\times$ stronger alignment with perceived recovery than AHI. By linking multimodal sleep physiology to patient-centered outcomes through an interpretable, bias-aware, and domain-structured framework, this work provides a practical foundation for recovery modeling across both clinical sleep studies and emerging smart and connected health settings.

cs.LG↗