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Exact Variance and Fano Factor for Arbitrary Level Crossings in Stationary Gaussian Processes

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

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.
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From Sleep Staging to Spindle Detection: A Case Study on End-to-End Automated Sleep Analysis

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.
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PhySense: Sensor Placement Optimization for Accurate Physics Sensing

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.
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Selection-Induced Contraction of Innovation Statistics in Gated Kalman Filters

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.
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RAVEN: Radar Adaptive Vision Encoders for Efficient Chirp-wise Object Detection and Segmentation

arXiv:2604.04490v1 Announce Type: cross Abstract: This paper presents RAVEN, a computationally efficient deep learning architecture for FMCW radar perception. The method processes raw ADC data in a chirp-wise streaming manner, preserves MIMO structure through independent receiver state-space encoders, and uses a learnable cross-antenna mixing module to recover compact virtual-array features. It also introduces an early-exit mechanism so the model can make decisions using only a subset of chirps when the latent state has stabilized. Across automotive radar benchmarks, the approach reports strong object detection and BEV free-space segmentation performance while substantially reducing computation and end-to-end latency compared with conventional frame-based radar pipelines.
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An AI Teaching Assistant for Motion Picture Engineering

arXiv:2604.04670v1 Announce Type: cross Abstract: The rapid rise of LLMs over the last few years has promoted growing experimentation with LLM-driven AI tutors. However, the details of implementation, as well as the benefit in a teaching environment, are still in the early days of exploration. This article addresses these issues in the context of implementation of an AI Teaching Assistant (AI-TA) using Retrieval Augmented Generation (RAG) for Trinity College Dublin's Master's Motion Picture Engineering (MPE) course. We provide details of our implementation (including the prompt to the LLM, and code), and highlight how we designed and tuned our RAG pipeline to meet course needs. We describe our survey instrument and report on the impact of the AI-TA through a number of quantitative metrics. The scale of our experiment (43 students, 296 sessions, 1,889 queries over 7 weeks) was sufficient to have confidence in our findings. Unlike previous studies, we experimented with allowing the use of the AI-TA in open-book examinations. Statistical analysis across three exams showed no performance differences regardless of AI-TA access (p > 0.05), demonstrating that thoughtfully designed assessments can maintain academic validity. Student feedback revealed that the AI-TA was beneficial (mean = 4.22/5), while students had mixed feelings about preferring it over human tutoring (mean = 2.78/5).
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Semantically Annotated Multimodal Dataset for RF Interpretation and Prediction

arXiv:2604.01433v1 Announce Type: cross Abstract: Current limitations in wireless modeling and radio frequency (RF)-based AI are primarily driven by a lack of high-quality, measurement-based datasets that connect RF signals to their physical environments. RF heatmaps, the typical form of such data, are high-dimensional and complex but lack the geometric and semantic context needed for interpretation, constraining the development of supervised machine learning models. To address this bottleneck, we propose a new class of multimodal datasets that combines RF measurements with auxiliary modalities like high-resolution cameras and lidar to bridge the gap between RF signals and their physical causes. The proposed data collection will span diverse indoor and outdoor environments, featuring both static and dynamic scenarios, including human activities ranging from walking to subtle gestures. By achieving precise spatial and temporal co-registration and creating digital replicas for voxel-level annotation, this dataset will enable transformative AI research. Key tasks include the forward problem of predicting RF heatmaps from visual data to revolutionize wireless system design, and the inverse problem of inferring scene semantics from RF signals, creating a new form of RF-based perception.
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Transformer self-attention encoder-decoder with multimodal deep learning for response time series forecasting and digital twin support in wind structural health monitoring

arXiv:2604.01712v1 Announce Type: cross Abstract: The wind-induced structural response forecasting capabilities of a novel transformer methodology are examined here. The model also provides a digital twin component for bridge structural health monitoring. Firstly, the approach uses the temporal characteristics of the system to train a forecasting model. Secondly, the vibration predictions are compared to the measured ones to detect large deviations. Finally, the identified cases are used as an early-warning indicator of structural change. The artificial intelligence-based model outperforms approaches for response forecasting as no assumption on wind stationarity or on structural normal vibration behavior is needed. Specifically, wind-excited dynamic behavior suffers from uncertainty related to obtaining poor predictions when the environmental or traffic conditions change. This results in a hard distinction of what constitutes normal vibration behavior. To this end, a framework is rigorously examined on real-world measurements from the Hardanger Bridge monitored by the Norwegian University of Science and Technology. The approach captures accurate structural behavior in realistic conditions, and with respect to the changes in the system excitation. The results, importantly, highlight the potential of transformer-based digital twin components to serve as next-generation tools for resilient infrastructure management, continuous learning, and adaptive monitoring over the system's lifecycle with respect to temporal characteristics.
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NeuroNarrator: A Generalist EEG-to-Text Foundation Model for Clinical Interpretation via Spectro-Spatial Grounding and Temporal State-Space Reasoning

arXiv:2603.16880v2 Announce Type: replace-cross Abstract: Electroencephalography (EEG) provides a non-invasive window into neural dynamics at high temporal resolution and plays a pivotal role in clinical neuroscience research. Despite this potential, prevailing computational approaches to EEG analysis remain largely confined to task-specific classification objectives or coarse-grained pattern recognition, offering limited support for clinically meaningful interpretation. To address these limitations, we introduce NeuroNarrator, the first generalist EEG-to-text foundation model designed to translate electrophysiological segments into precise clinical narratives. A cornerstone of this framework is the curation of NeuroCorpus-160K, the first harmonized large-scale resource pairing over 160,000 EEG segments with structured, clinically grounded natural-language descriptions. Our architecture first aligns temporal EEG waveforms with spatial topographic maps via a rigorous contrastive objective, establishing spectro-spatially grounded representations. Building on this grounding, we condition a Large Language Model through a state-space-inspired formulation that integrates historical temporal and spectral context to support coherent clinical narrative generation. This approach establishes a principled bridge between continuous signal dynamics and discrete clinical language, enabling interpretable narrative generation that facilitates expert interpretation and supports clinical reporting workflows. Extensive evaluations across diverse benchmarks and zero-shot transfer tasks highlight NeuroNarrator's capacity to integrate temporal, spectral, and spatial dynamics, positioning it as a foundational framework for time-frequency-aware, open-ended clinical interpretation of electrophysiological data.
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Multimodal Higher-Order Brain Networks: A Topological Signal Processing Perspective

arXiv:2603.29903v1 Announce Type: new Abstract: Brain connectomics is still largely dominated by pairwise-based models, such as graphs, which cannot represent circulatory or higher-order functional interactions. In this paper, we propose a multimodal framework based on Topological Signal Processing (TSP) that models the brain as a higher-order topological domain and treats functional interactions as discrete vector fields. We integrate diffusion MRI and resting-state fMRI to learn subject-specific brain cell complexes, where statistically validated structural connectivity defines a sparse scaffold and phase-coupling functional edge signals drive the inference of higher-order interactions (HOIs). Using Hodge-theoretic tools, spectral filtering, and sparse signal representations, our framework disentangles brain connectivity into divergence (source-sink organization), gradient (potential-driven coordination), and curl (circulatory HOIs), enabling the characterization of temporal dynamics through the lens of discrete vector calculus. Across 100 healthy young adults from Human Connectome Project, node-based HOIs are highly individualized, yet robust mesoscale structure emerges under functional-system aggregation. We identify a distributed default mode network-centered gradient backbone and limbic-centered rotational flows; divergence polarization and curl profiles defining circulation regimes with insightful occupancy and dwell-time statistics. These topological signatures yield significant brain-behavior associations, revealing a relevant higher-order organization intrinsic to edge-based models. By making divergence, circulation, and recurrent mesoscale coordination directly measurable, this work enables a principled and interpretable topological phenotyping of brain function.
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A Multi-Modal Dataset for Ground Reaction Force Estimation Using Consumer Wearable Sensors

arXiv:2603.28784v1 Announce Type: cross Abstract: This Data Descriptor presents a fully open, multi-modal dataset for estimating vertical ground reaction force (vGRF) from consumer-grade Apple Watch sensors with laboratory force plate ground truth. Ten healthy adults aged 26--41 years performed five activities: walking, jogging, running, heel drops, and step drops, while wearing two Apple Watches positioned at the left wrist and waist. The dataset contains 492 validated trials with time-aligned inertial measurement unit (IMU) recordings (approximately 100 Hz) and force plate vGRF (Force\_Z, 1000 Hz). The release includes raw and processed time series, trial-level metadata, quality-control flags, and machine-readable data dictionaries. Trial-level matching manifests link recordings across modalities using stable identifiers. Of the 492 validated trials, 395 are triad-complete, containing wrist, waist, and force plate data, enabling cross-sensor analyses and reproducible model evaluation. Dataset quality is characterised through a three-phase cross-sensor plausibility and consistency framework, repeatability analysis of peak vGRF (intraclass correlation coefficient 0.871--0.990), and systematic checks of force ranges and trial completeness. Monte Carlo sensitivity analysis showed that correlation-based validation metrics were robust to single-sample timing perturbations at the IMU sampling resolution. All data are released under CC BY 4.0, with analysis scripts archived alongside the dataset and mirrored on GitHub. This resource supports reproducible research in wearable biomechanics, benchmarking of machine learning models for vGRF estimation, and investigation of sensor placement effects using widely available consumer wearables.
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Smartphone-Based Identification of Unknown Liquids via Active Vibration Sensing

arXiv:2603.28787v1 Announce Type: cross Abstract: Traditional liquid identification instruments are often unavailable to the general public. This paper shows the feasibility of identifying unknown liquids with commercial lightweight devices, such as a smartphone. The key insight is that different liquid molecules have different viscosity coefficients and therefore must overcome different energy barriers during relative motion. With this intuition in mind, we introduce a novel model that measures liquids' viscosity based on active vibration. However, building a robust system using built-in smartphone accelerometers is challenging. Practical issues include under-sampling, self-interference, and the impact of liquid-volume changes. Instead of machine learning, we tackle these issues through multiple signal processing stages to reconstruct the original signals and cancel out the interference. Our approach estimates liquid viscosity with a mean relative error of 2.9% and distinguishes 30 types of liquids with an average accuracy of 95.47%.
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A Semi-amortized Lifted Learning-to-Optimize Masked (SALLO-M) Transformer Model for Scalable and Generalizable Beamforming

arXiv:2510.13077v3 Announce Type: replace-cross Abstract: We develop an unsupervised deep learning framework for real-time scalable and generalizable downlink beamforming in multi-user multiple-input single-output (MU-MISO) systems. The proposed semi-amortized lifted learning-to-optimize (SALLO) framework employs a multi-layer Transformer to iteratively refine an auxiliary variable and the beamformer solution, with a few projected gradient ascent steps at each layer. A key feature of our SALLO Transformer model is that it can handle varying numbers of users and antennas, enabled by a user-antenna dual tokenization and a structured sample/attention masking scheme, leading to generalization across different configurations without retraining. To improve convergence and robustness, we introduce three training strategies: (a) sliding-window training to stabilize gradient propagation, (b) curriculum learning with random masking to enable user-antenna configuration generalization and prevent poor early-stage convergence, and (c) sample replay to mitigate catastrophic forgetting during multi-stage training. Ablation studies validate several key architecture designs and show that the enhanced training scheme improves both generalizability and solution quality. Simulation results over both Gaussian and sparse channels show that the proposed scheme consistently outperforms existing deep learning baselines across diverse system configurations and channel conditions. The performance gain becomes more pronounced in overloaded regimes, highlighting improved robustness under challenging scenarios. Furthermore, our scheme surpasses the WMMSE benchmark in underloaded systems and even in overloaded systems when the overloading factor is below certain threshold. These gains are achieved with fast inference and a substantially more lightweight model than wireless foundation models.
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An Accurate and Interpretable Framework for Trustworthy Process Monitoring

arXiv:2302.10426v3 Announce Type: replace Abstract: Trustworthy process monitoring seeks to build an accurate and interpretable monitoring framework, which is critical for ensuring the safety of energy conversion plant (ECP) that operates under extreme working conditions such as high pressure and temperature. Contemporary self-attentive models, however, fall short in this domain for two main reasons. First, they rely on step-wise correlations that fail to involve physically meaningful semantics in ECP logs, resulting in suboptimal accuracy and interpretability. Second, attention matrices are frequently cluttered with spurious correlations that obscure physically meaningful ones, further impeding effective interpretation. To overcome these issues, we propose AttentionMixer, a framework aimed at improving both accuracy and interpretability of existing methods and establish a trustworthy ECP monitoring framework. Specifically, to tackle the first issue, we employ a spatial adaptive message passing block to capture variate-wise correlations. This block is coupled with a temporal adaptive message passing block through an \textit{mixing} operator, yielding a multi-faceted representation of ECP logs accounting for both step-wise and variate-wise correlations. Concurrently, to tackle the second issue, we employ a sparse message passing regularizer to filter out spurious correlations. We validate the efficacy of AttentionMixer using two real-world datasets from the radiation monitoring network for Chinese nuclear power plants.
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Human Presence Detection via Wi-Fi Range-Filtered Doppler Spectrum on Commodity Laptops

arXiv:2603.10845v2 Announce Type: replace-cross Abstract: Human Presence Detection (HPD) is key to enable intelligent power management and security features in everyday devices. In this paper we propose the first HPD solution that leverages monostatic Wi-Fi sensing and detects user position using only the built-in Wi-Fi hardware of a device, with no need for external devices, access points, or additional sensors. In contrast, existing HPD solutions for laptops require external dedicated sensors which add cost and complexity, or rely on camera-based approaches that introduce significant privacy concerns. We herewith introduce the Range-Filtered Doppler Spectrum (RF-DS), a novel Wi-Fi sensing technique for presence estimation that enables both range-selective and temporally windowed detection of user presence. By applying targeted range-area filtering in the Channel Impulse Response (CIR) domain before Doppler analysis, our method focuses processing on task-relevant spatial zones, significantly reducing computational complexity. In addition, the use of temporal windows in the spectrum domain provides greater estimator stability compared to conventional 2D Range-Doppler detectors. Furthermore, we propose an adaptive multi-rate processing framework that dynamically adjusts Channel State Information (CSI) sampling rates-operating at low frame rates (10Hz) during idle periods and high rates (100Hz) only when motion is detected. To our knowledge, this is the first low-complexity solution for occupancy detection using monostatic Wi-Fi sensing on a built-in Wi-Fi network interface controller (NIC) of a commercial off-the-shelf laptop that requires no external network infrastructure or specialized sensors. Our solution can scale across different environments and devices without calibration or retraining.
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Towards unified brain-to-text decoding across speech production and perception

arXiv:2603.12628v1 Announce Type: new Abstract: Speech production and perception are the main ways humans communicate daily. Prior brain-to-text decoding studies have largely focused on a single modality and alphabetic languages. Here, we present a unified brain-to-sentence decoding framework for both speech production and perception in Mandarin Chinese. The framework exhibits strong generalization ability, enabling sentence-level decoding when trained only on single-character data and supporting characters and syllables unseen during training. In addition, it allows direct and controlled comparison of neural dynamics across modalities. Mandarin speech is decoded by first classifying syllable components in Hanyu Pinyin, namely initials and finals, from neural signals, followed by a post-trained large language model (LLM) that maps sequences of toneless Pinyin syllables to Chinese sentences. To enhance LLM decoding, we designed a three-stage post-training and two-stage inference framework based on a 7-billion-parameter LLM, achieving overall performance that exceeds larger commercial LLMs with hundreds of billions of parameters or more. In addition, several characteristics were observed in Mandarin speech production and perception: speech production involved neural responses across broader cortical regions than auditory perception; channels responsive to both modalities exhibited similar activity patterns, with speech perception showing a temporal delay relative to production; and decoding performance was broadly comparable across hemispheres. Our work not only establishes the feasibility of a unified decoding framework but also provides insights into the neural characteristics of Mandarin speech production and perception. These advances contribute to brain-to-text decoding in logosyllabic languages and pave the way toward neural language decoding systems supporting multiple modalities.
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Synthetic Data Generation for Brain-Computer Interfaces: Overview, Benchmarking, and Future Directions

arXiv:2603.12296v1 Announce Type: cross Abstract: Deep learning has achieved transformative performance across diverse domains, largely driven by the large-scale, high-quality training data. In contrast, the development of brain-computer interfaces (BCIs) is fundamentally constrained by the limited, heterogeneous, and privacy-sensitive neural recordings. Generating synthetic yet physiologically plausible brain signals has therefore emerged as a compelling way to mitigate data scarcity and enhance model capacity. This survey provides a comprehensive review of brain signal generation for BCIs, covering methodological taxonomies, benchmark experiments, evaluation metrics, and key applications. We systematically categorize existing generative algorithms into four types: knowledge-based, feature-based, model-based, and translation-based approaches. Furthermore, we benchmark existing brain signal generation approaches across four representative BCI paradigms to provide an objective performance comparison. Finally, we discuss the potentials and challenges of current generation approaches and prospect future research on accurate, data-efficient, and privacy-aware BCI systems. The benchmark codebase is publicized at https://github.com/wzwvv/DG4BCI.
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Privacy-Preserving End-to-End Full-Duplex Speech Dialogue Models

arXiv:2603.08179v1 Announce Type: cross Abstract: End-to-end full-duplex speech models feed user audio through an always-on LLM backbone, yet the speaker privacy implications of their hidden representations remain unexamined. Following the VoicePrivacy 2024 protocol with a lazy-informed attacker, we show that the hidden states of SALM-Duplex and Moshi leak substantial speaker identity across all transformer layers. Layer-wise and turn-wise analyses reveal that leakage persists across all layers, with SALM-Duplex showing stronger leakage in early layers while Moshi leaks uniformly, and that Linkability rises sharply within the first few turns. We propose two streaming anonymization setups using Stream-Voice-Anon: a waveform-level front-end (Anon-W2W) and a feature-domain replacement (Anon-W2F). Anon-W2F raises EER by over 3.5x relative to the discrete encoder baseline (11.2% to 41.0%), approaching the 50% random-chance ceiling, while Anon-W2W retains 78-93% of baseline sBERT across setups with sub-second response latency (FRL under 0.8 s).
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Electrocardiogram Classification with Transformers Using Koopman and Wavelet Features

arXiv:2603.08339v1 Announce Type: cross Abstract: Electrocardiogram (ECG) analysis is vital for detecting cardiac abnormalities, yet robust automated classification is challenging due to the complexity and variability of physiological signals. In this work, we investigate transformer-based ECG classification using features derived from the Koopman operator and wavelet transforms. Two tasks are studied: (1) binary classification (Normal vs. Non-normal), and (2) four-class classification (Normal, Atrial Fibrillation, Ventricular Arrhythmia, Block). We use Extended Dynamic Mode Decomposition (EDMD) to approximate the Koopman operator. Our results show that wavelet features excel in binary classification, while Koopman features, when paired with transformers, achieve superior performance in the four-class setting. A simple hybrid of Koopman and wavelet features does not improve accuracy. However, selecting an appropriate EDMD dictionary -- specifically a radial basis function dictionary with tuned parameters -- yields significant gains, surpassing the wavelet-only baseline and the hybrid wavelet-Koopman system. We also present a Koopman-based reconstruction analysis for interpretable insights into the learned dynamics and compare against a recurrent neural network baseline. Overall, our findings demonstrate the effectiveness of Koopman-based feature learning with transformers and highlight promising directions for integrating dynamical systems theory into time-series classification.
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