PI-AMFM: Permutation-Invariant Learning for Variable-Cardinality AM-FM Mode Decomposition in Biomedical Signal Analysis

Foundation models for wearable biosignals have matched or exceeded supervised specialists across a range of clinical tasks, yet all rely on modalities that require deliberate user action--wearing a device or visiting a sleep lab. We introduce BCG-FM, the first foundation model for ambient mechanical biosignals. A piezoelectric sensor embedded in the bed surface records ballistocardiography (BCG) each night without user effort; we pretrain BCG-FM with participant-level contrastive learning and using a total of 2.75 million hours of nightly recordings from 145,985 individuals, the largest raw-waveform biosignal pretraining corpus to date. Frozen BCG-FM embeddings achieve 3.26-year MAE on biological-age estimation (the lowest reported for any ambient, contactless modality) and yield clinically relevant discrimination across 15 self-reported health conditions and three independent external cohorts. Pretrained representations from only 500 labeled participants outperform a fully supervised baseline trained on 3,372, and representation quality scales log-linearly with contrastive batch size. These results establish ambient, longitudinal mechanical biosignals as a viable modality for health foundation models.

Biosignals acquired from different locations on the body often provide temporally ordered views of the same underlying physiological process. However, most existing self supervised learning methods treat these signals as interchangeable views, overlooking the directional temporal dynamics that link them. A canonical example is the relationship between electrocardiography (ECG), which captures the electrical activation initiating each heartbeat, and photoplethysmography (PPG), which records the resulting peripheral pulse delayed by vascular dynamics. To capture this structured relationship, we introduce xMAE, a biosignal pretraining framework that leverages masked cross modal reconstruction across temporally ordered biosignals as a training time constraint to encourage physiologically meaningful timing structure in the learned representations. We show that pretraining with xMAE yields representations that outperform both unimodal and multimodal baselines on 15 of 19 downstream tasks, including cardiovascular outcome prediction, abnormal laboratory test detection, sleep staging, and demographic inference, while generalizing across devices, body locations, and acquisition settings. Further analysis suggests that the ECG PPG timing structure is reflected in the learned PPG representations. More broadly, xMAE demonstrates the effectiveness of incorporating temporal structure into multimodal pretraining when signals observe different stages of a shared underlying process. Code is available at https://github.com/hzhou3/xMAE.

Reliable periodic patterns serve as a fundamental basis for accurate multivariate time series forecasting. However, existing methods either implicitly extract periodicity through complex model architectures (e.g., Transformers) with high computational overhead or overlook the intrinsic phase-amplitude coupling when modeling periodic components explicitly. To address these issues, we propose a novel Cycle-aware Phase-Amplitude Modulation Network (PAMNet) that explicitly decomposes periodic patterns into complementary phase and amplitude components. The core innovation lies in its dual-branch modulator, featuring dedicated learnable embeddings for phase positioning and amplitude modulation. The phase branch employs cyclical embeddings to capture phase-dependent mean shifts, while the amplitude branch models intensity variations to adapt to changes in variance. A lightweight modulator with element-wise fusion efficiently combines these components, enabling explicit modeling of their interactions without complex attention mechanisms. Extensive experiments on twelve real-world datasets demonstrate that our method achieves state-of-the-art performance through its novel phase-amplitude decoupling mechanism, offering a new perspective for cyclical modeling in time series forecasting.