MOSAIC: A Differentiable Phase-Amplitude Coupling Transformer for Medical Time Series Classification

Neural oscillations interact through phase-amplitude coupling (PAC): the amplitude of a fast rhythm is modulated by the phase of a slow one. PAC is an established clinical biomarker, yet transformers for medical time series largely ignore it, treating signals as undifferentiated tokens. Classical PAC measures are typically computed offline on hand-chosen bands, so the bands that determine which coupling is detectable lie outside the classification objective. We present MOSAIC (Multi-Oscillatory Signal Attention with Integrated Coupling), which makes PAC estimation end-to-end differentiable. A spectrally applied learnable Gaussian filterbank lets gradients reach the band parameters, an FFT-based Hilbert transform gives instantaneous amplitude and phase, and a soft phase-binned amplitude histogram keeps the shape of the modulation rather than a single scalar. The resulting PAC tokens feed a cross-band transformer that learns which coupling pairs matter. On three subject-independent EEG and ECG benchmarks, jointly learning the bands and the coupling representation raises macro-F1 over fixed-band PAC features by 1.2× to 1.6×, and MOSAIC attains the highest reported accuracy, recall, and macro-F1 on all three against eleven published transformer baselines.