Aims: We propose a physiology-informed architecture, Wavelet-SSM, for interpretable single-beat electrocardiogram (ECG) arrhythmia classification. The model builds upon a neural state-space model (SSM) formulation in which latent dynamics evolve in the wavelet coefficient domain, providing a physiologically aligned time–frequency representation consistent with cardiac morphology.
Methodology: In Wavelet-SSM, the state transition matrix (A) is analytically derived from a discrete wavelet basis using High-order Polynomial Projection Operators (HiPPO) and remains fixed during training. Each latent dimension corresponds to a predefined wavelet scale, establishing a deterministic mapping between hidden states and frequency components, unlike standard neural SSMs (e.g., Mamba, S4) where (A) lacks interpretable spectral structure. The input projection (B) and output readout (C) matrices are learned following the selective parameterization of Mamba. Scale bounds are informed by physiological priors on QRS duration, and a QRS-centered HiPPO measure weights projections toward R-peak morphology. A 1-D convolutional stem reduces input sequence length before the SSM layers; a scale-gating module adaptively reweights latent scales before the classification head.
Results: Experiments are conducted on the MIT-BIH Arrhythmia Database; each beat is represented as a 500 ms segment centered on the R-peak, using a fixed patient-disjoint training/validation/test sets with a 60/10/30 split ratio. On the five-class AAMI-style task, Daubechies db3 achieves the strongest Wavelet-SSM result, with an F1 score of 93.23%. The db2, biorthogonal bior3.3, and db4 variants achieve F1 scores of 92.62%, 92.37%, and 91.71%, respectively, demonstrating the impact of basis choice on QRS-scale encoding; scale attribution patterns align with clinical beat characteristics, with ventricular beats consistently activating coarser scales, consistent with their wider QRS complex.
Conclusion: Wavelet-SSM attains performance competitive with state-of-the-art deep learning baselines while exposing scale-level importance patterns consistent with a wider QRS complex for ventricular beats, supporting its use as an interpretable deep model for arrhythmia beat labeling.