arXiv:2406.19581v3 Announce Type: replace Abstract: Decomposing surface electromyography (EMG) into the spike trains of individual motor neurons is a long-standing inverse problem and a key step toward motor-neuron-driven neural interfaces such as prosthetics and exoskeletons. The standard approach, independent component analysis (ICA) of the multichannel signal, assumes that the mixing from neurons to electrodes is stationary in time. This assumption fails during movement, when volume-conductor deformation makes the mixing time-varying, and current decomposition algorithms are correspondingly restricted to isometric contractions. We introduce HarmonICA, a quasi-time-invariant ICA formulation in which a static linear separator is preceded by a learned, low-rank, time-varying invertible transformation. The separator is trained with an independence loss on the uncompensated projection, and the transformation with a stationarity loss on the recovered source. Gradients are not shared between the two, so source extraction remains a classical linear-ICA problem while non-stationary distortion is absorbed by the transformation. The closed-form inverse of the transformation enables per-spike subtraction with a time-varying template during sequential peel-off. On a public simulated benchmark of dynamic high-density EMG with ground-truth spike trains, the method outperforms five adaptive ICA baselines at every recall threshold, recovering more units at a higher accuracy.