Signal Intensity-weighted coordinate channels improve learning stability and generalisation in 1D and 2D CNNs in localisation tasks on biomedical signals

Abstract: Localisation tasks in biomedical data often require models to learn meaningful spatial or temporal relationships from signals with complex intensity distributions. A common strategy, exemplified by CoordConv layers, is to append coordinate channels to convolutional inputs, enabling networks to learn absolute positions. In this work, we propose a signal intensity-weighted coordinate representation that replaces the pure coordinate channels with channels scaled by local signal intensity. This modification embeds an intensity-position coupling directly in the input representation, introducing a simple and modality-agnostic inductive bias. We evaluate the approach on two distinct localisation problems: (i) predicting the time of morphological transition in 20-second, two-lead ECG signals, and (ii) regressing the coordinates of nuclear centres in cytological images from the SiPaKMeD dataset. In both cases, the proposed representation yields faster convergence and higher generalisation performance relative to conventional coordinate-channel approaches, demonstrating its effectiveness across both one-dimensional and two-dimensional biomedical signals.