Markonv: a novel convolutional layer with inter-positional correlations modeled

Deep neural networks equipped with convolutional neural layers have been widely used in omics data analysis. Though highly efficient in data-oriented feature detection, the classical convolutional layer is designed with inter-positional independent filters, hardly modeling inter-positional correlations in various biological data. Here, we proposed Markonv layer (Markov convolutional neural layer), a novel convolutional neural layer with Markov transition matrices as its filters, to model the intrinsic dependence in inputs as Markov processes. Extensive evaluations based on both synthetic and real-world data showed that Markonv-based networks could not only identify functional motifs with inter-positional correlations in large-scale omics sequence data effectively, but also decode complex electrical signals generated by Oxford Nanopore sequencing efficiently. Designed as a drop-in replacement of the classical convolutional layer, Markonv layers enable an effective and efficient identification for inter-positional correlations from various biological data of different modalities. All source codes of a PyTorch-based implementation are publicly available on GitHub for academic usage.