Multi-Scale Representation Learning for Single-Cell Multi-Omics

Learning unified representations from single-cell multi-omics data is a fundamental challenge, yet existing deep learning models often overlook the inherent hierarchical structure of biological regulation. In this work, we introduce scWavelet, a novel deep learning framework that leverages a multi-scale inductive bias by learning representations in the cellular spatial-frequency domain. Our approach is grounded in a heuristic approximation-misspecification decomposition, which theoretically motivates the design of a scale-factorized architecture. scWavelet employs a learnable wavelet transform to decompose omics signals into distinct scales, which are then processed by scale-specific Omics Mixers to generate integrated latent representations. Extensive experiments demonstrate that scWavelet achieves state-of-the-art performance on challenging multi-omics integration and cross-omics translation benchmarks. Furthermore, interpretability analyses confirm that the learned multi-scale features effectively correspond to the biological hierarchy of cellular identity. Our project will be publicly available.