Yang, Chen

Abstract Spatial transcriptomics links gene expression to tissue architecture, but detecting spatially variable genes at atlas scale remains difficult because biologically relevant patterns are multiscale, sparse, and often non-parametric. Here we show that FlashS, a frequency-domain kernel test using random Fourier features, sparse sketching, and a kurtosis-corrected null, retains Gaussian-kernel flexibility at near-linear per-gene cost without permutation. Across 50 benchmark datasets spanning 9 spatial transcriptomics platforms, F lash S achieves the highest ranking accuracy among 14 compared methods while maintaining calibrated inference under simulation and full-atlas permutation. In human heart tissue, it recovers a mitochondrial biogenesis program that co-localizes with ventricular cardiomyocytes. On the Allen Brain MERFISH atlas containing 3.94 million cells, F lash S completes in minutes on a single workstation and separates biological signal from negative-control barcodes even when p-values saturate.