Frequency-domain kernels enable atlas-scale detection of spatially variable genes

Identifying spatially variable genes in spatial transcriptomics requires methods that are accurate, well calibrated and scalable, yet current approaches trade expressive kernels for tractable computation. We present F lash S, which moves spatial testing to the frequency domain: Random Fourier Features and sparse sketching enable multi-scale kernel testing on zero-inflated data without constructing distance matrices, and a kurtosis-corrected null preserves calibration. Across 50 datasets from 9 platforms, F lash S achieves a mean Kendall <b><i>τ</i></b> of 0.935, exceeding the next-best method by 0.049. On the Allen Brain MERFISH atlas of 3.94 million cells, it completes in 12.6 minutes using 21.5 GB memory and maintains near-nominal false-positive rates under permutation. In human cardiac tissue, this improved ranking recovers a ventricular cardiomyocyte-associated mitochondrial biogenesis program that largely eludes parametric alternatives and replicates in an independent cohort.