Multi-scale spatial testing recovers gene programs missed by existing detection methods

Identifying spatially variable genes (SVGs) is the first analytical step in spatial transcriptomics, determining which genes and pathways are prioritized for downstream validation. Yet the restricted spatial models of current detection methods create systematic blind spots that can exclude biologically coherent programs from discovery. Here we present FlashS, which reformulates kernel-based spatial testing in the frequency domain to detect arbitrary multi-scale expression patterns while scaling to millions of cells. In human cardiac tissue, this broader detection capacity recovers a coherent PGC-1α-regulated mitochondrial biogenesis program-40 of 49 pathway genes spatially associated with ventricular cardiomyocytes-that PreTSA, a leading parametric alternative, largely misses (1 of 49 genes), a finding replicated in an independent cohort. Across 50 benchmark datasets spanning 9 platforms, FlashS achieves state-of-the-art ranking accuracy (mean Kendall $\tau =0.935$ ) and completes on the Allen Brain MERFISH atlas (3.94 million cells) in 12.6 minutes with 21.5 GB memory.