Peak Performance in Matched Filtering: Fused Correlation and Statistically Controlled Screening on CPUs and GPUs

arXiv:2611.17229

Alexander H. Nitz, Keisi Kacanja, Collin D. Capano

Batched matched filtering and cross-correlation over large template banks are a primary computational cost in gravitational-wave astronomy, seismology, and radio transient searches. Standard pipelines pair a general-purpose inverse Fast Fourier Transform (FFT) with separate multiplication and peak-finding kernels, writing intermediate spectra and full correlation series to memory for every template. We fuse the conjugate product into the first inverse-transform butterflies and the peak reduction into the last so only candidate peaks leave processor registers, and tile batches in 2D so $K^2$ correlations reuse $2K$ cached spectra. This shifts filtering from a DRAM-bandwidth-bound to an on-chip cache-bandwidth-bound regime. In some situations, the signal-to-noise ratio (SNR) is concentrated toward lower frequencies while higher frequencies dominate the transform length. We develop a hierarchical screening method that exploits this via a sequence of short low-frequency transforms before evaluating the full band, deriving stage thresholds from the spectral power profile and matched-filter noise autocovariance to target a specified false-dismissal probability. We demonstrate these methods in the open-source matchedfilter library across eight CPU architectures and two integrated GPUs (AMD Radeon 8060S via Vulkan and Apple M2 via Metal). On an AMD Ryzen AI Max+ 395 at $N=4096$, fused peak-only filtering is $1.4\times$ faster than a standalone AOCL-FFTW inverse transform on one CPU core and $6.2\times$ faster than rocFFT on its Radeon 8060S GPU ($3.1\times$ over MLX FFT on the M2 GPU). For a fiducial gravitational-wave search ($ρ_\mathrm{th}=5.5$, $10^{-2}$ false-dismissal target), hierarchical screening yields a $26\times$ speedup over AOCL-FFTW on CPU, $21\times$ over rocFFT on the 8060S GPU, and $19\times$ over MLX FFT on the M2 GPU.