Operator layer
A CUDA sparse FFT (cuSFFT) that computes only the k components that matter.
What it is
Vector detects the k significant frequency components and emits certified (index, amplitude) tuples directly on the GPU — avoiding full N-sized dense-spectrum materialization in the sparse-output path. Where dense cuFFT computes the entire spectrum, Vector computes only what is significant. Measured against dense cuFFT + top-k, it delivers 16–128× fewer input bytes and a ~4–5× end-to-end speedup.
By the numbers
MeasuredHow it works
How the result is measured
Vector is measured head-to-head against dense cuFFT + top-k — same seeds, same top-k target. cuFFT computes the full dense spectrum; Vector computes only the k significant components. The sparse win is claimed only inside the supported range.
Baseline it is measured against
Dense cuFFT → magnitude → radix-select top-k, run as a fair pinned baseline. This is the dense FFT the sparse path is held to, head-to-head on the same seeds and the same top-k target.
The sparse path
Vector’s sparse producer emits B = V·L sampled / view points directly on the GPU and never materializes the full dense N-spectrum for sparse-output consumers.
Runtime
Measured about 4–5× faster end-to-end against the fair pinned dense baseline, on NVIDIA RTX 5070 Ti and GB10.
Byte reduction
16–128× fewer input bytes in the sparse-output path — the producer emits B = V·L points instead of consuming or materializing the full N-sized dense spectrum. Structural and pinning-invariant.
Where it works
Where it runs sparse, and where it falls back
The sparse path is claimed only where it is measured iso-correct. Everywhere else, Relay routes to the dense baseline, which is recall-authoritative.
| Regime | Status | Path | Claim |
|---|---|---|---|
| Clean / on-grid, k ≤ 300, N ≤ 4M | supported | sparse | measured iso-correct |
| Noisy AWGN, bounded dynamic range | supported when gates pass | sparse + certification | review gate: recall ≥ 0.97, precision ≥ 0.99, no p95 regression |
| Off-grid (0.25 bin) | supported | sparse | measured, bounded |
| High dynamic range | dense-better | fallback | no sparse claim |
| k ≥ 500 | dense-better / open | dense fallback | no sparse claim (GPU device-resident path) |
| N = 8M, k = 300 | open | fallback or caveat | not headlined |
Guardrails
Not claimed
- Not a universal cuFFT replacement.
- Not a dense-spectrum FFT win.
- Not controller-side / PIM hardware validation.
- Not a high-dynamic-range sparse win.
- Not a k ≥ 500 sparse win on the GPU device-resident path (the CPU sqrtn lane does win at k ≥ 500).
- Not real-data precision 1.0; real-data precision is signal-bound.
- Benefit requires sparse-tuple-compatible consumers; not every downstream consumer benefits.
- The claim is sparse-output path materialization / transfer reduction, not that the original signal never exists.
- Dense fallback stays authoritative when certification fails.
Vector emits the sparse output. SparseDSP Relay certifies it.
The operator layer is one half of the path. See how Relay verifies the result and guarantees a dense fallback.