Эксперимент: Implicitly padded FFT convolution (#914)

{ "worked": true, "confidence": 9, "verdict": "Built a readable mixed-radix implicitly padded DFT/IDFT and convolution MVP. The mechanism manifested: across 23 transform cases, maximum relative DFT error was 4.05e-14 and inverse error 1.88e-14; across 27 convolution cases, maximum error was 2.56e-14. The predicted storage reduction was observed at 2-4x for the tested lengths, but this unoptimized NumPy implementation was slower than explicit FFT convolution, so no wall-clock win was demonstrated.", "metrics": { "baseline": "Explicit padded NumPy FFT spectrum timing: 0.000290s, 0.000523s, and 0.000744s for (L,K)=(257,65),(1025,257),(2049,513).", "idea": "Implicit mixed-radix NumPy timing: 0.000779s, 0.002540s, and 0.005845s on the same cases; relative transform/convolution errors <=4.05e-14; analytical explicit-padding-storage / tile-buffer-storage ratio 2-4x." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 run_experiment.py", "files": [ "implicit_fft.py", "run_experiment.py", "results.json" ], "limitations": "Only CPU NumPy was tested; no CUDA kernel, fused masking, autograd/gradient check, CNN/SSM training loss, peak allocator memory measurement, or large B,C workload was evaluated. The MVP allocates tile and einsum intermediates, so its measured memory behavior is an analytical tile-buffer comparison rather than a production peak-memory benchmark." }