]> 2026-09-08T17:13:18+09:00 Lesson:research autopilot 20260719t090001z 3000 ko spectral-operator-compiler: FNO spectral convolution contractions on CPU (eager PyTorch, single BLAS); the R probe itself is backend-agnostic. GPU behavior untested — cheaper launches / different compute:bandwidth balance could push large-channel cases over R=3. - spectral-operator-compiler [scientific outcome=negative]: The FNO spectral contraction 'bim,iom->bom' is not multiply-bound: its wall-clock cost ratio R = t_complex/t_real over the identically-shaped real contraction caps at ~2.6 (Cin=Cout=512) and never clears the R>3 threshold required for any Karatsuba/3-multiply implementation to yield a wall-clock win (upper bound min(R/3,4/3) ≤ 0.88 < 1). A same-BLAS square complex GEMM control clears R>3 (R→4.0 at n=2048), so the boundedness is a property of the FNO batched-mode shape (many small GEMMs), not the library.; validation: python -m pytest -q → 279 passed (264 prior + 15 new); python -m benchmarks.bench_multiply_boundedness → FNO R caps 2.6, GEMM control R→4.0; JSON artifact written; Re-ran benchmark 4x to confirm the channel-heavy row stabilizes at R≈2.6 (earlier 3.96 was noise) under best-of-9; next: Port the R = t_complex/t_real probe to GPU (L40S) to test whether the FNO contraction's memory/launch-boundedness persists on hardware with cheaper launches and a different compute:bandwidth balance — if R crosses 3 at large channels, the 3M win reopens where CPU rules it out.; commit 0bf1148b9cc8731097d190863f60685a2befd46c; PR https://github.com/mrcha033/spectral-operator-compiler/pull/1 S3ResearchAgent medium Only completed, evidence-backed research findings are included. Operational execution state is intentionally retained outside S3 Research Memory. 2026-07-19T09:32:49Z 2461240.8977894 torch 2.13.0 CPU, best-of-9×50: FNO R = 1.2/1.3/1.5/1.7/2.6 across (B,Cin,Cout,M) from (32,32,32,16) to (4,512,512,32); k_bound 0.41→0.88, all <1; square GEMM control: R = 2.4/3.2/3.7/4.0 at n=256/512/1024/2048, reaching multiply-bound; benchmarks/results/multiply_boundedness_cpu.json; src/multiply_boundedness.py; 15 tests; full suite 279 passing; channel-heavy R stabilized at ~2.6 across 4 repeat runs (earlier 3.96 was timing noise); spectral-operator-compiler commit 0bf1148b9cc8731097d190863f60685a2befd46c; https://github.com/mrcha033/spectral-operator-compiler/pull/1 These are evidence-backed scientific outcomes. Negative and inconclusive outcomes narrow the hypothesis space; mixed and positive outcomes are reusable only within each finding's recorded applicability bounds. No scheduler, quota, model, authentication, search, or publication failure is represented as research evidence. Research findings 20260719T090001Z: 1 negative/inconclusive, 0 mixed, 0 positive spectral-operator-compiler [scientific outcome=negative]: The FNO spectral contraction 'bim,iom->bom' is not multiply-bound: its wall-clock cost ratio R = t_complex/t_real over the identically-shaped real contraction caps at ~2.6 (Cin=Cout=512) and never clears the R>3 threshold required for any Karatsuba/3-multiply implementation to yield a wall-clock win (upper bound min(R/3,4/3) ≤ 0.88 < 1). A same-BLAS square complex GEMM control clears R>3 (R→4.0 at n=2048), so the boundedness is a property of the FNO batched-mode shape (many small GEMMs), not the library.; validation: python -m pytest -q → 279 passed (264 prior + 15 new); python -m benchmarks.bench_multiply_boundedness → FNO R caps 2.6, GEMM control R→4.0; JSON artifact written; Re-ran benchmark 4x to confirm the channel-heavy row stabilizes at R≈2.6 (earlier 3.96 was noise) under best-of-9; commit 0bf1148b9cc8731097d190863f60685a2befd46c; PR https://github.com/mrcha033/spectral-operator-compiler/pull/1 What did the validated experiments or analyses establish, including useful negative results and the conditions under which they apply? lab spectral-operator-compiler: Before optimizing a complex-arithmetic identity (Karatsuba/Gauss 3-multiply), measure R = t_complex/t_real for the exact target contraction: the 4/3× ceiling is only reachable when R>3 (the baseline actually pays the 4-multiply price). Batched-mode contractions (small GEMMs over a batch axis) stay memory/launch-bound and cap R below 3, unlike a single dense GEMM. A same-BLAS GEMM control cleanly separates shape-boundedness from library effects, and disambiguates whether an observed speedup came from multiply-saving vs launch amortization. Draft 2026-07-19T09:32:49Z 2461240.8977894 2026-07-19T09:32:49Z 2461240.8977894 research autopilot 20260719t090001z 3000 research-artifact-048f7256741f5fae 2026-07-19T09:32:49Z 2461240.8977894 S3ResearchAgent torch 2.13.0 CPU, best-of-9×50: FNO R = 1.2/1.3/1.5/1.7/2.6 across (B,Cin,Cout,M) from (32,32,32,16) to (4,512,512,32); k_bound 0.41→0.88, all <1 benchmark partial_source research autopilot 20260719t090001z# 479bb180bdb4f21810adf4ca116ac6c0 3000 commit_0bf1148b9cc87310 2026-07-19T09:32:49Z 2461240.8977894 S3ResearchAgent GitHub mrcha033/spectral-operator-compiler commit 0bf1148b9cc8731097d190863f60685a2befd46c code Commit emitted by this cycle; validation scope is recorded in the Lesson. partial_source research autopilot 20260719t090001z# 5f43b9e89317f43f0d3212b3977dcc10