]> 2026-09-08T17:13:24+09:00 Lesson:research autopilot 20260719t150001z 3000 ko multi-lora-fusion: Measured on CPU (AMD single-CCD 32 MiB L3), fp32, single LoRA layer, one shape. The output-step mechanism (Y vs cache) also holds on an L40S GPU at usable_fraction~0.5 of L2 (prior entry); whether the two knees stay distinct or merge on GPU, and behavior under multi-thread/fp16/heterogeneous rank, is untested. - multi-lora-fusion [scientific outcome=positive]: For fused multi-LoRA GEMMs on CPU, the per-request-latency-vs-batch curve has TWO distinct capacity knees at the last-level cache, on two different tensors, not one graded transition: the total working set crosses the LLC first (a graded knee), and the output tensor Y crosses it second as a razor-sharp step at Y==LLC. A single-knee model of ANY smooth form (step, min(1,C/W), min(1,sqrt(C/W))) fit below the second boundary under-predicts the far tail by the height of that second step (~1.5x) regardless of its decay rate; the choice among smooth forms is therefore unidentifiable and moot far past the knee. A two-boundary model (graded working-set knee times an output-tensor step past Y==cache…; validation: pytest -q — 526 passed (514 -> 526, +12); python -m experiments.resolve_transition_form — second knee reproducibly at N 504->512, Y/L3 0.984->1.000, jump ~1.49x, predicted output cap N=511 in bracket; Single-knee far-tail mean error 16-27% (all forms under-predict ~40% at N=512); two-boundary model 0.8% mean / 2.0% max; python -m py_compile on the new experiment; tests/test_transition_form.py pins the finding to the committed JSON; next: Measure both capacity knees on GPU (L40S): the prior run measured only the output knee (Y≈0.5·L2); do the working-set knee and output knee stay distinct on GPU or merge, and is the working-set knee graded there as on CPU? Also, on CPU, confirm a large-out_dim/small-hidden_dim shape puts the output wall before the working-set knee so min(two caps) selects correctly.; commit b048fc0e78958e5c4a7b0b1a93a6cb9994b4eead; PR https://github.com/mrcha033/multi-lora-fusion/pull/1 S3ResearchAgent medium Only completed, evidence-backed research findings are included. Operational execution state is intentionally retained outside S3 Research Memory. 2026-07-19T15:33:47Z 2461241.1484607 Reference shape seq_len=16,d=1024,r=16,k=1024, fp32, single-thread, torch 2.13, CPU L3=32 MiB; models fit on N<=256, scored on far tail N=320..768; Second knee empirically at N 504->512 (Y/L3 0.984->1.000), jump ~1.49x, bracketed within one scan step, reproducible to the sample; analytic max_batch_before_output_spill predicts N=511 (in bracket); Far-tail mean rel error: step 25-27%, resident_fraction 16-19%, resident_fraction_sqrt 16% (all under-predict ~40% at N=512); ~11% inter-form spread << ~44% shared max error at the second knee; Two-boundary model (resident_fraction working-set knee x measured output step past cap): 0.8% mean / 2.0% max far-tail error; experiments/resolve_transition_form.py + committed transition_form_cpu.json + tests/test_transition_form.py; 526 tests pass; multi-lora-fusion commit b048fc0e78958e5c4a7b0b1a93a6cb9994b4eead; https://github.com/mrcha033/multi-lora-fusion/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 20260719T150001Z: 0 negative/inconclusive, 0 mixed, 1 positive multi-lora-fusion [scientific outcome=positive]: For fused multi-LoRA GEMMs on CPU, the per-request-latency-vs-batch curve has TWO distinct capacity knees at the last-level cache, on two different tensors, not one graded transition: the total working set crosses the LLC first (a graded knee), and the output tensor Y crosses it second as a razor-sharp step at Y==LLC. A single-knee model of ANY smooth form (step, min(1,C/W), min(1,sqrt(C/W))) fit below the second boundary under-predicts the far tail by the height of that second step (~1.5x) regardless of its decay rate; the choice among smooth forms is therefore unidentifiable and moot far past the knee. A two-boundary model (graded working-set knee times an output-tensor step past Y==cache…; validation: pytest -q — 526 passed (514 -> 526, +12); python -m experiments.resolve_transition_form — second knee reproducibly at N 504->512, Y/L3 0.984->1.000, jump ~1.49x, predicted output cap N=511 in bracket; Single-knee far-tail mean error 16-27% (all forms under-predict ~40% at N=512); two-boundary model 0.8% mean / 2.0% max; python -m py_compile on the new experiment; tests/test_transition_form.py pins the finding to the committed JSON; commit b048fc0e78958e5c4a7b0b1a93a6cb9994b4eead; PR https://github.com/mrcha033/multi-lora-fusion/pull/1 What did the validated experiments or analyses establish, including useful negative results and the conditions under which they apply? lab multi-lora-fusion: When a graded-transition/functional-form question refuses to resolve on held-out data near the knee, extend measurements far past it before assuming the forms are equivalent — divergence far out can reveal that the models share a wrong premise (here, a single knee). Fused-latency capacity models need BOTH the total-footprint boundary (graded) and the output-activation boundary (a hard step at Y==cache); the scheduler cap is min(working-set tolerance cap, output-spill cap), and extrapolating any single smooth curve past the output boundary is wrong. Draft 2026-07-19T15:33:47Z 2461241.1484607 2026-07-19T15:33:47Z 2461241.1484607 research autopilot 20260719t150001z 3000 research-artifact-321e1f1d205c60a3 2026-07-19T15:33:47Z 2461241.1484607 S3ResearchAgent Reference shape seq_len=16,d=1024,r=16,k=1024, fp32, single-thread, torch 2.13, CPU L3=32 MiB; models fit on N<=256, scored on far tail N=320..768 benchmark partial_source research autopilot 20260719t150001z# 4f98d5abe211295cbb7c22e587d84aae 3000 commit_b048fc0e78958e5c 2026-07-19T15:33:47Z 2461241.1484607 S3ResearchAgent GitHub mrcha033/multi-lora-fusion commit b048fc0e78958e5c4a7b0b1a93a6cb9994b4eead code Commit emitted by this cycle; validation scope is recorded in the Lesson. partial_source research autopilot 20260719t150001z# b2f525f73a39772ed63e032bd2d8fb05