# round 25 track b — ple loop inversion / scaling / history

## decision

**no production kernel changes recommended.** the proposed k-outer inversion preserves tested outputs but is slower on the m5 at large prompt sizes. accumulating directly in `bo[]` does not fix it. hc==4 scaling and history unrolling show no repeatable net win. the supplied patch is **optional test-harness improvements only**, not an optimization claim.

- scratch: `/tmp/sol_r25_ple/strata`
- clean patch: `/tmp/sol_r25_ple/sol_r25_ple.patch`
- sources/logs: `/tmp/sol_r25_ple/`; hashes: `sha256.json`
- baseline: vendor strata head `296b59d2f73c8f04a805df29c2fa97655adace78` plus pre-existing dirty working-tree metal sources copied at task start. `baseline.metal` is the exact captured ple source, not git head.
- no tracked vendor files changed; no server requests, full-model runs, or subagents.

## experiment contract and execution

owner is ple.metal's per-dispatch arithmetic; no buffers, public ABI, persistent state, or synchronization ordering should change. preserve each output's expert FMA order. reject any bitwise mismatch; require repeatable paired speed improvement, emphasizing T>=512 without clear smaller-T regressions. plan recorded before implementation in `/tmp/sol_r25_ple/plan.md`.

machine: `Apple M5`, local apple clang 21.0.0.21000327, safe metal math (runtime default, fast math disabled). fixed evaluator N=2560, HC=4, TOPK=10, seed 11+T, shuffled expert rows with occasional dropped slots. A/B compares residual and normalized buffers via `memcmp`; added history comparison uses separate identical initial history buffers. five paired timing samples alternate execution order, reporting median candidate/baseline ratios. timings below are GPU milliseconds, not wall time. use the paired-ratio median, which need not equal the ratio of independently reported median times.

build:

```text
cmake -S /tmp/sol_r25_ple/strata/metal -B /tmp/sol_r25_ple/build -G Ninja -DCMAKE_BUILD_TYPE=Release
cmake --build /tmp/sol_r25_ple/build --target ple_moe_parity
/tmp/sol_r25_ple/build/ple_moe_parity --ab /tmp/sol_r25_ple/baseline.metal T
```

candidate source is loaded from the scratch tree at runtime. exact snapshots are `all.metal`, `inversion.metal`, `direct.metal`, `unrolled.metal`, `scaling.metal`, `history.metal`. each log prefix names the candidate used. final scratch ple.metal is restored byte-for-byte to baseline.

## measured results

### full proposed set (`all-T*.log`)

bitwise pass at all requested T = 1,4,8,64,512,1024,2048 for moe norm, combined moe norm, query norm, and history. `ple_comb_query_gate_norm` is not covered by this evaluator; scaling there is therefore **not validated** and is not shipped. these are finite randomized parity checks, not exhaustive IEEE edge-value proofs.

| T | combined moe norm standalone ratio | with conv_res ratio |
|---:|---:|---:|
|1|0.5901|0.6676|
|4|0.5961|0.6393|
|8|0.5902|0.7654|
|64|1.0527|1.1091|
|512|1.1082|1.0802|
|1024|1.0826|1.0677|
|2048|1.0799|1.0622|

### ablations

- **inversion only**, preserving original division/history: standalone ratios at T512/1024/2048 = **1.0761 / 1.1009 / 1.0887**; with conv = **1.0574 / 1.0724 / 1.0599**. all pass.
- **direct bo accumulation** (parent follow-up): first run standalone ratios = **1.1440 / 1.1173 / 1.0564**, with conv = **1.0491 / 1.0584 / 1.0519**. confirmation T512/1024 = **1.0844 / 1.0798**, with conv **1.0658 / 1.0639**; T2048 confirmation became noisy. all completed checks pass. naming one fewer array does not establish lower actual register pressure: the compiler may already coalesce disjoint s/bo live ranges. no ISA/register counters were collected, so the physical cause is unproven.
- **cnt==10 i-outer k-inner full unroll**: no consistent standalone win; confirmation T512/1024/2048 ratios **1.0052 / 1.0233 / 1.0144**. combined-chain apparent gains occurred during severe drift and do not establish a win. all completed checks pass.
- **hc==4 scaling only**, with original division fallback for other hc: completed all seven requested T with parity passes for covered kernels; timings inconsistent. no confirmed benefit. do not replace division by a computed reciprocal for arbitrary hc if bitwise equivalence is required.
- **history-only unrolling**: all seven requested T pass; 128-repetition history timing ratios span **0.9780–1.1563**, with no consistent benefit. full unrolling does not itself prove removal of a spill; no generated-code inspection was done.

baseline-vs-baseline calibration at T512/1024/2048: standalone combined moe norm ratios **0.9994 / 0.9942 / 1.0015**, combined with conv **1.0059 / 1.0054 / 1.0086** (`calibration-T*.log`). some other runs show severe timing drift, including unchanged controls: those isolated apparent gains are inconclusive rather than winners. the repeated inversion slowdown in comparatively stable runs is enough to reject shipping it; it is not enough to diagnose hardware counters.

## optional patch and final verification

only `metal/tests/ple_moe_parity.cpp` changes:

- A/B history memcmp and timing with independent histories;
- A/B timing for `ple_moe_gate_norm` as well as combined norm;
- allow timing at small T;
- short A/B warmup (3 ms each) and two repetitions per timed sample, 128 for the tiny history kernel, to stay within the short-invocation budget. five alternating paired samples remain. this is screening, not high-confidence thermal/performance isolation.

final build passes. final baseline-vs-baseline A/B checks at all seven T exit 0 / ALL PASS (`final-test-T*.log`), wall times 0.167–1.970s. non-A/B unfused-chain and CPU history reference checks (`ple_moe_parity 2048`) exit 0 / ALL PASS in 0.454s (`final-nonab.log`). note the non-A/B default test skips the TB fusion case without bench, while its separate history reference loop includes 2048.

`git -C vendor/strata apply --check /tmp/sol_r25_ple/sol_r25_ple.patch` exits 0. final visual diff/context review completed. optional tests do not alter production behavior.

one cold compile for `unrolled-T1.log` hit the configured 5s timeout and was terminated (wall 5.025s, exit -15; no result). the candidate source was preserved and later separate T invocations completed. no longer timeout or full-model benchmark was used. initial full-set cold compile passed in 4.981s. no measurement is claimed for that interrupted unrolled T1 run.

## next step

keep production ple.metal unchanged. use the optional short A/B test patch if useful; otherwise retain only the negative-result report. an exclusive GPU/thermal window and generated-code inspection would be needed before attributing remaining small effects to instruction count or register allocation.