# llm_moe_hard_seeds_smol — the headroom rule on a second base lineage (SmolLM2-1.7B-Instruct)

**Claim tested (manuscript revision 2026-09-12).** Union (routing among intact specialists) beats
fusion (weight averaging) wherever the average falls short of attainable performance. Replicates
`llm_moe_hard_seeds` (hard task variant, 400 training tasks, 80 test tasks per family, soup / TIES /
oracle router / learned router, 3 training seeds) on `HuggingFaceTB/SmolLM2-1.7B-Instruct`. Ran in
7 min on one L40S (`hpc/llm_smol.pbs`). Numbers from `figures/stats_llm_smol.py`.

### Result — replicates, 3/3 seeds, larger margin than on Qwen
| contrast (SmolLM2, hard) | overall | worst family |
|---|---|---|
| routing (learned = oracle) − soup | **+0.162 ± 0.036** (3/3) | +0.221 ± 0.029 (3/3) |
| soup − best specialist | −0.029 ± 0.017 (3/3 below) | +0.012 ± 0.014 |
| *(Qwen2.5-0.5B)* routing − soup | +0.100 ± 0.090 (3/3) | +0.150 ± 0.075 (3/3) |
| *(Qwen)* soup − best specialist | −0.025 ± 0.122 (1/3 above) | 0.000 ± 0.102 |

Absolute levels (SmolLM2): best specialist 0.194, soup 0.165, routing 0.328 overall. Two riders carry
over unchanged: the learned router equals the oracle (the families are lexically separable, so routing
is easy here), and on this base the soup falls **below** the best single specialist in every seed,
the dilution the Qwen 0.5B hard run showed in one seed of three. Falsifier (not triggered): routing ≤
soup in a majority of seeds.