# Multi-seed LLM recombination (0.5B) — the claims with error bars

PNAS work-order Phase 3: removes the "one seed" objection on the three LLM recombination claims.
Protocol: **test sets fixed** (seed 1000+i per family), **training seed varied** (specialists cache
per-seed as `spec_<family>[_hard]_s<seed>`), so across-seed variance is training variance only.
Figure: `llm_seeds.png` (this dir) aggregates all three experiments, 95% CI over seeds.

### (A) Fisher–Muller, easy benchmark, 5 seeds (`llm_merge_seeds`)
| model | overall | worst-family |
|---|---|---|
| merge_ties | **0.647 ± 0.027** | **0.282 ± 0.020** |
| merge_soup | 0.632 ± 0.042 | 0.278 ± 0.028 |
| best specialist (strings) | 0.592 ± 0.009 | 0.078 ± 0.011 |
| base | 0.277 | 0.150 |

Both merges beat every specialist overall (ties: non-overlapping CIs; soup: marginal at 0.5B, as in
the single-seed run — decisive at 7B) and the **worst-family signature is unambiguous**: merges ≈0.28
vs ≤0.16 for any parent — only recombined models are competent everywhere.

### (B) Union vs fusion, hard benchmark, 3 seeds (`llm_moe_hard_seeds/`)
Routing (union) 0.274 ± 0.026 overall / 0.238 ± 0.024 worst-family; fusion soup 0.174 ± 0.102 / 0.088
± 0.093; ties similar; best specialist 0.199 ± 0.026. Union beats fusion on both metrics — **and a new
finding: fusion is seed-FRAGILE on hard tasks (CI ±0.10) while routing is seed-stable (±0.026).**
Averaging's outcome depends on which specialist minima the seeds happened to find; selection-based
recombination is reliable. (Learned router still = oracle: lexically distinct families, known rider.)

### (C) Directed offspring selection, hard, 3 seeds (`llm_directed_hard_seeds/`)
directed_overall 0.221 ± 0.026 (> soup 0.174 ± 0.102 and > best specialist); directed_balanced
worst-family 0.158 ± 0.036 (> soup 0.088 ± 0.093). Directed selection both beats and **stabilises**
the a-priori soup; per-input routing (B) remains above any single global blend, as before.

**Read together:** all three recombination claims hold under seed replication, and the operator
ordering (route > directed-select > soup, on headroom tasks) is not only a mean effect but a
*variance* effect — the union/selection operators are the reliable ones. Base: Qwen2.5-0.5B-Instruct;
statistical (per-seed) reproducibility per blueprint §4.