llm_directed: directed sex (breed offspring + select on verifier) — E10 in real weights

Adds the "directed sex" operator (E10) the moe regime-flip pointed to: don't
commit to one a-priori blend — breed a population of recombinant offspring
(specialists merged at Dirichlet-sampled weights), score each on a held-out
validation split with the verifier, and keep the fittest, reported on a fresh
test split. Two breeding objectives: best-overall and best-worst-family.
src/llm/directed.py + kind llm_directed, reusing the cached specialists.

Result — refinements pay off in proportion to how far the uniform soup is from
optimal:
- 0.5B (soup dilutes): directed selection beats soup on the bred objective —
  directed_overall 0.69 > soup 0.64; directed_balanced worst-family 0.37 > 0.26.
  Riders: single-objective selection trades off the other axis (overall-breed
  tanks lists to 0.17); a global blend still trails per-input routing (0.74).
- 7B (Imperial CX3, soup already composes to ceiling on near-saturated families,
  strings/arith 1.00): directed ~= soup (0.868 ~ 0.873, marginally below via a
  val/test overfit gap) — no fitter offspring to breed.

Through-line across all four LLM runs: "merge, don't average" and its refinements
(routing, directed selection) are weak-base / suboptimal-default phenomena — they
help at 0.5B and are inert at 7B. Honest limitation kept in the writeup: the 7B
families are near-saturated, which caps the headroom; a harder unsaturated
benchmark is the fair next test.

Also folds in the two llm_moe local manifest/config files missed in 8da0dac.
+3 directed unit tests (130 green). Results in results/llm_directed{,_hpc}/
(parquet gitignored).

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

figures/plot_llm_directed.py

@@ -0,0 +1,94 @@
+"""llm_directed figure — directed sex in weight space (E10): breed offspring, select the fittest.
+
+A population of recombinant offspring (weighted merges of the specialists) is scored on a held-out
+validation split by the verifier; the winners (best-overall, best-worst-family) are reported on a
+fresh test split against the uniform-soup blend and the best single specialist. Two panels: (A)
+per-family accuracy — directed offspring (green) vs soup (orange) vs specialists (blue); (B) overall
+vs worst-family, with the best-specialist bar as the parent ceiling. The suptitle reports whether
+directed selection beat the single a-priori soup. Reads only the committed bundle.
+
+Usage:  python figures/plot_llm_directed.py [results/llm_directed]
+"""
+
+from __future__ import annotations
+
+import sys
+from pathlib import Path
+
+import matplotlib.pyplot as plt
+import numpy as np
+
+sys.path.insert(0, str(Path(__file__).parent))
+from _figlib import load_bundle, savefig  # noqa: E402
+
+_FAMS = ["lists", "strings", "arith"]
+_DIRECTED = {"directed_overall": "directed:overall", "directed_balanced": "directed:balanced"}
+
+
+def _acc(df, model, metric):
+    r = df[(df["model"] == model) & (df["metric"] == metric)]["accuracy"]
+    return float(r.iloc[0]) if len(r) else float("nan")
+
+
+def main(results_dir: str = "results/llm_directed") -> None:
+    df, cfg = load_bundle(results_dir)
+    present = set(df["model"].unique())
+    specialists = sorted(m for m in present if m.startswith("spec_"))
+    directed = [m for m in _DIRECTED if m in present]
+    soup = ["merge_soup"] if "merge_soup" in present else []
+    models = ["base"] + specialists + soup + directed
+    labels = {"base": "base", **{s: s.replace("spec_", "spec:") for s in specialists},
+              "merge_soup": "soup (uniform)", **_DIRECTED}
+    colors = {"base": "#7f7f7f", **{s: "#1f77b4" for s in specialists},
+              "merge_soup": "#ff7f0e", **{m: "#2ca02c" for m in directed}}
+
+    fig, axes = plt.subplots(1, 2, figsize=(13, 5))
+
+    # Panel A: per-family accuracy.
+    ax = axes[0]
+    x = np.arange(len(_FAMS))
+    w = 0.8 / len(models)
+    for i, mdl in enumerate(models):
+        vals = [_acc(df, mdl, f) for f in _FAMS]
+        ax.bar(x + (i - (len(models) - 1) / 2) * w, vals, w, label=labels[mdl], color=colors[mdl],
+               alpha=0.9 if mdl in directed else 0.65)
+    ax.set_xticks(x); ax.set_xticklabels(_FAMS)
+    ax.set(ylabel="accuracy", title="Per-family: directed offspring (green), selected on the\n"
+           "verifier, vs the single uniform soup (orange) and the parents")
+    ax.legend(frameon=False, fontsize=8, ncol=2)
+
+    # Panel B: overall vs worst-family, with the best-specialist ceiling.
+    ax = axes[1]
+    x2 = np.arange(len(models))
+    for off, metric, hatch, lab in [(-0.2, "overall", "", "overall"),
+                                    (0.2, "worst_family", "//", "worst family")]:
+        ax.bar(x2 + off, [_acc(df, m, metric) for m in models], 0.38,
+               color=[colors[m] for m in models], hatch=hatch, alpha=0.85, label=lab,
+               edgecolor="white")
+    ax.set_xticks(x2); ax.set_xticklabels([labels[m] for m in models], rotation=25, ha="right",
+                                          fontsize=8)
+    if specialists:
+        ceil = max(_acc(df, s, "overall") for s in specialists)
+        ax.axhline(ceil, ls=":", c="#1f77b4", lw=1, alpha=0.7)      # best-parent ceiling
+    ax.set(ylabel="accuracy", title="Overall (solid) vs worst-family (hatched):\n"
+           "directed offspring vs soup vs the best parent (dotted)")
+    ax.legend(frameon=False, fontsize=9)
+
+    best_dir = max([_acc(df, m, "overall") for m in directed], default=float("nan"))
+    soup_o = _acc(df, "merge_soup", "overall")
+    best_spec = max([_acc(df, s, "overall") for s in specialists], default=float("nan"))
+    if best_dir > soup_o + 0.005:
+        verdict = f"directed {best_dir:.2f} > soup {soup_o:.2f} overall"
+    elif best_dir > soup_o - 0.005:
+        verdict = f"directed {best_dir:.2f} ≈ soup {soup_o:.2f} overall"
+    else:
+        verdict = f"directed {best_dir:.2f} < soup {soup_o:.2f} overall"
+    verdict += f" (best parent {best_spec:.2f})"
+    fig.suptitle(f"llm_directed — directed sex (breed offspring + select on the verifier): {verdict} "
+                 f"({cfg['base_model'].split('/')[-1]})", y=1.0, fontsize=12)
+    fig.tight_layout()
+    savefig(fig, results_dir, "llm_directed")
+
+
+if __name__ == "__main__":
+    main(*sys.argv[1:])