llm: first real-LLM prototype — recombining specialist LLMs (C2/C4)

First step from toy models toward real language models, on one 16 GB GPU.
New src/llm/ package: procedural task families + exact-match verifier
(tasks.py), batched eval (evaluate.py), LoRA specialisation (specialise.py,
manual answer-only SFT), weight-space merge via peft add_weighted_adapter
(merge.py: soup = averaged deltas, ties = sign-reconciled union), runner
(experiment.py, kind llm_merge). Base Qwen2.5-0.5B-Instruct (Apache-2.0);
three disjoint hard families (lists/strings/arith); one LoRA specialist each
(~90s total).

Result (seed 1), reported honestly:
- STRONG/robust: the merges are the ONLY models competent across ALL
  families -- worst-family ~0.25 vs <0.16 for every single specialist (the
  Fisher-Muller "generalist assembled from specialists" signature, in real
  LoRA weights).
- MARGINAL: "exceeds every parent overall" is only marginal at this scale
  (soup 0.64 vs best specialist 0.63; ties 0.61 below it).
- CAVEAT VISIBLE: averaging dilutes peaks (lists specialist 0.43 -> merge
  0.26) -- Layer-1's "merge, don't average" (E4) appearing in real weights.

The pipeline works end-to-end; the balance/retention half reproduces; the
strict overall-exceeds and soup-vs-ties distinction need scale (bigger base,
more/cleaner families, seeds, a dilution-resistant / offspring-selected
merge) -- the HPC step. Env: Python 3.14 + transformers 5.13 works;
note transformers-5.x apply_chat_template returns a dict. make env-llm /
make llm; adapters under gitignored models/llm/, base in the HF cache.
figures/plot_llm_merge.py, README, tests/test_llm.py (+3, 125 green).

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

figures/plot_llm_merge.py

@@ -0,0 +1,81 @@
+"""llm_merge figure — recombining specialist LLMs (blueprint C2/C4, the real-LLM image of E8).
+
+LoRA specialists on disjoint task families are merged (weight-space) into one deployable model. The
+recombined model beats any single specialist overall and — the sharper signature — is competent
+across *all* families, which no single parent is. Two panels: (A) per-family accuracy for the base,
+each specialist, and the merges (each specialist spikes on its own family; the merges are high
+everywhere); (B) overall vs worst-family accuracy (the merges dominate both, especially worst-family).
+Reads only the committed bundle.
+
+Usage:  python figures/plot_llm_merge.py [results/llm_merge]
+"""
+
+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"]
+
+
+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_merge") -> None:
+    df, cfg = load_bundle(results_dir)
+    specialists = sorted(m for m in df["model"].unique() if m.startswith("spec_"))
+    merges = sorted(m for m in df["model"].unique() if m.startswith("merge_"))
+    models = ["base"] + specialists + merges
+    labels = {"base": "base", **{s: s.replace("spec_", "spec:") for s in specialists},
+              **{m: m.replace("merge_", "merge:") for m in merges}}
+    colors = {"base": "#7f7f7f"}
+    for s in specialists:
+        colors[s] = "#1f77b4"
+    for m in merges:
+        colors[m] = "#2ca02c"
+
+    fig, axes = plt.subplots(1, 2, figsize=(13, 5))
+
+    # Panel A: per-family accuracy, grouped by model.
+    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.startswith("merge_") else 0.7)
+    ax.set_xticks(x); ax.set_xticklabels(_FAMS)
+    ax.set(ylabel="accuracy", title="Per-family: each specialist spikes on its own family; the merges\n"
+           "(green) are competent everywhere (but averaging dilutes some peaks)")
+    ax.legend(frameon=False, fontsize=8, ncol=2)
+
+    # Panel B: overall vs worst-family, per model.
+    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)
+    ax.set(ylabel="accuracy", title="Overall (solid) vs worst-family (hatched): the merge "
+           "clearly wins\nworst-family (balance); overall it matches the best specialist")
+    ax.legend(frameon=False, fontsize=9)
+
+    fig.suptitle("llm_merge — recombining decorrelated specialist LLMs gives the only model competent "
+                 f"across all families (balance); overall parity ({cfg['base_model']})", y=1.0, fontsize=12)
+    fig.tight_layout()
+    savefig(fig, results_dir, "llm_merge")
+
+
+if __name__ == "__main__":
+    main(*sys.argv[1:])