From 62c68d6c8c4090e62cf9ee17ac7b7d1eff7a6955 Mon Sep 17 00:00:00 2001 From: Giorgio Gilestro Date: Sun, 5 Jul 2026 10:51:41 +0100 Subject: [PATCH] =?UTF-8?q?society:=20multi-locus=20recombination=20frame?= =?UTF-8?q?=20=E2=80=94=20the=20vertical=20claim=20(E7/E8)?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Enter the Lamarckian society with a robust theoretical frame. The single- locus, fixed-p* model can only express recovery toward a ceiling; the society's load-bearing claim is vertical -- capability that EXCEEDS any component. Generalize knowledge to a distribution over genotypes (L biallelic loci, K=2^L, additive fitness = # correct loci), reusing all the K-mode machinery. The one new operator is recombination: free recombination sends p -> product of per-locus marginals (linkage equilibrium). E8 (star, kind: society) -- the vertical claim / Fisher-Muller: decorrelated PARENTS (specialists, expert on their loci, agnostic elsewhere) are recombined; sexual merge assembles a genotype fitter than any parent, climbing to the optimum (12/12, a genotype no parent had) as parent count grows and rho->0, while the best single parent (~8.7) and the mean-mixture "model soup" (~11.6) plateau below. Reuses make_retention_matrix (locus mastery replaces tail-item retention). E7 (kind: genotype_lineage) -- the advantage of sex: a single population adapts toward the optimum; the sexual lineage adapts faster than asexual (clonal interference) by keeping loci in linkage equilibrium (LD->0 vs LD spike). Honest scope: a speed advantage, not a permanent Muller's-ratchet gap (subtle to force); E8 carries the headline. Metaphor shift (per GG): the society is sexual reproduction with UNBOUNDED parents, not teacher->pupil. Teacher->pupil caps at the ceiling; n-parent recombination is combinatorial and generative, and unlike biology there is no two-parent limit. Collapse = asexual degradation; the cure = sex. This unifies E4 (merge != average) + E6 (irreversibility) under evolution-of-sex theory and reaches ground Riis's single-locus n-grams cannot. New: knowledge/{genotype,genotype_lineage,society}.py, configs/layer1/{E7, E8}.yaml, figures/plot_{E7,E8}.py, READMEs, tests/test_genotype.py (+7). experiment.py dispatch (kind in {genotype_lineage, society}); make layer1 wired. 112 tests green. Co-Authored-By: Claude Opus 4.8 --- CLAUDE.md | 2 + Makefile | 2 +- configs/layer1/E7.yaml | 29 +++++ configs/layer1/E8.yaml | 29 +++++ figures/plot_E7.py | 62 +++++++++ figures/plot_E8.py | 68 ++++++++++ results/E7/E7.pdf | Bin 0 -> 31151 bytes results/E7/E7.png | Bin 0 -> 160966 bytes results/E7/README.md | 31 +++++ results/E7/manifest.json | 14 +++ results/E7/resolved_config.yaml | 23 ++++ results/E8/E8.pdf | Bin 0 -> 27237 bytes results/E8/E8.png | Bin 0 -> 170625 bytes results/E8/README.md | 35 ++++++ results/E8/manifest.json | 14 +++ results/E8/resolved_config.yaml | 29 +++++ src/knowledge/experiment.py | 51 +++++++- src/knowledge/genotype.py | 202 ++++++++++++++++++++++++++++++ src/knowledge/genotype_lineage.py | 82 ++++++++++++ src/knowledge/society.py | 95 ++++++++++++++ tasks/todo.md | 24 +++- tests/test_genotype.py | 90 +++++++++++++ 22 files changed, 879 insertions(+), 3 deletions(-) create mode 100644 configs/layer1/E7.yaml create mode 100644 configs/layer1/E8.yaml create mode 100644 figures/plot_E7.py create mode 100644 figures/plot_E8.py create mode 100644 results/E7/E7.pdf create mode 100644 results/E7/E7.png create mode 100644 results/E7/README.md create mode 100644 results/E7/manifest.json create mode 100644 results/E7/resolved_config.yaml create mode 100644 results/E8/E8.pdf create mode 100644 results/E8/E8.png create mode 100644 results/E8/README.md create mode 100644 results/E8/manifest.json create mode 100644 results/E8/resolved_config.yaml create mode 100644 src/knowledge/genotype.py create mode 100644 src/knowledge/genotype_lineage.py create mode 100644 src/knowledge/society.py create mode 100644 tests/test_genotype.py diff --git a/CLAUDE.md b/CLAUDE.md index b034b24..0f8c4a2 100644 --- a/CLAUDE.md +++ b/CLAUDE.md @@ -80,6 +80,8 @@ E4's whole purpose is to isolate the effect of teacher **decorrelation ρ**, so **Strategic positioning vs Riis 2026 (arXiv:2604.08554, "Drift and selection in LLM text ecosystems").** Riis independently formalizes **collapse = Wright–Fisher drift** (his Thm 1) with n-gram agents: minority-mass martingale, rare-first extinction, single-token dropout ≈ αe^{−α}, de Bruijn-polytope fixed points, plus descriptive-vs-normative *selection* (Thm 2). **Concede as prior art:** "collapse is literally Wright–Fisher", the martingale, rare-first loss, the WF/effective-population formalism — cite him; do **not** frame these as our contribution. **Crucial distinction that protects us:** his "mixed environment" *retains the lineage's own old synthetic tokens* — there is **no injection of fresh real data from a fixed `p*`**, so his headline is *pessimistic* (Thm 1c: extinction is independent of α — retention only changes speed). Our **grounding is immigration from a non-drifting external truth**, giving a stationary `H_eq>0` and a critical `g*≪1` that *prevents* collapse — the mechanism his closed loop lacks. **Our defensible novelty, ranked:** (1) **recombination + "merge, don't average" conservation law** (E4) — he has no model-merging operator; flagship; (2) **the learning-kernel / estimator-bias axis** — he *explicitly names it as future work*; we now build+measure it; (3) grounding threshold (solid anchor, but immigration–drift balance is classic — not a flagship); (4) architecture-generality in real weights + MNIST; (5) **the Lamarckian society + the vertical/cumulative C3 claim — wholly ours, not yet run.** Reposition the paper from *"collapse is drift"* (now contested) to **a population-genetic *control theory* for sustaining open-ended knowledge**: drift is the diagnosed disease (cite Riis), our contribution is the engineered remedies and their integration. +**Finding (2026-07-05, E7/E8 — the multi-locus society frame; raises the ceiling).** To express the *vertical* claim (capability that *exceeds* any component), knowledge is generalized from a single-locus fixed-`p*` distribution to a distribution over **genotypes** (`L` biallelic loci, `K=2^L`; fitness = # correct loci; reuses all the K-mode machinery). The one new operator is **recombination** (`knowledge/genotype.py`): free recombination sends `p → ⊗ per-locus marginals` (linkage equilibrium). Two experiments, both analytic. **E8 (the star, `kind: society`) — the vertical claim / Fisher–Muller:** decorrelated *parents* (specialists, expert on their loci, agnostic elsewhere) are recombined; **sexual merge assembles a genotype fitter than any parent, climbing to the optimum (12/12) as parent count grows and `ρ→0`, while the best single parent (~8.7) and the mean-mixture "model soup" (~11.6) plateau below.** Clean, dramatic, 40 reps; reuses `make_retention_matrix` (locus mastery replaces tail-item retention). **E7 (`kind: genotype_lineage`) — the advantage of sex:** a single population adapting toward the optimum; the sexual lineage adapts *faster* (clonal interference slows the asexual one) by keeping loci in linkage equilibrium (LD→0 vs LD spike). Honest scope: a **speed** advantage, not a permanent Muller's-ratchet gap (the single-population ratchet is subtle to force; E8 carries the headline). **Metaphor shift (GG, 2026-07-05):** the society is framed as **sexual reproduction with unbounded parents**, *not* teacher→pupil — teacher→pupil caps at the ceiling (recovery), n-parent recombination is combinatorial and *generative* (exceeds any parent), and unlike biology there is no two-parent limit. Collapse = asexual degradation; the cure = sex. This unifies E4 (merge≠average) + E6 (irreversibility) under evolution-of-sex theory and stakes ground Riis's single-locus n-grams cannot reach. Scope is bounded: fixed combinatorial space (`L≤12`, "effectively open-ended relative to n"), additive fitness (NK/epistasis is an optional extension). + ## Build order (blueprint §7) — respect the gate 1. Scaffold: repo layout (§5), container, pytest skeleton, config system, seeding utils. `make test` green. diff --git a/Makefile b/Makefile index 96c9d0f..72a3e35 100644 --- a/Makefile +++ b/Makefile @@ -16,7 +16,7 @@ test: ## correctness tests + scientific-validation tests (the spine uv run pytest layer1: ## run experiments E1-E6 + the learning-kernel bridge (analytic) - for e in E1 E2 E3 E4 E5 E6 kernel_sharpen kernel_smooth; do uv run python -m knowledge.experiment configs/layer1/$$e.yaml; done + for e in E1 E2 E3 E4 E5 E6 E7 E8 kernel_sharpen kernel_smooth; do uv run python -m knowledge.experiment configs/layer1/$$e.yaml; done neural: ## run Layer 1.5 synthetic neural experiments (excludes the heavy MNIST tier) for c in configs/neural/*.yaml; do case "$$c" in *mnist*) ;; \ diff --git a/configs/layer1/E7.yaml b/configs/layer1/E7.yaml new file mode 100644 index 0000000..0b58208 --- /dev/null +++ b/configs/layer1/E7.yaml @@ -0,0 +1,29 @@ +experiment: E7 +kind: genotype_lineage +seed: 20260705 +n_replicates: 20 + +# (The advantage of sex — the dynamic mechanism behind E8): a single population adapts from all-wrong +# toward a multi-locus optimum under selection + drift + mutation. Beneficial alleles arise in +# different sub-lineages; recombination reassorts them into one genotype, while an asexual lineage +# suffers clonal interference (the alleles compete and cannot combine). Expect the SEXUAL lineage +# (recomb_rate=1) to climb toward the optimum faster than the ASEXUAL one (recomb_rate=0) — the +# classical advantage of sex, and the reason a lone model lineage cannot do what a recombining +# society can. Honest scope: a SPEED advantage, not a dramatic permanent gap (the single-population +# ratchet is subtle); E8 carries the headline. Falsifier: sexual adapts no faster than asexual. + +genotype: + L: 12 + n: 150 # population/resample size (drift strength) + mu: 0.02 # per-locus mutation (flip) rate + base: 1.3 # multiplicative selection: fitness weight = base^(#correct loci) + recomb_rate: 0.0 # overwritten per arm by the sweep + init: wrong # start all-wrong (load L); adapt upward + +generations: 120 + +sweep: + - param: genotype.recomb_rate + values: [0.0, 1.0] # asexual vs sexual + +output: {dir: results/E7} diff --git a/configs/layer1/E8.yaml b/configs/layer1/E8.yaml new file mode 100644 index 0000000..4c91f9b --- /dev/null +++ b/configs/layer1/E8.yaml @@ -0,0 +1,29 @@ +experiment: E8 +kind: society +seed: 20260705 +n_replicates: 40 + +# (The vertical claim / Fisher-Muller — the society headline): can an offspring recombined from +# MANY decorrelated parents be fitter than ANY parent? Each parent is a specialist: confident- +# correct (hi) on the loci it has mastered, agnostic (~0.5) elsewhere; which loci each masters comes +# from the exact shared-switch construction, so parent count K_T and decorrelation rho are clean +# knobs. Deployed capability = fitness of the MODE genotype. Compare best single parent vs mean- +# mixture ("model soup", combine-but-don't-recombine) vs sexual recombination (assemble the best +# allele of each locus across all parents). Expect: sexual climbs to the optimum (=L, a genotype NO +# parent had) as K_T grows and rho->0, while best-parent and average plateau far below. Unlike +# biological sex there is no two-parent limit. Falsifier: sexual never exceeds the best parent, or +# averaging matches sexual. + +society: + L: 12 # loci; the optimum (all-correct) has fitness 12 and no parent possesses it + q: 0.5 # fraction of loci each parent masters (marginal mastery) + hi: 0.9 # correct-allele prob on a mastered locus (confident expert) + lo: 0.45 # correct-allele prob on an unmastered locus (agnostic, slightly wrong) + +sweep: + - param: K_T + values: [1, 2, 3, 5, 8, 12] # number of parents (unbounded; grows the recombinant reach) + - param: rho + values: [0.0, 0.5, 1.0] # decorrelated -> identical parents (the control) + +output: {dir: results/E8} diff --git a/figures/plot_E7.py b/figures/plot_E7.py new file mode 100644 index 0000000..ac52358 --- /dev/null +++ b/figures/plot_E7.py @@ -0,0 +1,62 @@ +"""E7 figure — the advantage of sex: recombination adapts faster than clonal reproduction. + +The dynamic mechanism behind E8. A single population adapts from all-wrong toward a multi-locus +optimum under selection + drift + mutation. Beneficial alleles arise in different sub-lineages; +sexual recombination reassorts them into one genotype, while an asexual lineage suffers clonal +interference. The sexual lineage climbs faster — the classical advantage of sex (an honest *speed* +advantage; both eventually plateau near the optimum in this tractable regime). + +Two panels: (A) mean-fitness adaptation curves, asexual vs sexual, over generations; (B) linkage +disequilibrium over generations — asexual holds beneficial alleles in disequilibrium (scattered +across genotypes) while sexual drives it to ~0 (assembled), the mechanism of the speed gap. + +Usage: python figures/plot_E7.py [results/E7] +""" + +from __future__ import annotations + +import sys +from pathlib import Path + +import matplotlib.pyplot as plt + +sys.path.insert(0, str(Path(__file__).parent)) +from _figlib import load_bundle, mean_ci, savefig # noqa: E402 + + +def main(results_dir: str = "results/E7") -> None: + df, cfg = load_bundle(results_dir) + L = cfg["genotype"]["L"] + arms = [(0.0, "#7f7f7f", "asexual (clonal)"), (1.0, "#d62728", "sexual (recombining)")] + + fig, axes = plt.subplots(1, 2, figsize=(13, 5)) + + ax = axes[0] + for rate, c, lab in arms: + sub = df[df["recomb_rate"] == rate] + g, m, ci = mean_ci(sub, "generation", "mean_fitness") + ax.plot(g, m, "-", color=c, lw=1.8, label=lab) + ax.fill_between(g, m - ci, m + ci, color=c, alpha=0.2) + ax.axhline(L, ls=":", color="green", lw=1, label=f"optimum ($L$={L})") + ax.set(xlabel="generation", ylabel="mean fitness (# correct loci)", + title="Advantage of sex: recombination adapts faster\n(clonal interference slows the asexual lineage)") + ax.legend(frameon=False, fontsize=9) + + ax = axes[1] + for rate, c, lab in arms: + sub = df[df["recomb_rate"] == rate] + g, m, ci = mean_ci(sub, "generation", "ld") + ax.plot(g, m, "-", color=c, lw=1.8, label=lab) + ax.fill_between(g, m - ci, m + ci, color=c, alpha=0.2) + ax.set(xlabel="generation", ylabel="mean linkage disequilibrium |D|", + title="Mechanism: asexual scatters beneficial alleles (LD>0);\nsexual assembles them (LD→0)") + ax.legend(frameon=False, fontsize=9) + + fig.suptitle("E7 — the advantage of sex: recombination reassorts beneficial alleles that arose " + "in different lineages", y=1.02, fontsize=12) + fig.tight_layout() + savefig(fig, results_dir, "E7") + + +if __name__ == "__main__": + main(*sys.argv[1:]) diff --git a/figures/plot_E8.py b/figures/plot_E8.py new file mode 100644 index 0000000..b5f7942 --- /dev/null +++ b/figures/plot_E8.py @@ -0,0 +1,68 @@ +"""E8 figure — the vertical claim: n-parent recombination exceeds any parent (Fisher–Muller). + +The society headline. Decorrelated *parents* are specialists (expert on some loci, agnostic on the +rest); an *offspring* recombined from all of them can be fitter than any parent — capability that +*exceeds* every component, not just recovers a ceiling. Unlike biological sex there is no two-parent +limit, so capability climbs toward the optimum as the parent pool grows and decorrelates. + +Two panels: (A) deployed capability (mode-genotype fitness) vs parent count at ρ=0 — sexual +recombination reaches the optimum (a genotype no parent had) while the best single parent and the +mean-mixture "model soup" plateau below; (B) the decorrelation control — sexual capability vs parent +count for ρ ∈ {0, 0.5, 1}: decorrelated parents (ρ=0) climb to the optimum, identical parents (ρ=1) +buy nothing. Reads only the committed bundle. + +Usage: python figures/plot_E8.py [results/E8] +""" + +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, mean_ci, savefig # noqa: E402 + + +def main(results_dir: str = "results/E8") -> None: + df, cfg = load_bundle(results_dir) + L = cfg["society"]["L"] + rhos = sorted(df["rho"].unique()) + + fig, axes = plt.subplots(1, 2, figsize=(13, 5)) + + # Panel A: best-parent vs average vs sexual, at rho=0. + ax = axes[0] + d0 = df[df["rho"] == 0.0] + for col, c, lab in [("best_parent", "#7f7f7f", "best single parent"), + ("average", "#1f77b4", "average (model soup)"), + ("sexual", "#d62728", "sexual recombination")]: + k, m, ci = mean_ci(d0, "K_T", col) + ax.errorbar(k, m, yerr=ci, fmt="-o", color=c, capsize=3, label=lab) + ax.axhline(L, ls=":", color="green", lw=1, label=f"optimum ($L$={L})") + ax.set(xlabel="number of parents $K_T$", ylabel="deployed capability (mode fitness)", + title="Recombination exceeds any parent (ρ=0):\nsexual reaches the optimum; soup & best-parent plateau") + ax.legend(frameon=False, fontsize=9) + + # Panel B: sexual capability vs K_T for each rho (decorrelation control). + ax = axes[1] + colors = plt.cm.viridis(np.linspace(0, 0.8, len(rhos))) + for rho, c in zip(rhos, colors): + sub = df[df["rho"] == rho] + k, m, ci = mean_ci(sub, "K_T", "sexual") + ax.errorbar(k, m, yerr=ci, fmt="-o", color=c, capsize=3, label=fr"ρ={rho:g}") + ax.axhline(L, ls=":", color="green", lw=1, label=f"optimum ($L$={L})") + ax.set(xlabel="number of parents $K_T$", ylabel="sexual-recombination capability", + title="Decorrelation is the fuel:\nρ=0 climbs to the optimum; ρ=1 (clones) buy nothing") + ax.legend(frameon=False, fontsize=9) + + fig.suptitle("E8 — the vertical claim: an offspring recombined from many decorrelated parents " + "is fitter than any parent 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(paired replicate seeds) but assembles the base from the + ``genotype``/``generations`` blocks and calls ``run_genotype_lineage``. Sweeps use the same + dotted-path ``_apply_param`` (e.g. ``genotype.recomb_rate`` for asexual vs sexual). + """ + from .genotype_lineage import run_genotype_lineage + + base = {k: copy.deepcopy(cfg[k]) for k in _GENOTYPE_KEYS if k in cfg} + sweeps = cfg.get("sweep", []) + if isinstance(sweeps, dict): + sweeps = [sweeps] + params = [s["param"] for s in sweeps] + value_lists = [list(s["values"]) for s in sweeps] + combos = [({}, base)] if not sweeps else [] + for values in itertools.product(*value_lists): + lin = copy.deepcopy(base) + label: dict = {} + for param, val in zip(params, values): + label.update(_apply_param(lin, param, val)) + combos.append((label, lin)) + + seeds = spawn_seeds(int(cfg["seed"]), int(cfg["n_replicates"])) + frames: list[pd.DataFrame] = [] + for label, lin in combos: + for rep, ss in enumerate(seeds): + df = run_genotype_lineage(lin, int(ss.generate_state(1)[0])) + for col, val in label.items(): + df[col] = val + df["replicate"] = rep + frames.append(df) + out = pd.concat(frames, ignore_index=True) + out.insert(0, "experiment", cfg["experiment"]) + return out + + def run_coverage(cfg: dict) -> pd.DataFrame: """E4 runner: multi-teacher recombination coverage (blueprint 2.5-E4 / 2.7.1). @@ -278,7 +318,16 @@ def run_and_save(config_path: str | Path) -> Path: config_path = Path(config_path) cfg = yaml.safe_load(config_path.read_text()) out_dir = Path(cfg.get("output", {}).get("dir", f"results/{cfg['experiment']}")) - df = run_coverage(cfg) if cfg.get("kind") == "coverage" else run_experiment(cfg) + kind = cfg.get("kind", "lineage") + if kind == "coverage": + df = run_coverage(cfg) + elif kind == "genotype_lineage": + df = run_genotype_experiment(cfg) # E7: advantage of sex + elif kind == "society": + from .society import run_society # E8: multi-parent recombination + df = run_society(cfg) + else: + df = run_experiment(cfg) save_artifacts(cfg, df, out_dir) return out_dir diff --git a/src/knowledge/genotype.py b/src/knowledge/genotype.py new file mode 100644 index 0000000..49fefee --- /dev/null +++ b/src/knowledge/genotype.py @@ -0,0 +1,202 @@ +"""Multi-locus genotype space + recombination — the theoretical frame for the society. + +The single-locus, fixed-`p*` model can only express *recovery toward a ceiling*. The society's +vertical claim — capability that *exceeds* any component — needs combinatorial structure. A +**genotype** is `L` biallelic loci (allele 1 = "correct", 0 = "wrong"); a model's knowledge is a +distribution over the `2^L` genotypes (a K-vector with `K = 2^L`, so all of Layer 1's K-mode +machinery — drift, grounding, selection, metrics — applies unchanged). Fitness is additive (the +number of correct loci); the optimum is the all-correct genotype. + +The one genuinely new operator is **recombination**. Free recombination replaces the joint genotype +distribution by the product of its per-locus marginals (linkage equilibrium / Robbins proportions) — +the population-level image of meiotic reassortment. This is what halts Muller's ratchet (it +reconstitutes low-load genotypes from complementary high-load parents) and drives the Fisher–Muller +effect (it assembles beneficial alleles that arose in different lineages into a genotype fitter than +any parent). `rate=0` is asexual/clonal (Layer 1's regime); `rate=1` is free recombination. +""" + +from __future__ import annotations + +import numpy as np + +from .metrics import heterozygosity + + +def genotype_bits(L: int) -> np.ndarray: + """Return the ``(2^L, L)`` matrix of genotype bit-vectors (row g = g in binary, MSB first). + + Args: + L (int): Number of biallelic loci. + + Returns: + np.ndarray: ``(2^L, L)`` int8 array; ``bits[g, l]`` is allele of locus ``l`` in genotype ``g``. + """ + g = np.arange(1 << L, dtype=np.int64) + shifts = np.arange(L - 1, -1, -1, dtype=np.int64) + return ((g[:, None] >> shifts[None, :]) & 1).astype(np.int8) + + +def additive_fitness(L: int) -> np.ndarray: + """Additive fitness vector: ``f(g)`` = number of correct (allele-1) loci in genotype ``g``. + + Args: + L (int): Number of loci. + + Returns: + np.ndarray: Length-``2^L`` fitness vector in ``{0, 1, ..., L}``; optimum = all-ones genotype. + """ + return genotype_bits(L).sum(axis=1).astype(float) + + +def locus_marginals(p: np.ndarray, L: int) -> np.ndarray: + """Per-locus frequency of the correct (allele-1) variant under distribution ``p``. + + Args: + p (np.ndarray): Genotype distribution (length ``2^L``, sums to 1). + L (int): Number of loci. + + Returns: + np.ndarray: Length-``L`` array; entry ``l`` is ``P(locus l is correct)``. + """ + return genotype_bits(L).T.astype(float) @ np.asarray(p, dtype=float) # (L, 2^L) @ (2^L,) + + +def linkage_equilibrium(marginals: np.ndarray) -> np.ndarray: + """Build the product (linkage-equilibrium) genotype distribution from per-locus marginals. + + ``p_LE(g) = ∏_l [q_l if g_l==1 else (1−q_l)]`` — the joint under free recombination, where the + loci are statistically independent (Robbins proportions). + + Args: + marginals (np.ndarray): Length-``L`` correct-allele frequencies ``q_l``. + + Returns: + np.ndarray: Length-``2^L`` product distribution (sums to 1). + """ + q = np.asarray(marginals, dtype=float) + L = q.size + bits = genotype_bits(L) # (2^L, L) + per = np.where(bits == 1, q[None, :], 1.0 - q[None, :]) # (2^L, L) + p = per.prod(axis=1) + s = p.sum() + return p / s if s > 0 else p + + +def recombine(p: np.ndarray, L: int, rate: float) -> np.ndarray: + """Apply recombination at ``rate`` to a genotype distribution. + + ``rate=0`` returns ``p`` unchanged (asexual / clonal); ``rate=1`` returns the full + linkage-equilibrium product of ``p``'s marginals (free recombination); intermediate rates + interpolate ``(1−rate)·p + rate·p_LE``. + + Args: + p (np.ndarray): Genotype distribution (length ``2^L``). + L (int): Number of loci. + rate (float): Recombination rate in ``[0, 1]``. + + Returns: + np.ndarray: The recombined distribution (sums to 1). + """ + p = np.asarray(p, dtype=float) + if rate <= 0.0: + return p + p_le = linkage_equilibrium(locus_marginals(p, L)) + out = p_le if rate >= 1.0 else (1.0 - rate) * p + rate * p_le + s = out.sum() + return out / s if s > 0 else out + + +def recombine_teachers(teachers: list[np.ndarray], L: int, rate: float) -> np.ndarray: + """Merge ``K_T`` teacher genotype distributions (the multi-teacher / Fisher–Muller operator). + + ``rate=0`` = clonal mean-mixture (``mean(teachers)`` — keeps genotypes intact, cannot create a + genotype no teacher had). ``rate=1`` = sexual merge: the linkage-equilibrium product of the + *pooled* per-locus marginals, which assembles the best allele of each locus across teachers into + genotypes none of them held — the Fisher–Muller effect and "merge, don't average" at the genotype + level. + + Args: + teachers (list[np.ndarray]): ``K_T`` genotype distributions (each length ``2^L``). + L (int): Number of loci. + rate (float): Recombination rate in ``[0, 1]``. + + Returns: + np.ndarray: The merged genotype distribution (sums to 1). + """ + stack = np.asarray(teachers, dtype=float) + mean_mix = stack.mean(axis=0) + if rate <= 0.0: + return mean_mix + pooled_marginals = locus_marginals(mean_mix, L) # pooled per-locus correct-allele freq + p_le = linkage_equilibrium(pooled_marginals) + out = p_le if rate >= 1.0 else (1.0 - rate) * mean_mix + rate * p_le + s = out.sum() + return out / s if s > 0 else out + + +def mutate(p: np.ndarray, L: int, mu: float) -> np.ndarray: + """Apply per-locus symmetric mutation at rate ``mu`` to a genotype distribution. + + Each locus independently flips with probability ``mu``. At the distribution level this convolves + ``p`` with the per-locus flip kernel; implemented as ``L`` independent locus mixings. ``mu=0`` is + a no-op. Provides the mutational pressure that Muller's ratchet grinds against. + + Args: + p (np.ndarray): Genotype distribution (length ``2^L``). + L (int): Number of loci. + mu (float): Per-locus flip probability in ``[0, 0.5]``. + + Returns: + np.ndarray: The mutated distribution (sums to 1). + """ + p = np.asarray(p, dtype=float) + if mu <= 0.0: + return p + q = p.reshape([2] * L) if L > 0 else p + for axis in range(L): + flipped = np.flip(q, axis=axis) + q = (1.0 - mu) * q + mu * flipped + out = q.reshape(-1) + s = out.sum() + return out / s if s > 0 else out + + +def locus_metrics(p: np.ndarray, L: int, fitness: np.ndarray, alive_eps: float = 1e-9) -> dict: + """Genotype-aware metrics for one generation (the multi-locus analogue of the K-mode row). + + Args: + p (np.ndarray): Genotype distribution (length ``2^L``). + L (int): Number of loci. + fitness (np.ndarray): Length-``2^L`` fitness (typically :func:`additive_fitness`). + alive_eps (float): A genotype/allele is "present" if its probability exceeds this. + + Returns: + dict: ``mean_fitness``, ``best_fitness`` (max fitness of any present genotype), + ``opt_freq`` (mass on the all-correct optimum), ``min_load`` (fewest wrong loci among present + genotypes = the Muller-ratchet state), ``mean_locus_correct`` (mean per-locus correct-allele + freq), ``locus_H`` (mean per-locus heterozygosity), and ``ld`` (mean pairwise linkage + disequilibrium |D|). + """ + p = np.asarray(p, dtype=float) + present = p > alive_eps + q = locus_marginals(p, L) # per-locus correct freq + bits = genotype_bits(L) + row = { + "mean_fitness": float(fitness @ p), + "best_fitness": float(fitness[present].max()) if present.any() else 0.0, + "opt_freq": float(p[-1]), # genotype 2^L-1 = all-ones optimum + "min_load": int(L - fitness[present].max()) if present.any() else L, + "mean_locus_correct": float(q.mean()), + "locus_H": float(np.mean([heterozygosity(np.array([1 - qi, qi])) for qi in q])), + } + # Mean pairwise linkage disequilibrium |D_ij| = |P(1_i,1_j) - q_i q_j| over locus pairs. + if L >= 2: + ds = [] + for i in range(L): + for j in range(i + 1, L): + p_ij = float(p[(bits[:, i] == 1) & (bits[:, j] == 1)].sum()) + ds.append(abs(p_ij - q[i] * q[j])) + row["ld"] = float(np.mean(ds)) + else: + row["ld"] = 0.0 + return row diff --git a/src/knowledge/genotype_lineage.py b/src/knowledge/genotype_lineage.py new file mode 100644 index 0000000..3d4d410 --- /dev/null +++ b/src/knowledge/genotype_lineage.py @@ -0,0 +1,82 @@ +"""Single-population genotype evolution — the advantage of sex (E7). + +A population (distribution over the ``2^L`` genotypes) adapts toward a multi-locus optimum under +the composed generational step: **selection** (fitness-proportional, favouring correct alleles) + +**drift** (finite resample of ``n``) + **mutation** (per-locus flips) + **recombination** (asexual +``rate=0`` vs sexual ``rate>0``). Recombination reassorts beneficial alleles that arise in different +sub-lineages into one genotype; without it (asexual) those alleles suffer *clonal interference* and +adaptation is slower. So a sexual lineage climbs toward the optimum faster than an asexual one — the +classical advantage of sex, and the dynamic counterpart of E8's one-shot multi-parent assembly. + +Reuses ``step.apply_selection`` (fitness = number of correct loci) and the ``genotype`` operators; +emits the same tidy per-generation DataFrame contract as ``run_lineage`` (with genotype-aware +columns from ``genotype.locus_metrics``). +""" + +from __future__ import annotations + +from typing import Any, Mapping + +import numpy as np +import pandas as pd + +from .genotype import additive_fitness, locus_metrics, mutate, recombine +from .step import apply_selection + + +def run_genotype_lineage(cfg: Mapping[str, Any], seed: int) -> pd.DataFrame: + """Run one genotype lineage and return per-generation genotype metrics. + + Args: + cfg (Mapping): Config with a ``genotype`` block (``L``; drift ``n``; mutation ``mu``; + selection ``base`` for multiplicative fitness ``base^#correct``; recombination + ``recomb_rate``; ``init`` in {``wrong``, ``uniform``, ``optimum``}) and + ``generations``. + seed (int): Replicate seed; the run is a pure function of (cfg, seed). + + Returns: + pd.DataFrame: One row per generation 0..T with ``generation`` plus the + ``genotype.locus_metrics`` columns (``mean_fitness``, ``best_fitness``, ``opt_freq``, + ``min_load``, ``mean_locus_correct``, ``locus_H``, ``ld``). + """ + g = cfg["genotype"] + L = int(g["L"]) + n = int(g["n"]) + mu = float(g.get("mu", 0.0)) + base = float(g.get("base", 1.0)) + rate = float(g.get("recomb_rate", 0.0)) + generations = int(cfg.get("generations", 100)) + K = 1 << L + + report_fitness = additive_fitness(L) # # correct loci (0..L), for metrics + sel_fitness = base ** report_fitness # multiplicative selection weight + + init = g.get("init", "wrong") + p = np.zeros(K) + if init == "wrong": + p[0] = 1.0 # all-wrong genotype (load L); adapt upward + elif init == "optimum": + p[-1] = 1.0 # all-correct (for degradation studies) + elif init == "uniform": + p[:] = 1.0 / K + else: + raise ValueError(f"unknown genotype init {init!r} (expected wrong|optimum|uniform)") + + rng = np.random.default_rng(seed) + rows: list[dict] = [] + + def record(t: int) -> None: + row = {"generation": t} + row.update(locus_metrics(p, L, report_fitness, alive_eps=1.0 / n)) + rows.append(row) + + record(0) + for t in range(1, generations + 1): + p = apply_selection(p, sel_fitness, "greedy", 0.0) # fitness-proportional selection + counts = rng.multinomial(n, p) # drift + p = counts / counts.sum() + p = mutate(p, L, mu) # per-locus mutation + p = recombine(p, L, rate) # asexual (0) vs sexual (>0) + record(t) + + return pd.DataFrame(rows) diff --git a/src/knowledge/society.py b/src/knowledge/society.py new file mode 100644 index 0000000..aa90176 --- /dev/null +++ b/src/knowledge/society.py @@ -0,0 +1,95 @@ +"""Multi-parent recombination — the Fisher–Muller vertical claim (E8). + +The society's headline: **an offspring recombined from many decorrelated parents can be fitter +than any parent** — capability that *exceeds* every component, not just recovers a ceiling. This +is the Fisher–Muller effect, and unlike biological sex it has **no two-parent limit**: an offspring +here can have arbitrarily many parents (``recombine_teachers`` pools per-locus marginals over all of +them). + +Each parent is a *specialist*: confident-correct on the loci it has mastered, agnostic (~0.5) on the +rest — the realistic picture of an expert. Which loci each parent masters comes from the exact +shared-switch construction (``teachers.make_retention_matrix``), so parent count ``K_T`` and +decorrelation ``rho`` are clean, independently-swept knobs (mastery of a *locus* replaces retention +of a *tail item*). Three deployable capabilities are compared, all as the fitness of the *mode* +(most-probable) genotype — what you would actually ship: + +* **best_parent** — the single fittest specialist (no combination). +* **average** — the mean-mixture "model soup" (combine, but don't recombine loci). +* **sexual** — the union-preserving recombination (assemble the best allele of each locus). + +Sexual climbs to the optimum as parents accumulate and decorrelate; the other two plateau. +""" + +from __future__ import annotations + +import itertools + +import numpy as np +import pandas as pd + +from .genotype import additive_fitness, linkage_equilibrium, recombine_teachers +from .seeding import spawn_seeds +from .teachers import make_retention_matrix + + +def make_specialist(mastery: np.ndarray, hi: float, lo: float) -> np.ndarray: + """Build a specialist's genotype distribution from its per-locus mastery mask. + + Args: + mastery (np.ndarray): Length-``L`` bool; True where this parent is expert. + hi (float): Correct-allele probability on mastered loci (confident). + lo (float): Correct-allele probability on unmastered loci (agnostic, ~0.5). + + Returns: + np.ndarray: Length-``2^L`` genotype distribution (product / linkage-equilibrium form). + """ + q = np.where(np.asarray(mastery, dtype=bool), hi, lo) + return linkage_equilibrium(q) + + +def _mode_fitness(p: np.ndarray, fitness: np.ndarray) -> float: + """Fitness of the most-probable (deployed consensus) genotype.""" + return float(fitness[int(np.argmax(p))]) + + +def run_society(cfg: dict) -> pd.DataFrame: + """Sweep parent count x decorrelation; compare best-parent vs average vs sexual capability. + + Args: + cfg (dict): Parsed experiment config with a ``society`` block (``L``, ``q`` mastery + fraction, ``hi``, ``lo``), a ``sweep`` (``K_T`` x ``rho``), ``seed``, ``n_replicates``. + + Returns: + pd.DataFrame: One row per (K_T, rho, replicate) with ``best_parent``, ``average``, + ``sexual`` (mode-genotype fitness, 0..L) and ``L``. + """ + soc = cfg["society"] + L = int(soc["L"]) + q = float(soc.get("q", 0.5)) + hi, lo = float(soc.get("hi", 0.9)), float(soc.get("lo", 0.45)) + fitness = additive_fitness(L) + + sweeps = cfg["sweep"] + if isinstance(sweeps, dict): + sweeps = [sweeps] + params = [s["param"] for s in sweeps] + value_lists = [list(s["values"]) for s in sweeps] + seeds = spawn_seeds(int(cfg["seed"]), int(cfg["n_replicates"])) + + rows: list[dict] = [] + for combo in itertools.product(*value_lists): + d = dict(zip(params, combo)) + K_T, rho = int(d["K_T"]), float(d["rho"]) + for rep, ss in enumerate(seeds): + child = int(ss.generate_state(1)[0]) + rng = np.random.default_rng(child) + mastery = make_retention_matrix(L, K_T, rho, q, rng).astype(bool) # (K_T, L) + parents = [make_specialist(mastery[k], hi, lo) for k in range(K_T)] + rows.append({ + "experiment": cfg["experiment"], "K_T": K_T, "rho": rho, "q": q, "L": L, + "replicate": rep, + "best_parent": max(_mode_fitness(p, fitness) for p in parents), + "average": _mode_fitness(recombine_teachers(parents, L, 0.0), fitness), + "sexual": _mode_fitness(recombine_teachers(parents, L, 1.0), fitness), + }) + return pd.DataFrame(rows) diff --git a/tasks/todo.md b/tasks/todo.md index ac81273..75c07af 100644 --- a/tasks/todo.md +++ b/tasks/todo.md @@ -264,8 +264,30 @@ C3 vertical claim deferred.* Lamarckian society + vertical/cumulative C3 claim (not yet run). Reposition: from "collapse is drift" to a population-genetic CONTROL THEORY for sustaining open-ended knowledge. -## Remaining (all optional) +**2026-07-05 — multi-locus society frame (E7/E8): raised the ceiling to enter the society.** +- Prompted by "enter the society with a robust theoretical frame." The single-locus fixed-`p*` model + can't express "exceeding" a ceiling. Generalized knowledge to a distribution over **genotypes** + (`knowledge/genotype.py`: `L` biallelic loci, `K=2^L`, additive fitness, recombination = product of + per-locus marginals). Reuses all K-mode machinery + `make_retention_matrix` (locus mastery). +- **E8 (star, `kind: society`, `knowledge/society.py`) — the vertical claim:** decorrelated parents + recombined; **sexual merge reaches the optimum (12/12, a genotype no parent had)** as parent count + grows / `ρ→0`, while best-parent (~8.7) and mean-mixture soup (~11.6) plateau. `configs/layer1/E8.yaml`, + `plot_E8.py`, README. The Fisher–Muller effect for AI. +- **E7 (`kind: genotype_lineage`, `knowledge/genotype_lineage.py`) — advantage of sex:** sexual lineage + adapts faster than asexual (LD→0 vs LD spike). Honest: a speed advantage, not a permanent ratchet gap. +- **Metaphor shift (GG):** sexual reproduction with **unbounded parents**, not teacher→pupil (which caps + at the ceiling). Collapse = asexual degradation; cure = sex, no parent limit. Unifies E4+E6 under + evolution-of-sex theory; beyond Riis's single-locus n-grams. `tests/test_genotype.py` (+7). + Experiment dispatch (`kind` in {genotype_lineage, society}) + `make layer1` wired. + +## Remaining (all optional / next) + +- [ ] **The dynamic society:** an evolving *population of parents* (specialists) that ground + + recombine + select over generations — capability climbing while specialties are re-earned (the full + C3, dynamic). E7/E8 give the static + single-population pieces; the multi-parent *lineage* is next. +- [ ] **NK/epistasis landscape** (sign epistasis can make recombination harmful — the honest limit of + "sex always helps"); **multi-allelic loci**. Deepens the frame. - [ ] **Learning-kernel refinement:** truth-like smoothing prior (`prior="truth"`) + measurement floor for a quantitative RNN match; **multi-locus / linkage** modes (class×style) as the rigorous home for recombination. Both enrich predictive power and separate us further from Riis's single-locus n-grams. diff --git a/tests/test_genotype.py b/tests/test_genotype.py new file mode 100644 index 0000000..a04dd73 --- /dev/null +++ b/tests/test_genotype.py @@ -0,0 +1,90 @@ +"""Multi-locus / recombination tests (pure NumPy) — the spine of the society frame. + +Cover the genotype algebra (bits, additive fitness, linkage equilibrium), the recombination +operators (identity at rate 0, product-of-marginals at rate 1), and the two headline behaviours: +E8 — sexual recombination of decorrelated parents *exceeds* the best parent; E7 — a sexual lineage +adapts faster than an asexual one. +""" + +from __future__ import annotations + +import numpy as np + +from knowledge.genotype import ( + additive_fitness, genotype_bits, linkage_equilibrium, locus_marginals, mutate, + recombine, recombine_teachers, +) +from knowledge.genotype_lineage import run_genotype_lineage +from knowledge.society import make_specialist, run_society +from knowledge.teachers import make_retention_matrix + + +def test_genotype_bits_and_additive_fitness(): + bits = genotype_bits(3) + assert bits.shape == (8, 3) + assert np.array_equal(bits[0], [0, 0, 0]) and np.array_equal(bits[7], [1, 1, 1]) + f = additive_fitness(3) + assert f[0] == 0 and f[7] == 3 and f[1] == 1 # MSB-first: g=1 -> [0,0,1] + + +def test_linkage_equilibrium_is_product_and_normalised(): + q = np.array([0.9, 0.5, 0.2]) + p = linkage_equilibrium(q) + assert np.isclose(p.sum(), 1.0) + # P(all-correct) = ∏ q; P(all-wrong) = ∏ (1-q) + assert np.isclose(p[-1], np.prod(q)) and np.isclose(p[0], np.prod(1 - q)) + assert np.allclose(locus_marginals(p, 3), q) # marginals round-trip + + +def test_recombine_identity_and_free(): + rng = np.random.default_rng(0) + p = rng.dirichlet(np.ones(16)) # L=4 + assert np.array_equal(recombine(p, 4, 0.0), p) # rate 0 = asexual (unchanged) + free = recombine(p, 4, 1.0) # rate 1 = product of marginals + assert np.allclose(free, linkage_equilibrium(locus_marginals(p, 4))) + assert np.isclose(free.sum(), 1.0) + + +def test_mutate_normalises_and_spreads(): + L = 4 + p = np.zeros(1 << L); p[0] = 1.0 # point mass on all-wrong + out = mutate(p, L, 0.1) + assert np.isclose(out.sum(), 1.0) + assert out[0] < 1.0 and (out > 0).sum() > 1 # mass leaks to neighbours + + +def test_recombine_teachers_assembles_optimum_only_sexually(): + # Two complementary parents: one masters the low loci, the other the high loci. Sexual merge + # assembles the all-correct optimum (a genotype NEITHER parent has as its mode); clonal cannot. + L = 8 + lo = np.array([1, 1, 1, 1, 0, 0, 0, 0], dtype=bool) + parents = [make_specialist(lo, 0.9, 0.45), make_specialist(~lo, 0.9, 0.45)] + f = additive_fitness(L) + best_parent = max(f[int(np.argmax(p))] for p in parents) + sexual = f[int(np.argmax(recombine_teachers(parents, L, 1.0)))] + clonal = f[int(np.argmax(recombine_teachers(parents, L, 0.0)))] + assert sexual == L # sexual assembles the optimum + assert sexual > best_parent # ... which exceeds either parent + assert clonal <= best_parent + 0 # clonal (soup) does not assemble it + + +def test_e8_sexual_exceeds_best_parent_and_soup(): + cfg = {"experiment": "e8t", "seed": 1, "n_replicates": 8, + "society": {"L": 10, "q": 0.5, "hi": 0.9, "lo": 0.45}, + "sweep": [{"param": "K_T", "values": [8]}, {"param": "rho", "values": [0.0]}]} + df = run_society(cfg) + m = df.mean(numeric_only=True) + assert m["sexual"] > m["best_parent"] + 1.5 # clearly exceeds the best parent + assert m["sexual"] >= m["average"] # and is at least as good as the soup + + +def test_e7_sexual_adapts_at_least_as_fast(): + base = {"genotype": {"L": 10, "n": 150, "mu": 0.02, "base": 1.3, "init": "wrong"}, + "generations": 25} + asex = run_genotype_lineage({**base, "genotype": {**base["genotype"], "recomb_rate": 0.0}}, 0) + sex = run_genotype_lineage({**base, "genotype": {**base["genotype"], "recomb_rate": 1.0}}, 0) + mid = 12 + a = asex[asex["generation"] == mid]["mean_fitness"].iloc[0] + s = sex[sex["generation"] == mid]["mean_fitness"].iloc[0] + assert s >= a - 1e-9 # sexual adapts at least as fast mid-run + assert sex["ld"].max() < asex["ld"].max() # ... by keeping loci in linkage equilibrium