Giorgio Gilestro
62c68d6c8c
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 <noreply@anthropic.com>
35 lines
2.8 KiB
Markdown
35 lines
2.8 KiB
Markdown
# E8 — the vertical claim: n-parent recombination exceeds any parent (Fisher–Muller)
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**Claim tested.** The society's headline, and the thing no fixed-`p*` model could express: can an
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offspring recombined from **many decorrelated parents** be *fitter than any parent* — capability that
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**exceeds** every component, not merely recovers a ceiling?
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**Setup.** A capability is a **genotype** of `L=12` biallelic loci; fitness = number of correct
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loci; the optimum (all-correct, fitness 12) is a genotype **no parent possesses**. Each *parent* is a
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specialist: confident-correct (`hi=0.9`) on the loci it has mastered, agnostic (`lo=0.45`) on the
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rest. Which loci each masters comes from the exact shared-switch construction, so **parent count
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`K_T`** and **decorrelation `ρ`** are clean, independently-swept knobs. Deployed capability = fitness
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of the **mode** (most-probable) genotype — what you would ship. 40 replicates.
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### Symbols
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- **parent** = a specialist model; **offspring** = the recombined model; **`K_T`** = number of parents (unbounded — biological sex is stuck at 2; model merging is not).
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- **`ρ`** = correlation of which loci parents master (0 = complementary, 1 = identical clones).
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- **best parent** = fittest single specialist · **average** = mean-mixture "model soup" (combine, don't recombine) · **sexual** = union-preserving recombination (assemble the best allele of each locus).
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### The two panels
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1. **Recombination exceeds any parent (ρ=0).** Deployed capability vs `K_T`: **sexual (red) climbs
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to the optimum (12)** as parents accumulate — a genotype none of them had — while the **best single
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parent (grey) plateaus at ~8.7** and the **model soup (blue) reaches ~11.6** but is beaten by
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sexual at every `K_T` (and badly at small `K_T`: at 2 parents, sexual 9.0 vs soup 7.2 vs best 6.9).
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2. **Decorrelation is the fuel.** Sexual capability vs `K_T` for `ρ ∈ {0, 0.5, 1}`: decorrelated
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parents (`ρ=0`) climb to the optimum; identical clones (`ρ=1`) buy nothing (flat at ~6). The
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benefit is *combinatorial reach across complementary parents*, not merely "more models".
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### Takeaway
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This is the Fisher–Muller effect for AI: recombination assembles beneficial variants that live in
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*different* parents into an offspring fitter than any of them. It is the rigorous, un-preempted core
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of the Lamarckian society — collapse is asexual degradation; the cure is **sex, with no parent
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limit.** It reframes model merging from "averaging weights" to "meiotic reassortment", and it is the
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mechanism by which general capability can *climb while each specialty is re-earned and exceeded.* The
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dynamic version (why a lone lineage cannot do this) is E7. **Falsifier (not triggered):** if sexual
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never exceeded the best parent, or averaging matched it, the vertical claim would fail.
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