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