Giorgio Gilestro
84124de143
Clarity pass over the main text (36-item audit), Discussion rewrite and cut, acknowledgements, Souly et al. as ref 62, lettered SI panels, model section moved under Results; plus the untracked curriculum/society/compose/smol configs, runners, figures, stats and tests that the SI already cites. Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01Y64o8FKP7rCuXzC48pxpMm |
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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.