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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E9 — landscape robustness: when recombination helps, and the outbreeding-depression risk
Claim tested. E8 showed sexual recombination assembling super-parent offspring — but on an additive landscape, where recombination trivially helps. The honest, credibility-critical question (the classic "why sex?" problem): does the benefit survive epistasis, or does merging entangled models break them?
Setup. Parents are local optima ("trained models") of a Kauffman NK landscape (L=12),
whose ruggedness K (epistatic interactions per locus) is swept together with the recombination
rate. K=0 is additive/smooth; larger K is rugged (co-adapted allele blocks, many local optima).
Fitness ∈ [0,1]. 24 replicate landscapes; 200 offspring per point.
Symbols
- NK landscape — tunable-ruggedness fitness landscape;
K= epistasis (0 = additive, high = rugged). - recombination rate — per-gap crossover probability (0 = clonal / copy a parent; 0.5 = free recombination, loci independent).
- outbreeding depression — offspring less fit than parents because recombination broke co-adapted allele blocks.
The two panels
- The risk. Mean offspring fitness minus best parent, vs recombination rate, one curve per
ruggedness
K. On the additive landscape (K=0) it's flat at 0; asKgrows the curves plunge negative, and deeper the higher the recombination rate — outbreeding depression, worse the more entangled the skills and the more you mix (K=8, free recombination: ≈ −0.23). - With selection, an optimal rate re-emerges. Best-of-brood fitness (offspring selection) vs
rate per
K, with parents dotted. On rugged landscapes a nonzero intermediate recombination rate is best — enough mixing to find new combinations, not so much that it shatters good blocks.
Takeaway
Recombination is not a free lunch. Merge freely when skills are complementary/additive; merge sparingly — and always select offspring — when they are entangled. This is the celebrated population-genetics result (recombination load / outbreeding depression) reproduced for AI model merging, and it turns the sexual metaphor from a lucky demo into a law with a design rule. The rescue — directed sex with offspring selection — is E10. Falsifier (not triggered): if recombination rate had no effect, or free recombination never underperformed the parents on rugged landscapes, the epistasis caveat would be moot.