Giorgio Gilestro
48181a1c84
Deepen the sexual-reproduction frame before entering the full society, on
the two facets GG chose: landscape robustness and directed recombination.
Adds a Kauffman NK landscape (genotype.nk_fitness, tunable ruggedness),
finite n-parent crossover (genotype.crossover, per-gap recombination rate),
and hill-climb (parents = local optima = trained models).
E9 (recomb_landscape) -- the "why sex?" test: E8's dramatic super-parent
result used an ADDITIVE landscape. On rugged/epistatic landscapes, blindly
recombining local optima causes OUTBREEDING DEPRESSION -- offspring fall
below the parents, worse with both ruggedness and recombination rate (K=8,
free recomb: ~ -0.23), and the optimal recombination rate shrinks as
ruggedness grows. Design rule: merge freely when skills are complementary/
additive; sparingly (and with selection) when entangled.
E10 (directed_sex) -- directed sex beats biological sex: biology is stuck
with 2 random-mating parents and no offspring preview; an AI can choose
complementary mates, evaluate many recombinant offspring, keep the fittest,
and use unbounded parents (iterated recombine-then-select). Random
("biological") sex craters with ruggedness (0.66->0.51); directed sex
tracks/exceeds the best parent at every ruggedness -- converting the
outbreeding-depression catastrophe into a win. No biological analog.
Complete sexual-transmission picture: dramatic super-parent offspring when
skills are complementary (E8); outbreeding-depression risk when entangled
(E9); directed sex resolves the risk (E10). configs/layer1/{E9,E10}.yaml,
figures/plot_{E9,E10}.py, READMEs, +5 tests (117 green).
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
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| E9.pdf | ||
| E9.png | ||
| manifest.json | ||
| README.md | ||
| resolved_config.yaml | ||
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.