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