MachineSex/results/figS12_quality_diversity

E5 — Quality-diversity selection preserves diversity where greedy selection destroys it

Claim tested: if each generation you select which outputs to keep, does chasing the "best" outputs (greedy) accelerate collapse — and does rewarding novelty instead prevent it?

Setup (Layer 1, pure math). K = 500 items, Zipf truth, n = 200, 400 generations, 100 repeats, all arms given the same grounding. Three selection modes: none (grounding only, no selection), greedy (keep the fittest — highest-p* — items), and quality-diversity (QD) (a novelty bonus w_i ∝ f_i · p_i^{-α} that up-weights rare items). The novelty exponent α is swept over {0.5, 1, 2}.

Symbols

• greedy — select toward the fittest/most-probable items (directional pressure).
• QD (quality-diversity) — select for fitness and novelty; α = strength of the novelty bonus.
• H diversity; support = number of distinct items surviving.

The three panels

1. Diversity trajectories. H over generations: red = greedy (crashes toward ~0, i.e. fixation on a few items); orange/blue = QD at α = 1, 2 (holds a high plateau); green = none (reference). Greedy selection is a second collapse engine on top of drift.
2. Novelty dose–response. Stationary H vs the novelty exponent α for QD (orange dots), with greedy (red dashed) and none (green dashed) as reference lines. QD sits above greedy for every α, and rises as the novelty bonus strengthens.
3. Surviving items per arm. Stationary support (number of distinct items alive) as bars: greedy is lowest; QD arms keep progressively more items alive as α grows; none is the reference.

Takeaway

Optimising only for "what looks best" (greedy) collapses the population onto a handful of winners; a novelty-rewarding, quality-diversity objective actively re-introduces and holds the tail. Key numbers: greedy H ≈ 0.01 (near-total fixation) vs QD H ≈ 0.48–0.88 rising with α. Falsifier (not triggered): if QD's stationary H had been ≤ greedy's, quality-diversity would be doing no work.