The culmination. A finite population of agents (genotypes, L loci) evolves
on a rugged NK landscape that IS reality (knowledge/dynamic_society.py),
composing the four operators the whole study built toward: grounding,
directed recombination (sex), quality-diversity selection, and mutation.
Grounding is made load-bearing via the consensus-conformity (self-
consumption) mechanism (GG decision): selection acts on
g*true_fitness + (1-g)*conformity, where conformity = agreement with the
population's own consensus, so at g=0 the society optimises fitting-the-
crowd rather than reality.
4-arm ablation (12 reps), each breaking distinctly, only the full society
climbing (global_opt ~ 0.79):
- full 0.78 climbs to the optimum, diversity maintained longest
- no_sex 0.77 can't recombine to escape local optima
- no_diversity 0.74 greedy: collapses diversity fastest, worse local optimum
- no_grounding 0.48 self-consumption collapse to an unfit consensus
(trains on the crowd -> confident-but-wrong mean;
conformity-true gap ~ 0.5)
This integrates E1-E6 + the learning kernel + E7-E10 into one system and
shows the Lamarckian society needs ALL of grounding + directed sex +
diversity: on a rugged landscape you need diversity to explore basins, sex
to recombine them, and grounding to select on reality -- remove any one and
you fail differently. Closes the C3 vertical claim analytically; the LLM
rung remains the eventual empirical instantiation.
New: knowledge/dynamic_society.py, configs/layer1/E11.yaml, figures/
plot_E11.py, README, tests/test_dynamic_society.py (+5). kind:
dynamic_society dispatch; make layer1 wired. 122 tests green.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
143 lines
6.3 KiB
Python
143 lines
6.3 KiB
Python
"""The dynamic Lamarckian society — the vertical claim (E11 / C3).
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A finite population of ``N`` agents (genotypes of ``L`` biallelic loci) evolves on a Kauffman NK
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landscape that *is* reality. The society climbs in real capability by composing the four operators the
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whole study built toward — **grounding**, **directed recombination (sex)**, **quality-diversity
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selection**, and mutation — and an ablation shows each is load-bearing.
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The crux is what happens WITHOUT grounding. A plain genetic algorithm on true fitness would just
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improve, so grounding must corrupt the *selection signal* to cause collapse. Here selection acts on a
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**grounded score** ``g·true_fitness + (1−g)·conformity``, where conformity is agreement with the
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population's own consensus (modal genotype). At ``g=0`` selection rewards fitting the crowd rather
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than reality — self-consumption — and the society drifts to a fit-looking but actually-poor consensus,
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losing diversity: the direct analogue of training on the majority of AI-generated outputs.
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Four ablation arms, each breaking distinctly (only ``full`` avoids all three failures):
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``full`` (climbs) · ``no_grounding`` (conformity collapse) · ``no_sex`` (stuck at local optima) ·
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``no_diversity`` (collapses to one lineage, recombination starves).
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"""
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from __future__ import annotations
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from typing import Any, Mapping
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import numpy as np
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import pandas as pd
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from .genotype import bits_to_index, crossover, genotype_bits, nk_fitness
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def _consensus(pop_bits: np.ndarray) -> np.ndarray:
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"""Population consensus genotype: the modal allele at each locus (majority vote)."""
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return (pop_bits.mean(axis=0) >= 0.5).astype(pop_bits.dtype)
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def _conformity(pop_bits: np.ndarray, consensus: np.ndarray) -> np.ndarray:
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"""Per-agent agreement with the consensus (fraction of loci matching the majority)."""
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return (pop_bits == consensus[None, :]).mean(axis=1)
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def _novelty(pop_bits: np.ndarray) -> np.ndarray:
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"""Per-agent novelty: mean Hamming distance to the rest of the population (diversity signal)."""
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N, L = pop_bits.shape
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if N < 2:
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return np.zeros(N)
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# pairwise Hamming via allele agreement: distance_ij = L - matches; mean over j != i.
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match = (pop_bits[:, None, :] == pop_bits[None, :, :]).sum(axis=2) # (N, N) matches
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ham = L - match
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return (ham.sum(axis=1) / (N - 1)) / L # normalised to [0,1]
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def _directed_offspring(pop_bits, fitness, n_off, rate, rng):
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"""Directed sex: make ``n_off`` recombinants from the whole population, return them ranked-ready.
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Unbounded-parent crossover (the AI move); offspring selection happens in the survival step, so
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here we just generate the candidate offspring bit-matrix.
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"""
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return np.stack([crossover(pop_bits, rate, rng) for _ in range(n_off)])
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def run_dynamic_society(cfg: Mapping[str, Any], seed: int) -> pd.DataFrame:
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"""Run one dynamic-society lineage; return per-generation metrics.
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Args:
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cfg (Mapping): Config with a ``society`` block (``L``, ``K`` landscape ruggedness, ``N``
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population, ``g`` grounding, ``mu`` mutation, ``novelty`` QD weight, ``n_off`` offspring
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pool, ``recomb_rate``, ``sex`` on/off, ``select`` in {``qd``, ``greedy``}) and
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``generations``.
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seed (int): Replicate seed; the landscape and the run are a pure function of it.
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Returns:
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pd.DataFrame: One row per generation with ``best_fitness`` (real), ``mean_fitness`` (real),
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``diversity`` (mean normalised pairwise Hamming), ``consensus_fitness``,
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``conformity_true_gap`` (mean conformity − mean true fitness; exposes the no-grounding
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collapse), and ``global_opt``.
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"""
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soc = cfg["society"]
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L, K, N = int(soc["L"]), int(soc["K"]), int(soc["N"])
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g = float(soc.get("g", 1.0))
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mu = float(soc.get("mu", 0.02))
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novelty_w = float(soc.get("novelty", 0.0))
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n_off = int(soc.get("n_off", N))
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rate = float(soc.get("recomb_rate", 0.2))
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sex = bool(soc.get("sex", True))
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select = soc.get("select", "qd")
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generations = int(cfg.get("generations", 100))
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fitness = nk_fitness(L, K, seed) # reality
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global_opt = float(fitness.max())
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all_bits = genotype_bits(L)
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rng = np.random.default_rng(seed)
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# Initialise a diverse population of random genotypes.
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pop = rng.integers(0, 2, size=(N, L)).astype(all_bits.dtype)
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def true_fit(bits):
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return np.array([fitness[bits_to_index(b)] for b in bits])
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rows: list[dict] = []
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def record(t: int) -> None:
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tf = true_fit(pop)
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cons = _consensus(pop)
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conf = _conformity(pop, cons)
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rows.append({
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"generation": t,
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"best_fitness": float(tf.max()),
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"mean_fitness": float(tf.mean()),
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"diversity": float(_novelty(pop).mean()),
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"consensus_fitness": float(fitness[bits_to_index(cons)]),
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"conformity_true_gap": float(conf.mean() - tf.mean()),
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"global_opt": global_opt,
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})
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record(0)
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for t in range(1, generations + 1):
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# (1) candidate pool = current population + directed offspring (sex) or mutated clones.
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if sex:
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offspring = _directed_offspring(pop, fitness, n_off, rate, rng)
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else: # asexual: offspring are mutated copies
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idx = rng.integers(0, N, size=n_off)
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offspring = pop[idx].copy()
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# mutation on the offspring
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flip = rng.random(offspring.shape) < mu
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offspring = np.where(flip, 1 - offspring, offspring).astype(pop.dtype)
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pool = np.concatenate([pop, offspring], axis=0)
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# (2) grounded score: g*true_fitness + (1-g)*conformity (conformity vs the *current* consensus).
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cons = _consensus(pop)
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tf = true_fit(pool)
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conf = _conformity(pool, cons)
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score = g * tf + (1.0 - g) * conf
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# (3) survival: QD (score + novelty) keeps diverse high-scorers; greedy keeps top score only.
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if select == "qd" and novelty_w > 0.0:
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nov = _novelty(pool)
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merit = score + novelty_w * nov
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else:
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merit = score
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keep = np.argsort(merit)[-N:] # elitist truncation survival
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pop = pool[keep]
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record(t)
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return pd.DataFrame(rows)
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