Experiments

Experiment 2: Emergent World Model

Experiment 2: Emergent World Model

Question: When does a pattern's internal state carry predictive information about the environment beyond current observations?

Method: Prediction gap W(τ)=MSE[fenv]−MSE[ffull]\mathcal{W}(\tau) = \text{MSE}[f_{\text{env}}] - \text{MSE}[f_{\text{full}}] using Ridge regression with 5-fold CV.

SeedCwm\mathcal{C}_{\text{wm}} (early)Cwm\mathcal{C}_{\text{wm}} (late)HwmH_{\text{wm}} (late)% with WM
1230.00040.028220.0100%
420.00020.00025.340%
70.00100.00027.960%

Finding: World model signal present but weak. Seed 123 at bottleneck shows 100x amplification. World models are amplified by bottleneck selection, not gradual evolution. To be clear about magnitude: Cwm≈0.0002\mathcal{C}_{\text{wm}} \approx 0.0002 for most seeds means the internal state predicts the environment barely better than the environment alone. Only seed 123 at maximum bottleneck pressure reaches 0.028 — detectable but still small. These patterns are not building substantial world models; they carry a faint trace of environmental predictive information, amplified briefly under extreme selection.

Experiment 2 world model summary
Experiment 2: World model summary. (a) World model capacity over evolution — note the y-axis scale (0.000–0.030). Seed 123 shows a dramatic late spike; seeds 42 and 7 remain near zero throughout. (b) World model horizon in recording steps. (c) Prediction gap at late evolution — seed 123 maintains a flat, elevated prediction gap across all horizons, consistent with a genuine (if weak) internal model.
World model capacity vs pattern longevity
World model vs pattern longevity (r = 0.084). Near-zero correlation: having a world model does not help a pattern survive longer. Most points cluster at C_wm ≈ 0 regardless of lifetime. The few high-C_wm outliers are long-lived patterns at cycle 29 — the world model emerges as a byproduct of bottleneck survival, not as a survival advantage.

Source code