Experiments

Experiment 3: Internal Representation Structure

Question: When do patterns develop low-dimensional, compositional representations?

Seed	$d_{\text{eff}}$ (early to late)	$\mathcal{A}$	$\mathcal{D}$	$K_{\text{comp}}$
123	6.6 to 5.6	0.90 to 0.92	0.27 to 0.38	0.20 to 0.12
42	7.3 to 7.5	0.89 to 0.89	0.23 to 0.23	0.23 to 0.25
7	7.7 to 8.8	0.89 to 0.87	0.24 to 0.22	0.20 to 0.27

Finding: Compression is cheap — $d_{\text{eff}} \approx 7$ /68 from cycle 0. But quality only improves under bottleneck selection. Note the asymmetry: abstraction ( $\mathcal{A} \approx 0.89$ ) is high and stable from the start — the system compresses efficiently without effort. But disentanglement ( $\mathcal{D} \approx 0.25$ ) remains low — the compressed representations are tangled, not cleanly factored. Disentanglement requires active information-seeking that this substrate lacks.

Experiment 3 representation structure summary — **Experiment 3: Representation structure summary.** (a) Effective dimensionality: 5.6–8.8 out of 68 possible — strong compression from cycle 0. Seed 123 compresses further over evolution. (b) Abstraction (A ≈ 0.89) is high and stable; disentanglement (D ≈ 0.25) remains low. The gap confirms the theory: compression is cheap but clean factoring requires agency. (c) Compositionality error — lowest for seed 123 at bottleneck, consistent with the bottleneck amplification pattern from Exp 2.

Eigenspectrum of internal state: early vs late evolution — **Internal state eigenspectrum, early vs late.** Log-scale variance fraction by PCA dimension. Seeds 123 and 42 show the late eigenspectrum becoming more concentrated in the top components — genuine compression under evolutionary pressure. Seed 7 stays relatively flat, consistent with its lack of world-model development.

Source code

v13_representation.py — Representation analysis
v13_representation_run.py — Runner