Preliminary Results: Where the Ladder Stalls
Preliminary Results: Where the Ladder Stalls
We have begun running a simplified version of this experiment using Lenia (continuous CA, toroidal grid) with resource dynamics, measuring via partition prediction loss, via mass change, via state change rate, and via trajectory PCA. The results so far are instructive—not because they confirm the predictions above, but because of where they fail.
The central lesson: the ladder requires heritable variation. Emergent CA patterns achieve rungs 1–3 of the ladder (microdynamics attractors boundaries) from physics alone. The transition to rung 4 (functional integration) requires evolutionary selection acting on heritable variation in the trait that determines integration response.
Substrate: Lenia with resource depletion/regeneration (Michaelis-Menten growth modulation). Perturbation: Drought (resource regeneration ). Measure: under drought.
Conditions:
- No evolution (V11.0). Naive patterns under drought: decreases by . Same decomposition dynamics as LLMs.
- Homogeneous evolution (V11.1). In-situ selection for -robustness (fitness ). Still decomposes (). All patterns share identical growth function—selection prunes but cannot innovate.
- Heterogeneous chemistry (V11.2). Per-cell growth parameters ( fields) creating spatially diverse viability manifolds. After 40 cycles of evolution on GPU: vs naive . A +2.1pp shift toward the biological pattern. Evolved patterns also show better recovery— returns above baseline after drought, while naive patterns do not fully recover.
- Multi-channel coupling (V11.3). Three coupled channels—Structure (), Metabolism (), Signaling ()—with cross-channel coupling matrix and sigmoid gate. Introduces a new measurement: channel-partition (remove one channel, measure growth impact on remaining channels). Local test: channel , spatial —channels couple weakly at 3 degrees of freedom.
- High-dimensional channels (V11.4). continuous channels with fully vectorized physics. Spectral via coupling-weighted covariance effective rank. 30-cycle GPU result: evolved vs naive under severe drought—evolution had negligible effect. Both decompose mildly, suggesting that 64 symmetric channels provide enough internal buffering to resist drought regardless of evolutionary tuning. Mean robustness across all 30 cycles. The Yerkes-Dodson pattern persists: mild stress increases by –.
- Hierarchical coupling (V11.5). Same physics as V11.4, but with asymmetric coupling (feedforward/feedback pathways between four tiers: Sensory Processing Memory Prediction). 30-cycle GPU result: evolved patterns have higher baseline ( vs naive) and higher self-model salience ( vs ), but under severe drought they decompose more () while naive patterns integrate (). Evolution overfits to the mild training stress, creating fragile high- configurations. Key lesson: the hierarchy must live in the coupling structure, not in the physics; imposing different timescales per tier caused extinction. Functional specialization should emerge from selection.
- Metabolic maintenance cost (V11.6). Addresses the autopoietic gap directly: patterns pay a constant metabolic drain proportional to mass ( each step). 30-cycle GPU result (): evolved-metabolic vs naive under severe drought. Evolution again produced higher--but-more-fragile patterns. Critically, the maintenance rate () was not lethal enough—naive patterns retained population through drought. The autopoietic gap remains open: a small metabolic drain on top of local physics does not produce active self-maintenance, because patterns have no mechanism for non-local resource detection. They cannot “forage” when they cannot “see” beyond kernel radius .
- Curriculum evolution (V11.7). Fixes V11.5’s stress overfitting by graduating stress intensity across cycles (resource regeneration ramped from to baseline over 30 cycles) with random noise and variable drought duration (500–1900 steps per cycle). The critical test: evolved patterns evaluated on novel stress patterns never seen during training. 30-cycle GPU result (): robustness . Curriculum-evolved patterns outperform naive on all four novel stressors: mild , moderate , severe , extreme . Under mild novel stress, evolved patterns actually integrate () while naive decompose (). The overfitting problem is substantially reduced—not eliminated, but the shift is consistently positive across the full severity range.
Unexpected: (1) Mild stress consistently increases by 60–190\% (Yerkes-Dodson–like inverted-U). Only severe stress causes decomposition. (2) In V11.5, evolution increased vulnerability to severe stress despite improving baseline —a stress overfitting effect. (3) V11.7’s curriculum training substantially reduces this overfitting: graduated, noisy stress exposure produces patterns that generalize to novel stressors. The shift from naive is positive across all four novel severity levels tested ( to percentage points). (4) V11.6’s metabolic cost was intended to create lethal drought, but at the drought was not lethal—naive patterns retained population. Evolved-metabolic patterns decomposed while naive held at , repeating the fragility pattern of V11.5. The deeper lesson: adding metabolic cost to a substrate with fixed-radius perception produces efficient passivity, not active foraging. The anxiety parallel deepens: V11.5 shows that fixed-stress training produces maladaptive fragility, V11.7 shows that graduated exposure (cf.\ systematic desensitization) builds genuine robustness, and V11.6 shows that existential stakes alone do not produce adaptation when the organism cannot perceive beyond its local neighborhood.
The trajectory from V11.0 through V11.7 reveals two orthogonal axes of improvement. The first is substrate complexity: each step from V11.0 to V11.5 adds internal degrees of freedom for evolution to select on—heterogeneous chemistry (V11.2), multiple coupled channels (V11.3–V11.4), hierarchical coupling (V11.5). The second, revealed by V11.6–V11.7, is selection pressure quality: the substrate matters less than how you stress it. V11.7’s curriculum training on the same V11.4 substrate produces better generalization than V11.5’s hierarchical architecture trained with fixed stress. V11.6 goes further, changing the stakes: metabolic cost makes drought lethal, not merely weakening.
V11.5 introduces directed coupling structure (feedforward/feedback pathways) to test whether functional specialization emerges under selection. The critical insight: attempting to impose different physics per tier (different timescales, custom growth gates) caused immediate extinction at —the channels designed to be “memory” simply died. The working approach uses identical physics across all channels (proven V11.4 dynamics) with an asymmetric coupling matrix that biases information flow directionally. This is more than a technical fix; it reflects a theoretical prediction: in biological cortex, all neurons use the same basic biophysics. The hierarchy emerges from connectivity and learning, not from different physics per layer.
The V11.5 stress test reveals an unexpected phenomenon: stress overfitting. Evolved patterns have 10.5\% higher baseline and 19\% higher self-model salience than naive patterns—but under severe drought they decompose 9.3\% while naive patterns actually integrate by 6.2\%. Evolution selected for high- configurations tuned to mild stress (which each training cycle applies), creating states that are simultaneously more integrated and more fragile than their unoptimized counterparts.
This has a direct parallel in affective neuroscience: anxiety disorders involve heightened integration and self-monitoring that is adaptive under moderate threat but catastrophically maladaptive under extreme stress. The suffering motif—high , low , high —may describe a system that has been selected too precisely for a particular threat level. The evolved CA patterns show exactly this signature: high baseline (0.076) with high self-model salience (0.99) that collapses under a regime shift.
Whether evolution on this substrate can discover integration strategies that are robust to novel stresses—not just the training distribution—likely requires curriculum learning (gradually increasing stress intensity) or environmental diversity (varying the type and severity of perturbation). This connects to the forcing function framework developed in the next section: the quality of the forcing function matters as much as its presence.
At what channel count does the substrate have enough internal degrees of freedom for evolution to discover biological-like integration (where increases under threat)? The -sweep suggests that mid-range (–) accidentally produces integration-like responses—the coupling bandwidth happens to match the channel count—while high (–) decomposes, the coupling space being too large for random configurations. Is there a critical above which a phase transition occurs, or does evolution continuously improve robustness at any ? Each rung of the ladder may require a minimum internal dimensionality—the substrate must be rich enough for selection to sculpt.
The critical lesson evolves with the experiments. V11.0–V11.5 showed that evolution helps but in surprising ways—it creates higher- states that are also more fragile. V11.7 demonstrates that the training regime matters: curriculum learning produces genuine generalization across novel stressors. V11.6 showed that making drought metabolically costly produces efficient passivity rather than active foraging—the patterns cannot perceive beyond their local neighborhood, so existential stakes alone do not generate the distant-resource-seeking behavior that would require integration. The remaining gap was between “decomposes less” and “integrates under threat,” and the locality ceiling explains why.
V12’s results confirm that the ceiling is real and that the predicted remedy partially works. Replacing fixed convolution with evolvable windowed self-attention—the only change to the physics—shifts mean robustness from to , moving the system to the threshold where is approximately preserved under stress rather than destroyed. Eight substrate modifications (V11.0–V11.7) could not achieve even this. The single change that mattered is exactly what the attention bottleneck hypothesis predicted: state-dependent interaction topology. But the effect is modest—the system reaches the threshold without clearly crossing it. Attention is necessary but not sufficient for the full biological pattern.
The V11.5 results show that selecting for -robustness under mild stress creates patterns that are less robust to severe stress than unselected patterns. V11.7 provides a partial answer: curriculum training with graduated, noisy stress exposure produces patterns that generalize to novel stressors ( to shift over naive across four novel severity levels). But the effect is modest—evolved patterns still decompose under severe novel stress (), just less than naive (). The remaining questions: (1) Can curriculum training with longer schedules or wider stress distributions close this gap further? (2) Does combining curriculum training with metabolic cost (V11.6’s lethal resource dependence) produce qualitatively different dynamics—active foraging rather than passive persistence? (3) Does the biological developmental sequence (graduated stressors from embryogenesis through maturation) achieve robust integration precisely because it is a curriculum over the full threat distribution? [V11.6 + curriculum combination not yet tested.]