Activity-Dependent Plasticity in Morphogenetically-Grown Recurrent Networks

Abstract

Developmental approaches to neural architecture search grow functional networks from compact genomes through self-organisation, but the resulting networks operate with fixed post-growth weights. We characterise Hebbian and anti-Hebbian plasticity across 50,000 morphogenetically grown recurrent controllers (5M+ configurations on CartPole and Acrobot), then test whether co-evolutionary experiments -- where plasticity parameters are encoded in the genome and evolved alongside the developmental architecture -- recover these patterns independently. Our characterisation reveals that (1) anti-Hebbian plasticity significantly outperforms Hebbian for competent networks (Cohen's d = 0.53-0.64), (2) regret (fraction of oracle improvement lost under the best fixed setting) reaches 52-100%, and (3) plasticity's role shifts from fine-tuning to genuine adaptation under non-stationarity. Co-evolution independently discovers these patterns: on CartPole, 70% of runs evolve anti-Hebbian plasticity (p = 0.043); on Acrobot, evolution finds near-zero eta with mixed signs -- exactly matching the characterisation. A random-RNN control shows that anti-Hebbian dominance is generic to small recurrent networks, but the degree of topology-dependence is developmental-specific: regret is 2-6x higher for morphogenetically grown networks than for random graphs with matched topology statistics.

Figures (6)

• Figure 1: Developmental dynamics of a MorphoNAS network on a $10 \times 10$ grid. Background colour encodes morphogen concentrations (RGB = 3 morphogens); white squares = neurons; white lines = connections. From a single progenitor cell (Step 2), reaction-diffusion dynamics drive cell division, differentiation, and chemotactic axon growth, producing a 7-neuron, 13-connection recurrent controller by Step 200.
• Figure 2: CartPole High-mid stratum: mean $\Delta r$ across the $\eta \times \lambda$ grid (248-point extended grid). Anti-Hebbian ($\eta < 0$) with moderate decay ($\lambda = 0.01$) yields the best results. Hebbian ($\eta > 0$) is consistently harmful.
• Figure 3: CartPole: Cohen's $d$ (anti-Hebbian $-$ Hebbian) by stratum. Anti-Hebbian significantly outperforms Hebbian for competent strata ($d = 0.53$--$0.64$, all $p < 0.001$). The effect reverses for Weak and Perfect networks with small magnitudes.
• Figure 4: CartPole adaptation premium (non-stationary plasticity benefit minus static plasticity benefit) for two perturbation types. Gravity-2$\times$ yields significant positive premiums for competent strata (***$p<0.001$), indicating genuine adaptation beyond static fine-tuning. Heavy-pole shows near-zero premiums (n.s.).
• Figure 5: Acrobot fraction of episodes unsolved over time under non-stationarity (2$\times$ link mass at step 50). Solid: per-network oracle plasticity; dashed: no plasticity. Lower is better. Oracle plasticity accelerates solving across all strata---most visibly for High-mid and Near-perfect, where the unsolved fraction at step 300 drops from 66%/31% (no plasticity) to 40%/18% (oracle plasticity).