Functional equivalence without structural convergence: a Monte Carlo study of evolutionary and evolution-strategy search in small neural network architectures

Manuscript prepared for Cognitive Neurodynamics (Springer). Neural systems can often produce similar function from different circuit parameters (degeneracy). The study asks how far independent optimisation routes with different encodings land on the same network architecture when they reach comparable function. Symmetric weighted networks (N = 8, 12, 16) are searched for high values of three information-theoretic functionals (neural complexity, a Phi-like minimum-bipartition measure, synergy dominance) by a DNA-encoded genetic algorithm, the same genetic algorithm on continuous genes, a (1+lambda) evolution strategy and random search at equal evaluation budget, under linear equilibrium, linear AR(1) and nonlinear rate dynamics. Structural similarity is measured with five permutation-invariant descriptors and, for the nonlinear network, with a perturbation response computed from simulated trajectories. Exploratory computational study; the functionals are proxies and the results do not bear on cognition or consciousness. Code, tests and results: https://github.com/sandlerleon/shapesearch-functional-equivalence.