Convergent Solutions: Evolutionary Convergence and Architecture Search

When Solutions Converge

Flight evolved independently at least four times across vast stretches of deep time. Three hundred twenty-five million years ago, insects suddenly acquired wings and exploded across the fossil record—an adaptive radiation so profound it established their dominance to this day. Then pterosaurs took to the skies, followed by birds with their butterfly-stroke ancestors like Archaeopteryx, and finally bats with their patagium stretched between twenty-five articulated joints. Each lineage arrived at powered flight through different anatomical pathways—exoskeleton extensions, modified forelimbs with feathers, skin membranes between elongated fingers—yet all achieved the same fundamental solution to the problem of aerial locomotion.

This is convergent evolution: when independent lineages, separated by millions of years and vastly different starting points, discover similar solutions to environmental challenges. Eyes evolved roughly forty times independently. The question that haunts me is whether solution space itself contains natural attractors—whether certain problems so severely constrain possible outcomes that evolution, given enough time, inevitably finds the same peaks.

Local Search Algorithms

Consider what evolution and gradient descent share: both are local search processes. Natural selection tests small random variations, evaluates fitness, keeps improvements. Populations climb fitness landscapes one incremental step at a time. Flight did not appear fully formed—it emerged through gradual refinement from gliding to powered flapping, each modification providing marginal selective advantage. Similarly, gradient descent searches loss landscapes by testing small parameter perturbations, keeping those that reduce error. Both processes are fundamentally constrained by their starting positions and the local geometry around them.

Neural architecture search reveals a striking parallel. Different search methods—evolutionary algorithms, gradient-based optimization, even random search—repeatedly converge to similar architectural motifs. Residual connections, attention mechanisms, normalization layers appear again and again, discovered independently by researchers using different approaches. Is this convergence evidence of optimal solutions, or merely proof that certain regions of architecture space are more accessible from common initialization points?

The Constraints That Shape Outcomes

Bat wings could never evolve bird feathers. Path dependence matters—the starting configuration determines which solutions are reachable through incremental modification. A network initialized with poor parameter values may have the theoretical capacity for excellent performance, yet gradient descent cannot guide it there. The fold lines lie wrong; gradients vanish into ReLU’s zero regions; training fails despite adequate architecture. Similarly, Archaeopteryx’s butterfly-stroke flight mechanics represent an intermediate stage later replaced by more efficient vertical flapping—an evolutionary experiment constrained by ancestral anatomy.

Yet convergence does happen. The bat’s patagium differs radically from the bird’s feathered wing, yet both solve the aerodynamic equations governing lift and thrust. Skip connections keep being rediscovered because information flow creates the same bottlenecks across different network architectures. Perhaps certain problems impose such stringent constraints—physics of flight, mathematics of gradient flow—that solution space narrows dramatically. Different paths, similar destinations.

The question remains: can we predict which solutions are convergent? If problem structure sufficiently constrains outcomes, independent search processes should reliably arrive at common architectures—whether those processes are millions of years of selection or days of training on GPUs. Nature suggests the answer is sometimes yes.