Linear Proposal Operators and Stochastic Search Geometry in SOMA and Differential Evolution

What the math gives to ML

The paper separates objective-independent variation from boundary repair and fitness-based selection, making the geometry of evolutionary proposals analytically tractable. Its most transferable result is the exact moment analysis of masked leader-directed affine moves: a Bernoulli coordinate mask provides explicit control over mean attraction, covariance, expected step length, active dimensionality, and coordinate coverage. This suggests a practical zeroth-order optimizer for low-dimensional neural parameterizations such as LoRA, prompt embeddings, adapter weights, or hyperparameters, where gradients are unavailable or deliberately avoided. The safest initial transfer is to use the derived moments to schedule mask probability and migration distance rather than applying the full population algorithm to all neural weights.