The Lande equation describes how a population's mean phenotype shifts under selection. It says the change equals the genetic covariance matrix times the selection gradient — how much variation exists, multiplied by which direction fitness increases. Quantitative geneticists have used it for decades as an empirical tool. Vanchurin (arXiv:2603.15198) shows it is something more specific: a covariant gradient ascent equation on a Riemannian manifold where the metric tensor is the inverse of the covariance matrix.
This is not analogy. The maximum entropy principle yields a fundamental identification between the inverse metric and the covariance matrix. In this geometry, populations don't just climb fitness landscapes — they climb them using the natural gradient, the same algorithm that outperforms naive gradient descent in machine learning by accounting for the curvature of the parameter space. The learning rate is the covariance. The curvature is the standing genetic variation.
The specific learning algorithm — whether evolution resembles Adam, SGD, or something else — depends on the functional relationship between the metric tensor and the noise covariance from microscopic dynamics. This relationship has never been measured. The metric (genetic covariance) is well-characterized empirically. The noise covariance (the variance of evolutionary changes across replicates) is not. The framework predicts they are related, but the form of the relation is the open question.
Evolution is a learning algorithm. We know its architecture. We don't yet know its hyperparameters.