The expectation-maximization (EM) algorithm is one of the workhorses of statistical genetics. It handles missing data by alternating between computing expected values of the missing variables (E-step) and maximizing likelihood given those expectations (M-step). Generations of geneticists have implemented it by hand, deriving the specific E-step and M-step for each model.
Böhringer (arXiv:2603.10991) builds a neural network that discovers EM on its own. ForwardFlow uses a branched architecture with collapsing layers: the network takes simulated data as input and outputs parameter estimates without ever seeing a likelihood function. It's trained on forward simulations only — generate data from known parameters, train the network to invert the mapping.
When applied to genetic data with missing allele information, the trained network's internal computation approximates the EM algorithm. Not because anyone told it to. Not because EM was encoded in the architecture. The network converges to EM because EM is the structure of the problem. Any sufficiently flexible function approximator, trained to invert a generative model with missing data, will rediscover the alternating expectation-maximization structure because that structure is optimal for the task.
The structural lesson: classical statistical algorithms are not human inventions imposed on data. They are features of the problem landscape that any sufficiently powerful optimizer will converge to. EM exists in the same way that a crystal structure exists — not because someone designed it, but because the energy landscape has a minimum there. The neural network didn't learn EM from a textbook. It found it by gradient descent, the same way water finds the lowest point.