Maximum Likelihood Estimation on the Grassmannian of Lines

What the math gives to ML

The paper treats positive Grassmannian points as normalized probability distributions over d-subsets, with probabilities given by positive Plücker coordinates. The transferable asset is a structured output layer whose probabilities are not independent categorical logits: they are maximal minors of a low-dimensional matrix and therefore obey decomposability and positivity constraints. This can replace an O(binomial(n,d))-parameter subset classifier with an O(dn)-parameter differentiable head, while preserving a valid distribution over subsets. The most practical experiment is a Grassmannian subset-prediction head trained by likelihood and compared against an unconstrained softmax and a standard low-rank subset model.