We study the estimation of a
K-dimensional simplex from
N i.i.d.\ points sampled uniformly from its interior; the observations are convex combinations of
K+1 unknown prototypes. Existing polynomial-time estimators need cubic per-sample work or
O(NK) storage and are impractical at
N∼106--
108. We propose DeepMVSA, which re-expresses the minimum-volume principle in neural implicit form: a lightweight coordinate network generates the mixing weights and a triangular LU-type parameterization the dual simplex matrix, reducing the trainable-state memory to
O(K2), independent of
N, and the cost per data pass to
O(NK2). We prove a non-asymptotic sample-complexity bound of the polynomial-time benchmark order for a localized surrogate estimator; an oracle inequality for every global minimizer of the neural objective, with volume-inflation control and an explicit shrinkage bias; a conditional end-to-end error budget separating statistical, approximation, optimization, and enclosure-residual terms on an explicit envelope event; and two-point lower bounds: at any noise level
σ>0 fixed independently of
N, the
N−1/2 scaling is unimprovable in its
N-exponent. Experiments with up to
N=108 synthetic observations are consistent with the predicted accuracy and scaling, and feasibility on real scenes of
∼107 pixels is demonstrated.