אומדן פשוטות מינימליות בנפח

תקציר מקורי באנגליתarXiv:2609.25576v2 Announce Type: replace-cross Abstract: 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 $N\sim 10^6$--$10^8$. 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 $O(K^2)$, independent of $N$, and the cost per data pass to $O(NK^2)$. We prove a non-asymptotic sample-complexity bound of the polynomial-time benchmark order for a loc