This paper develops a rotation-invariant neural network to jointly learn how to regularize both the eigenvalues and marginal volatility of a large stock covariance matrix and how to lag-transform past returns to provide a global minimum variance portfolio. This explicit mathematical mapping provides a clear interpretability of the role of each module, so that the model cannot be considered a pure black box. The architecture reflects the analytical form of the global minimum variance solution, but is dimensionless, so that a single model can be calibrated to a panel of hundreds of stocks and applied to 1,000 U.S. stocks without retraining. This is a cross-sectional jump that demonstrates strong out-of-sample generalization. The loss function is the future realized minimum portfolio variance, optimized end-to-end for actual daily returns. In out-of-sample tests from January 2000 to December 2024, this estimator systematically provides lower realized volatility, smaller maximum loss, and higher Sharpe ratio than the best analytical competitors, including state-of-the-art nonlinear shrinkage. Furthermore, while the model is trained end-to-end to generate unconstrained (long-short) minimum variance portfolios, the learned covariance representation can be used in general optimization programs under long-only constraints, with little loss of performance advantage over competing estimators. These advantages persist when the strategy is implemented in a highly realistic implementation framework that models market orders in auctions and takes into account empirical slippage, transaction fees, and funding costs for leverage, and remain stable even during periods of severe market stress.
