Before revision:  The deep neural network is trained on a randomly generated dataset using the Cholesky factorization. This method, benchmarked on synthetic datasets as well as on some S P500 stock returns covariance matrices ,  achieves comparable results to several state-of-the-art techniques, while outperforming all existing algorithms in terms of computational time.
After revision:  The deep neural network is trained on a randomly generated dataset P500 stock returns covariance matrices , achieves comparable results to several state-of-the-art techniques, while outperforming all existing algorithms in terms of computational time.