These theoretical findings are supported by experimental results.

Modern deep learning is driven by first-order stochastic optimization algorithms.

Modern deep learning is driven by first-order stochastic optimization algorithms.

We next discuss two lines of related literature.

Quantum Algorithms (VQAs) have emerged to obtain possible quantum advantage. In particular, how to effectively incorporate hard constraints in VQAs remains a critical and open question.

This work is also the first effort to benchmark the stability of causal discovery algorithms with respect to the values of their hyperparameters.