Relating uniform-initialization statistics to trained-parameter statistics

Determine how coefficient statistics computed under uniform parameter sampling—such as variances, correlations, and spectral-bias signatures—relate to the corresponding statistics under the trained parameter distribution for parametrized quantum circuits.

Background

Many closed-form results in the paper are population statements under uniform parameter sampling on the parameter torus, yielding clean factorisations via character orthogonality. The authors note that after training, parameter distributions deviate from uniform, potentially altering these statistics, and explicitly pose this as an open question.