  The discovery of sparse subnetworks that are able to perform as well as full
models has found broad applied and theoretical interest. While many pruning
methods have been developed to this end, the na\"ive approach of removing
parameters based on their magnitude has been found to be as robust as more
complex, state-of-the-art algorithms. The lack of theory behind magnitude
pruning's success, especially pre-convergence, and its relation to other
pruning methods, such as gradient based pruning, are outstanding open questions
in the field that are in need of being addressed. We make use of recent
advances in dynamical systems theory, namely Koopman operator theory, to define
a new class of theoretically motivated pruning algorithms. We show that these
algorithms can be equivalent to magnitude and gradient based pruning, unifying
these seemingly disparate methods, and find that they can be used to shed light
on magnitude pruning's performance during the early part of training.
