  Recent work has highlighted the complex influence training hyperparameters,
e.g., the number of training epochs, can have on the prunability of machine
learning models. Perhaps surprisingly, a systematic approach to predict
precisely how adjusting a specific hyperparameter will affect prunability
remains elusive. To address this gap, we introduce a phenomenological model
grounded in the statistical mechanics of learning. Our approach uses
temperature-like and load-like parameters to model the impact of neural network
(NN) training hyperparameters on pruning performance. A key empirical result we
identify is a sharp transition phenomenon: depending on the value of a
load-like parameter in the pruned model, increasing the value of a
temperature-like parameter in the pre-pruned model may either enhance or impair
subsequent pruning performance. Based on this transition, we build a
three-regime model by taxonomizing the global structure of the pruned NN loss
landscape. Our model reveals that the dichotomous effect of high temperature is
associated with transitions between distinct types of global structures in the
post-pruned model. Based on our results, we present three case-studies: 1)
determining whether to increase or decrease a hyperparameter for improved
pruning; 2) selecting the best model to prune from a family of models; and 3)
tuning the hyperparameter of the Sharpness Aware Minimization method for better
pruning performance.
