What is Coarse-to-Fine in the context of neural networks?
"Coarse to Fine" usually refers to the hyperparameter optimization of a neural network during which you would like to try out different combinations of the hyperparameters and evaluate the performance of the network. 

However, due to the large number of parameters AND the big range of their values, it is almost impossible to check all the available combinations. For that reason, you usually discretize the available value range of each parameter into a "coarse" grid of values (i.e. val = 5,6,7,8,9) to estimate the effect of increasing or decreasing the value of that parameter. After selecting the value that seems most promising/meaningful (i.e. val = 6), you perform a "finer" search around it (i.e. val = 5.8, 5.9, 6.0, 6.1, 6.2) to optimize even further.