Is there any model agnostic way to calculate the weight importance for neural networks given a set of inputs? I was curious if it's possible to calculate what weights are important and what weights are redundant (or have high redundancy) for separate tasks in neural networks?
And if this is doable in a model agnostic way (maybe also differentiable..)?
You should look into fisher matrices. Elastic weight consolidation finds weights which are important for dataset 1 when training dataset 2 by finding the fisher matrix and slows the tuning of them down by adding a regularization term to the loss function. It's non trivial though and I got a lot of trouble implementing it in PyTorch.
The paper which proposed elastic weight consolidation is here: https://arxiv.org/pdf/1612.00796.pdf