A model like a neural network or an SVM is called for only if the interactions between the features and the target is non-linear, otherwise we're better off using linear or logistic regression.
But all of the feature selection methods I've come across use linear criteria for determining feature importance: For example if two features are highly correlated then we can discard one and use only one of them. Same thing with LASSO or using a variance threshold. They only make sense to me if we assume a linear relationship to the output.
So how does one then perform feature selection for non linear supervised models?