I think we basically agree on the state of the empirical evidence—the question is just whether NTK/GP/random-sampling methods will continue to match the performance of SGD-trained nets on more complex problems, or if they’ll break down, ultimately being a first-order approximation to some more complex dynamics. I think the latter is more likely, mostly based on the lack of feature learning in NTK/GP/random limits.
re: the architecture being the source of inductive bias—I certainly think this is true in the sense that architecture choice will have a bigger effect on generalization than hyperparameters, or the choice of which local optimizer to use. But I do think that using a local optimizer at all, as opposed to randomly sampling parameters, is likely to have a large effect.
I think we basically agree on the state of the empirical evidence—the question is just whether NTK/GP/random-sampling methods will continue to match the performance of SGD-trained nets on more complex problems, or if they’ll break down, ultimately being a first-order approximation to some more complex dynamics. I think the latter is more likely, mostly based on the lack of feature learning in NTK/GP/random limits.
re: the architecture being the source of inductive bias—I certainly think this is true in the sense that architecture choice will have a bigger effect on generalization than hyperparameters, or the choice of which local optimizer to use. But I do think that using a local optimizer at all, as opposed to randomly sampling parameters, is likely to have a large effect.