This isn’t quite true; the determinant being small is consistent with small changes in input making arbitrarily large changes in output, just so long as small changes in input in a different direction make sufficiently small changes in output.
Hmm, good point. I suppose why that’s not why we’re minimizing determinant, but rather frobenius norm. Hence:
An alternative definition of the frobenius norm better highlights its connection to the motivation of regularizing the Jacobian frobenius
I suppose why that’s not why we’re minimizing determinant, but rather frobenius norm.
Yes, although another reason is that the determinant is only defined if the input and output spaces have the same dimension, which they typically don’t.
Hmm, good point. I suppose why that’s not why we’re minimizing determinant, but rather frobenius norm. Hence:
Makes sense.
Yes, although another reason is that the determinant is only defined if the input and output spaces have the same dimension, which they typically don’t.