From my read of the paper. This new formula also gives an exponential time algorithm. It’s not of interest as a practical method for computing determinants. It

From my read of the paper. This new formula also gives an exponential time algorithm. It’s not of interest as a practical method for computing determinants. It does however have interesting geometric and combinatorial properties and they used it to give new bounds for the tensor rank and Waring rank of a determinant respectively. You can think of these ranks loosely as measures of the “complexity” of a determinant (but not in the sense of computational complexity). These ranks are of interest in pure mathematics but I can’t really say more about them because it’s been too many years since I’ve studied related math.