how to calculate gradient without calculating function outputs

[wayhoww]

The expression is y = A' * B where A, B are vectors. Calculating A' * B is useless when calculating dy/dA and dy/dB, but are time consuming.

These kind of problems won't significantly affect the speed in deep learning scenarios but adds a lot of consumed time when the "network" is really shallow.

So is there any way to calculate gradient without calculating function outputs?