Gradient descent is based on the observation that if the multi-variable function F ( x ) {\displaystyle F(\mathbf {x} )} is defined and differentiable in a neighborhood of a point a {\displaystyle \mathbf {a} } , then F ( x ) {\displaystyle F(\mathbf {x} )} decreases fastest if one goes from a {\displaystyle \mathbf {a} } in the direction of the negative gradient of F {\displaystyle F} at a , − ∇ F ( a ) {\displaystyle \mathbf {a} ,-\nabla F(\mathbf {a} )} . It follows that, if