 If one fixes formula_17, one can thus define a smooth vector field "pointing at formula_17" by formula_20 This is the gradient of the scalar-valued function "half SED from formula_17", where the half cancels the two in the power rule.Writing half the squared distance from formula_17 as formula_23, one has formula_24 Alternatively, one can consider the vector field pointing "from" formula_17, and omit the minus sign.In information geometry, the notion of a vector field of "pointing from one point to another" can be generalized to statistical manifolds – one can use an affine connection to connect tangent vectors at different points and the exponential map to flow from one point to another, and on a statistical manifold this is invertible, defining a unique "difference vector" from any given point to another.