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1 The substitution matrix is the inverse of the Hessian and, thus, negative deﬁnite. 2 Negative Slope: @x i @w i 0 3 Symmetric Effects: @ x i @w j = @ j @w i These derivations were done for the 2-input case, it turns out that it is straightforward to generalize it to the n-input case using matrix algebra y.