Converting an n-dimensional vector to a probability distribution over n objects isacommonly used component inmanymachine learning tasks likemulticlass classification,multilabelclassification,attentionmechanismsetc.

In this case, points on the boundary of K have one or more zero coordinates. In contrast, softmax(s) exp(s)is always strictly inside the simplex. Alternatively, observe that it is enough to find Z. In this section, we present the active set method [63, Chapters 16.4 & 16.5] as applied to the SparseMAPoptimizationproblem(Eq.4)[13]. Denote the solution of Eq. 13, (extended with zeroes), by ˆξ |Z|.

Inline 95,j istheindexinto the feature vector (defined in44 lines 93-95).