Sparsemax Function
Created
2025 Mar 10 12:41Sparsemax(z)=argminp∈ΔK∥p−z∥22,where ΔK={p∈RK∣∑i=1Kpi=1,pi≥0}. This
projects the input vector
z onto the
Probability simplex, yielding a sparse
Probability Distribution.
Solution
Sparsemax(z)i=max(zi−τ,0),where τ satisfies ∑i=1Kmax(zi−τ,0)=1.τ=∣S∣∑j∈Szj−1andS={i∣zi−τ>0}.