The noticeable difference is that now both partition functions include extra cost terms, either task-specific ( (y, Y(E)) in Z ) or with soft constraints (u g(x, y) in Z u ).
if we set a single constrained feature g 1 (x, y) := I( (y, Y(E)) = 0) with weight u 1 → +∞, all non-zero-cost summands in Z u (w, x) Figure 2: Comparison of saddle-point and penalized PR for Spanish, using the setup in §5.5.