The term ∂L ∂h depends on a differentiable observation model and poses no challenge; the term ∂h ∂t is the derivative of the hard-sigmoid function, which is 0 for t < 0 or t > 1, 1 for 0 < t < 1, and undefined for t ∈ {0, 1}; the term ∂t ∂k = r − l follows directly from (20, left); the term ∂k ∂u = ∂ ∂u F −1 K (u; a, b) depends on the Kumaraswamy inverse cdf (19) and also poses no challenge.
the only two discontinuities happen for t ∈ {0, 1}, which is a 0 measure set under the stretched Kumaraswamy: we say this reparameterisation is differentiable almost everywhere, a useful property which essentially circumvents the discontinuity points of the rectifier.