  In this paper we present a differential semantics of Lazy AR Propagation
(LARP) in discrete Bayesian networks. We describe how both single and multi
dimensional partial derivatives of the evidence may easily be calculated from a
junction tree in LARP equilibrium. We show that the simplicity of the
calculations stems from the nature of LARP. Based on the differential semantics
we describe how variable propagation in the LARP architecture may give access
to additional partial derivatives. The cautious LARP (cLARP) scheme is derived
to produce a flexible cLARP equilibrium that offers additional opportunities
for calculating single and multidimensional partial derivatives of the evidence
and subsets of the evidence from a single propagation. The results of an
empirical evaluation illustrates how the access to a largely increased number
of partial derivatives comes at a low computational cost.
