We can now use the topology of the NP program, in a bucket-brigade style backward propagation, to refine the credit scores at each node. There is a wealth of literature on propagation of values through networks. Our current research includes an investigation into an understanding the effects of these various methods so that we can incorporate the most effective paradigm into the IRNP mechanism.
For the experiment described in this paper we will use the simplest mechanism possible: each node X will be given the maximum of the credit scores of nodes such that one of the outputs of X is an input to that node and that node was effected by the values output by X. If this were a highly connected graph and the arity of all nodes was equal to the number of their inputs, then this bucket-brigade operation would simply fill the entire Credit-Blame map with the maximum value in the map. In practice, this does not happen exactly because the neural programs have many arcs whose values are ignored (even though very few of the node values are ignored). For example, a node Y with a function value of the constant value ``6'' outputs its value at each time step and ignores all values it receives as input. So even if this constant is relevant to a node with a high credit score (and so node Y, in turn, receives a high credit score) the nodes whose outputs are inputs to Y will receive no boost in credit score from this source.
In general, the arcs in an NP program are given credit scores that
differ from either their source or destination nodes (though this new
value is a function of the two node credit scores). For this paper,
we will simply assign each arc from node X to node Y the
credit-score pair ( 
, 
).