This article presents a new approach to the important challenge of localizing function in a neurocontroller. The approach is based on the basic functional contribution analysis (FCA) presented earlier, which assigns contribution values to the elements of the network, such that the ability to predict the network's performance in response to multi-unit lesions is maximized. These contribution values quantify the importance of each element to the tasks the agent performs. Here we present a generalization of the basic FCA to high-dimensional analysis, using high-order compound elements. Such elements are composed of conjunctions of simple elements. Their usage enables the explicit expression of sets of neurons or synapses whose contributions are interdependent, a prerequisite for localizing the function of complex neurocontrollers. High-dimensional FCA is shown to significantly improve on the accuracy of the basic analysis, to provide new insights concerning the main subsets of simple elements in the network that interact in a complex nonlinear manner, and to systematically reveal the types of interactions that characterize the evolved neurocontroller.