Symbolic knowledge extraction from trained neural networks: A sound approach

Although neural networks have shown very good performance in many application domains, one of their main drawbacks lies in the incapacity to provide an explanation for the underlying reasoning mechanisms. The “explanation capability” of neural networks can be achieved by the extraction of symbolic knowledge. In this paper, we present a new method of extraction that captures nonmonotonic rules encoded in the network, and prove that such a method is sound. We start by discussing some of the main problems of knowledge extraction methods. We then discuss how these problems may be ameliorated. To this end, a partial ordering on the set of input vectors of a network is defined, as well as a number of pruning and simplification rules. The pruning rules are then used to reduce the search space of the extraction algorithm during a pedagogical extraction, whereas the simplification rules are used to reduce the size of the extracted set of rules. We show that, in the case of regular networks, the extraction algorithm is sound and complete. We proceed to extend the extraction algorithm to the class of non-regular networks, the general case. We show that non-regular networks always contain regularities in their subnetworks. As a result, the underlying extraction method for regular networks can be applied, but now in a decompositional fashion. In order to combine the sets of rules extracted from each subnetwork into the final set of rules, we use a method whereby we are able to keep the soundness of the extraction algorithm. Finally, we present the results of an empirical analysis of the extraction system, using traditional examples and real-world application problems. The results have shown that a very high fidelity between the extracted set of rules and the network can be achieved

Normative Autonomy and Normative Co-ordination: Declarative Power, Representation, and Mandate

In this paper we provide a formal analysis of the idea of normative co-ordination. We argue that this idea is based on the assumption that agents can achieve flexible co-ordination by conferring normative positions to other agents. These positions include duties, permissions, and powers. In particular, we explain the idea of declarative power, which consists in the capacity of the power-holder of creating normative positions, involving other agents, simply by "proclaiming" such positions. In addition, we account also for the concepts of representation, namely the representative's capacity of acting in the name of his principal, and of mandate, which is the mandatee's duty to act as the mandator has requested. Finally, we show how the framework can be applied to represent the contract-net protocol. Some brief remarks on future research and applications conclude this contribution

The performance of coalescent-based species tree estimation methods under models of missing data

Abstract Background Estimation of species trees from multiple genes is complicated by processes such as incomplete lineage sorting, gene duplication and loss, and horizontal gene transfer, that result in gene trees that differ from each other and from the species phylogeny. Methods to estimate species trees in the presence of gene tree discord due to incomplete lineage sorting have been developed and proved to be statistically consistent when gene tree discord is due only to incomplete lineage sorting and every gene tree includes the full set of species. Results We establish statistical consistency of certain coalescent-based species tree estimation methods under some models of taxon deletion from genes. We also evaluate the impact of missing data on four species tree estimation methods (ASTRAL-II, ASTRID, MP-EST, and SVDquartets) using simulated datasets with varying levels of incomplete lineage sorting, gene tree estimation error, and degrees/patterns of missing data. Conclusions All the species tree estimation methods improved in accuracy as the number of genes increased and often produced highly accurate species trees even when the amount of missing data was large. These results together indicate that accurate species tree estimation is possible under a variety of conditions, even when there are substantial amounts of missing data