Policy-Adaptable Methods For Resolving Normative Conflicts Through Argumentation and Graph Colouring

In a multi-agent system, one may choose to govern the behaviour of an agent by imposing norms, which act as guidelines for how agents should act either all of the time or in given situations. However, imposing multiple norms on one or more agents may result in situations where these norms conflict over how the agent should behave. In any system with normative conflicts (such as safe reinforcement models or systems which monitor safety protocols), one must decide which norms should be followed such that the most important and most relevant norms are maintained. We introduce a new method for resolving normative conflicts through argumentation and graph colouring which is compatible with a variety of normative conflict resolution policies. We prove that this method always creates an admissible set of arguments under argumentation semantics, meaning that it produces coherent outputs. We also introduce more robust variants of this method, each building upon their predecessor to create a superior output, and we include further mathematical proof of their coherence. Our most advanced variant uses the existing concept of curtailment, where one norm may supersede another without fully eliminating it. The methods we introduce are all compatible with various pre-existing policies for resolving normative conflicts. Empirical evaluations are also performed to compare our algorithms to each other and to others in existing literature.

Polynomial Threshold Functions of Bounded Tree-Width: Some Explainability and Complexity Aspects

The tree-width of a multivariate polynomial is the tree-width of the hypergraph with hyperedges corresponding to its terms. Multivariate polynomials of bounded tree-width have been studied by Makowsky and Meer as a new sparsity condition that allows for polynomial solvability of problems which are intractable in general. We consider a variation on this theme for Boolean variables. A representation of a Boolean function as the sign of a polynomial is called a polynomial threshold representation. We discuss Boolean functions representable as polynomial threshold functions of bounded tree-width and present two applications to Bayesian network classifiers, a probabilistic graphical model. Both applications are in Explainable Artificial Intelligence (XAI), the research area dealing with the black-box nature of many recent machine learning models. We also give a separation result between the representational power of positive and general polynomial threshold functions.

Algebraic Representations for Faster Predictions in Convolutional Neural Networks

Convolutional neural networks (CNNs) are a popular choice of model for tasks in computer vision. When CNNs are made with many layers, resulting in a deep neural network, skip connections may be added to create an easier gradient optimization problem while retaining model expressiveness. In this paper, we show that arbitrarily complex, trained, linear CNNs with skip connections can be simplified into a single-layer model, resulting in greatly reduced computational requirements during prediction time. We also present a method for training nonlinear models with skip connections that are gradually removed throughout training, giving the benefits of skip connections without requiring computational overhead during during prediction time. These results are demonstrated with practical examples on Residual Networks (ResNet) architecture.