Related papers: On the Existence of Balanced Chain Rule Task Sets
Human behavior emerges from planning over elaborate decompositions of tasks into goals, subgoals, and low-level actions. How are these decompositions created and used? Here, we propose and evaluate a normative framework for task…
Graphs represent interconnected structures prevalent in a myriad of real-world scenarios. Effective graph analytics, such as graph learning methods, enables users to gain profound insights from graph data, underpinning various tasks…
Chain graphs combine directed and undirected graphs and their underlying mathematics combines properties of the two. This paper gives a simplified definition of chain graphs based on a hierarchical combination of Bayesian (directed) and…
Suppose a finite, unweighted, combinatorial graph $G = (V,E)$ is the union of several (degree-)regular graphs which are then additionally connected with a few additional edges. $G$ will then have only a small number of vertices $v \in V$…
Certifying feasibility in decision-making, critical in many industries, can be framed as a constraint satisfaction problem. This paper focuses on characterising a subset of parameter values from an a priori set that satisfy constraints on a…
Recent years have witnessed the great success of graph pre-training for graph representation learning. With hundreds of graph pre-training tasks proposed, integrating knowledge acquired from multiple pre-training tasks has become a popular…
Functional graphs (FGs) model the graph structures used to analyse the behaviour of functions from a discrete set to itself. In turn, such functions are used to study real complex phenomena evolving in time. As the systems involved can be…
A task decomposition method for iterative learning model predictive control is presented. We consider a constrained nonlinear dynamical system and assume the availability of state-input pair datasets which solve a task T1. Our objective is…
Neural networks that compute over graph structures are a natural fit for problems in a variety of domains, including natural language (parse trees) and cheminformatics (molecular graphs). However, since the computation graph has a different…
Graph classes of bounded tree rank were introduced recently in the context of the model checking problem for first-order logic of graphs. These graph classes are a common generalization of graph classes of bounded degree and bounded…
We present a novel methodology to jointly perform multi-task learning and infer intrinsic relationship among tasks by an interpretable and sparse graph. Unlike existing multi-task learning methodologies, the graph structure is not assumed…
A new method to construct task graphs for \mcH-matrix arithmetic is introduced, which uses the information associated with all tasks of the standard recursive \mcH-matrix algorithms, e.g., the block index set of the matrix blocks involved…
Graph neural networks are widely used to learn global representations of graphs, which are then used for regression or classification tasks. Typically, the graphs in such data sets are connected, i.e. each training sample consists of a…
Given a complete graph with positive weights on its edges, we define the weight of a subset of edges as the product of weights of the edges in the subset and consider sums (partition functions) of weights over subsets of various kinds:…
In this paper, we study the exact learning problem for weighted graphs, where we are given the vertex set, $V$, of a weighted graph, $G=(V,E,w)$, but we are not given $E$. The problem, which is also known as graph reconstruction, is to…
A key feature of neural network architectures is their ability to support the simultaneous interaction among large numbers of units in the learning and processing of representations. However, how the richness of such interactions trades off…
We propose a functional view of matrix decomposition problems on graphs such as geometric matrix completion and graph regularized dimensionality reduction. Our unifying framework is based on the key idea that using a reduced basis to…
Graphs provide a natural representation of relational structure that arises across diverse domains. Despite this ubiquity, graph structure is typically learned in a modality- and task-isolated manner, where graph representations are…
Machine learning on graph structured data has attracted much research interest due to its ubiquity in real world data. However, how to efficiently represent graph data in a general way is still an open problem. Traditional methods use…
Fundamental to many applications in data analysis are the decompositions of a graph, i.e. partitions of the node set into component-inducing subsets. One way of encoding decompositions is by multicuts, the subsets of those edges that…