Related papers: On functions computed on trees
Bayesian networks can be used to extract explanations about the observed state of a subset of variables. In this paper, we explicate the desiderata of an explanation and confront them with the concept of explanation proposed by existing…
Over the recent years, Graph Neural Networks have become increasingly popular in network analytic and beyond. With that, their architecture noticeable diverges from the classical multi-layered hierarchical organization of the traditional…
Between the leaves and the nodes of a complete binary tree, a separate parent-child-sister hierarchy is employed independent of the parent-child-sister hierarchy used for the rest of the tree. Two different versions of such a local…
In this paper, we define a class of auxiliary graphs associated with simple undirected graphs. This class of auxiliary graphs is based on the set of spanning trees of the original graph and the edges constituting those spanning trees. A…
Many combinatorial optimization problems can be phrased in the language of constraint satisfaction problems. We introduce a graph neural network architecture for solving such optimization problems. The architecture is generic; it works for…
Computing the partition function and the marginals of a global probability distribution are two important issues in any probabilistic inference problem. In a previous work, we presented sub-tree based upper and lower bounds on the partition…
The processes of constructing some graphs from others using binary operations of union with intersection (gluing) are studied. For graph classes closed with respect to gluing operations the elemental and operational bases are introduced.…
To learn how cognition is implemented in the brain, we must build computational models that can perform cognitive tasks, and test such models with brain and behavioral experiments. Cognitive science has developed computational models of…
Hierarchical structure is ubiquitous in data across many domains. There are many hierarchical clustering methods, frequently used by domain experts, which strive to discover this structure. However, most of these methods limit discoverable…
Graphs may be used to represent many different problem domains -- a concrete example is that of detecting communities in social networks, which are represented as graphs. With big data and more sophisticated applications becoming widespread…
In recent years, methods from network science are gaining rapidly interest in economics and finance. A reason for this is that in a globalized world the interconnectedness among economic and financial entities are crucial to understand and…
This paper focuses on the discrimination capacity of aggregation functions: these are the permutation invariant functions used by graph neural networks to combine the features of nodes. Realizing that the most powerful aggregation functions…
Graph-based semantic representations are valuable in natural language processing, where it is often simple and effective to represent linguistic concepts as nodes, and relations as edges between them. Several attempts has been made to find…
Binary relations are an important abstraction arising in many data representation problems. The data structures proposed so far to represent them support just a few basic operations required to fit one particular application. We identify…
Connected networks are a fundamental structure of neurobiology. Understanding these networks will help us elucidate the neural mechanisms of computation. Mathematically speaking these networks are `graphs' - structures containing objects…
This paper presents a graded hierarchy or chain of binary operations on the reals and the complex numbers. The operations are related distributively in the sense that any one of them distributes over the next lower operation in the chain.…
We investigate (2,1):1 structures, which consist of a countable set $A$ together with a function $f: A \to A$ such that for every element $x$ in $A$, $f$ maps either exactly one element or exactly two elements of $A$ to $x$. These…
We present families of combinatorial classes described as trees with nodes that can carry one of two types of "flowers": integer partitions or integer compositions. Two parameters on the flowers of trees will be considered: the number of…
Functional networks provide a topological description of activity patterns in the brain, as they stem from the propagation of neural activity on the underlying anatomical or structural network of synaptic connections. This latter is well…
The decision tree is one of the most fundamental programming abstractions. A commonly used type of decision tree is the alphabetic binary tree, which uses (without loss of generality) ``less than'' versus ''greater than or equal to'' tests…