Related papers: On functions computed on trees

We propose a novel approach for studying rooted trees by using functions that we will call descent functions. We provide a construction method for rooted trees that allows to study their properties through the use of descent functions.…

We investigate the spectral properties of rooted trees with the intention of improving the currently existing results that deal with this matter. The concept of an assigned rational function is recursively defined for each vertex of a…

This paper investigates the execution of tree-shaped task graphs using multiple processors. Each edge of such a tree represents some large data. A task can only be executed if all input and output data fit into memory, and a data can only…

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…

The brain can be regarded as a network: a connected system where nodes, or units, represent different specialized regions and links, or connections, represent communication pathways. From a functional perspective communication is coded by…

Large graphs abound in machine learning, data mining, and several related areas. A useful step towards analyzing such graphs is that of obtaining certain summary statistics - e.g., or the expected length of a shortest path between two…

Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order…

The study of networks has witnessed an explosive growth over the past decades with several ground-breaking methods introduced. A particularly interesting -- and prevalent in several fields of study -- problem is that of inferring a function…

This paper investigates the execution of tree-shaped task graphs using multiple processors. Each edge of such a tree represents a large IO file. A task can only be executed if all input and output files fit into memory, and a file can only…

One major challenge of neuroscience is finding interesting structures in a seemingly disorganized neural activity. Often these structures have computational implications that help to understand the functional role of a particular brain…

This paper establishes the rate region for a class of source coding function computation setups where sources of information are available at the nodes of a tree and where a function of these sources must be computed at the root. The rate…

We generalize the concept of ascending and descending runs from permutations to rooted labelled trees and mappings, i.e., functions from the set $\{1, \dots, n\}$ into itself. A combinatorial decomposition of the corresponding functional…

A binary relation on graphs is recursively enumerable if and only if it can be computed by a formula in monadic second-order logic. The latter means that the formula defines a set of graphs, in the usual way, such that each "computation…

Neural networks with tree-based sentence encoders have shown better results on many downstream tasks. Most of existing tree-based encoders adopt syntactic parsing trees as the explicit structure prior. To study the effectiveness of…

Traditionally, most complex intelligence architectures are extremely non-convex, which could not be well performed by convex optimization. However, this paper decomposes complex structures into three types of nodes: operators, algorithms…

Since they became observable, neuron morphologies have been informally compared with biological trees but they are studied by distinct communities, neuroscientists, and ecologists. The apparent structural similarity suggests there may be…

We extend the hyperplane arrangement framework for neural network expressivity from the braid to discriminantal arrangements. Compatible piecewise linear functions are characterized by circuit relations and admit a matroidal description via…

Though modern neural networks have achieved impressive performance in both vision and language tasks, we know little about the functions that they implement. One possibility is that neural networks implicitly break down complex tasks into…

We formalize an existing computability-theoretic method of presenting first-order structures whose domains have the cardinality of the continuum. Work using these methods until now has emphasized their topological properties. We shift the…

Much information about a graph can be obtained by studying its spanning trees. On the other hand, a graph can be regarded as a 1-dimensional cell complex, raising the question of developing a theory of trees in higher dimension. As observed…