相关论文: Modularization, Composition, and Hierarchization o…

We present a differentiable framework capable of learning a wide variety of compositions of simple policies that we call skills. By recursively composing skills with themselves, we can create hierarchies that display complex behavior. Skill…

We present a general and natural framework to study the dynamics of composition operators on spaces of measurable functions, in which we then reconsider the characterizations for hypercyclic and mixing composition operators obtained by…

A new general decomposition theory inspired from modular graph decomposition is presented. This helps unifying modular decomposition on different structures, including (but not restricted to) graphs. Moreover, even in the case of graphs,…

We propose to employ the hierarchical coarse-grained structure in the artificial neural networks explicitly to improve the interpretability without degrading performance. The idea has been applied in two situations. One is a neural network…

Network-theoretic tools contribute to understanding real-world system dynamics, e.g., in wildlife conservation, epidemics, and power outages. Network visualization helps illustrate structural heterogeneity; however, details about…

This document gives an algebraic and two polygraphic translations of Petri nets, all three providing an easier way to describe reductions and to identify some of them. The first one sees places as generators of a commutative monoid and…

Hierarchical feature learning based on convolutional neural networks (CNN) has recently shown significant potential in various computer vision tasks. While allowing high-quality discriminative feature learning, the downside of CNNs is the…

This paper aims to undertake an exploration of the behavior of the moduli space of line arrangements while establishing its combinatorial interplay with the incidence structure of the arrangement. In the first part, we investigate…

This paper introduces and studies the sequential composition and decomposition of propositional logic programs. We show that acyclic programs can be decomposed into single-rule programs and provide a general decomposition result for…

Reaction networks, or equivalently Petri nets, are a general framework for describing processes in which entities of various kinds interact and turn into other entities. In chemistry, where the reactions are assigned "rate constants", any…

We introduce a novel representation of structured polynomial ideals, which we refer to as chordal networks. The sparsity structure of a polynomial system is often described by a graph that captures the interactions among the variables.…

To deal with global problems we suggest to consider complex systems not in space and time, but in a possible deeper reality, i.e., the hierarchical network of prime integer relations. Encoded by arithmetic through the self-organization…

A hallmark of human intelligence is the ability to construct self-contained chunks of knowledge and adequately reuse them in novel combinations for solving different yet structurally related problems. Learning such compositional structures…

It is often the case that the performance of a neural network can be improved by adding layers. In real-world practices, we always train dozens of neural network architectures in parallel which is a wasteful process. We explored $CompNet$,…

We identify and demonstrate a weakness of Petri Nets (PN) in specifying composite behavior of reactive systems. Specifically, we show how, when specifying multiple requirements in one PN model, modelers are obliged to specify mechanisms for…

Several networks occurring in real life have modular structures that are arranged in an hierarchical fashion. In this paper, we have proposed a model for such networks, using a stochastic generation method. Using this model we show that,…

Modularity is a general principle present in many fields. It offers attractive advantages, including, among others, ease of conceptualization, interpretability, scalability, module combinability, and module reusability. The deep learning…

Networked systems are systems of interconnected components, in which the dynamics of each component are influenced by the behavior of neighboring components. Examples of networked systems include biological networks, critical…

A theory is developed which uses "networks" (directed acyclic graphs with some extra structure) as a formalism for expressions in multilinear algebra. It is shown that this formalism is valid for arbitrary PROPs (short for 'PROducts and…

The global availability of communication services makes it possible to interconnect independently developed systems, called constituent systems, to provide new synergistic services and more efficient economic processes. The characteristics…