Related papers: Composing Behaviors of Networks
Invariant theory is concerned with functions that do not change under the action of a given group. Here we communicate an approach based on tensor networks to represent polynomial local unitary invariants of quantum states. This graphical…
The compositional generalization abilities of neural models have been sought after for human-like linguistic competence. The popular method to evaluate such abilities is to assess the models' input-output behavior. However, that does not…
Random networks are increasingly used to analyse complex transportation networks, such as airline routes, roads and rail networks. So far, this research has been focused on describing the properties of the networks with the help of random…
Networks can be combined in various ways, such as overlaying one on top of another or setting two side by side. We introduce "network models" to encode these ways of combining networks. Different network models describe different kinds of…
The abstraction of musical structures (notes, melodies, chords, harmonic or rhythmic progressions, etc.) as mathematical objects in a geometrical space is one of the great accomplishments of contemporary music theory. Building on this…
Graph convolutional networks (GCNs) have gained popularity due to high performance achievable on several downstream tasks including node classification. Several architectural variants of these networks have been proposed and investigated…
A formal description of the compositionality of neural networks is associated directly with the formal grammar-structure of the objects it seeks to represent. This formal grammar-structure specifies the kind of components that make up an…
Interactions between units in phyical, biological, technological, and social systems usually give rise to intrincate networks with non-trivial structure, which critically affects the dynamics and properties of the system. The focus of most…
Descriptive and inferential social network analysis has become common in public administration studies of network governance and management. A large literature has developed in two broad categories: antecedents of network structure, and…
This paper presents a unified algebraic, topological, and logical framework for electrical one-port networks based on \v{S}are's $m$-theory. Within this formalism, networks are represented by $m$-words (jorbs) over an ordered alphabet,…
In recent years, a new interest for the use of graph-theory based networks has emerged within the field of cognitive science. This has played a key role in mining the large amount of data generated by word association norms. In the present…
We develop a technique to formulate quantum field theory on arbitrary network, based on different, randomly disposed sets of scattering's. We define R-matrix of the whole network as a product of R-matrices attached to each of scattering…
Entangled quantum networks provide great flexibilities and scalabilities for quantum information processing or quantum Internet. Most of results are focused on the nonlocalities of quantum networks. Our goal in this work is to explore new…
We describe a basic correspondence between linear algebraic structures within vector embeddings in artificial neural networks and conditional independence constraints on the probability distributions modeled by these networks. Our framework…
Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…
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…
An Automata Network is a map ${f:Q^n\rightarrow Q^n}$ where $Q$ is a finite alphabet. It can be viewed as a network of $n$ entities, each holding a state from $Q$, and evolving according to a deterministic synchronous update rule in such a…
The increasing interest in complex networks research has been a consequence of several intrinsic features of this area, such as the generality of the approach to represent and model virtually any discrete system, and the incorporation of…
Network representations of systems from various scientific and societal domains are neither completely random nor fully regular, but instead appear to contain recurring structural building blocks. These features tend to be shared by…
Most existing neural networks for learning graphs address permutation invariance by conceiving of the network as a message passing scheme, where each node sums the feature vectors coming from its neighbors. We argue that this imposes a…