Related papers: Cell Complex Neural Networks
Deep Neural Networks are, from a physical perspective, graphs whose `links` and `vertices` iteratively process data and solve tasks sub-optimally. We use Complex Network Theory (CNT) to represents Deep Neural Networks (DNNs) as directed…
Convolutional neural networks (CNNs) leverage the great power in representation learning on regular grid data such as image and video. Recently, increasing attention has been paid on generalizing CNNs to graph or network data which is…
Graphs are ubiquitous data structures for representing interactions between entities. With an emphasis on the use of graphs to represent chemical molecules, we explore the task of learning to generate graphs that conform to a distribution…
In the last decade or so, we have witnessed deep learning reinvigorating the machine learning field. It has solved many problems in the domains of computer vision, speech recognition, natural language processing, and various other tasks…
Recently, self-sustained oscillations in complex networks consisting of nonoscillatory nodes (network oscillators) have attracted great interest in diverse natural and social fields. Due to complexity of network behaviors, little is known…
We present an intuitive formalism for implementing cellular automata on arbitrary topologies. By that means, we identify a symmetry operation in the class of elementary cellular automata. Moreover, we determine the subset of topologically…
Identify the cells' nuclei is the important point for most medical analyses. To assist doctors finding the accurate cell' nuclei location automatically is highly demanded in the clinical practice. Recently, fully convolutional neural…
This article introduces descriptive cellular homology on cell complexes, which is an extension of J.H.C. Whitehead's CW topology. A main result is that a descriptive cellular complex is a topology on fibres in a fibre bundle. An application…
As a popular machine learning method, neural networks can be used to solve many complex tasks. Their strong generalization ability comes from the representation ability of the basic neuron model. The most popular neuron is the MP neuron,…
Graphs neural networks (GNNs) learn node features by aggregating and combining neighbor information, which have achieved promising performance on many graph tasks. However, GNNs are mostly treated as black-boxes and lack human intelligible…
Patterns stored within pre-trained deep neural networks compose large and powerful descriptive languages that can be used for many different purposes. Typically, deep network representations are implemented within vector embedding spaces,…
The representation of complex systems as networks is inappropriate for the study of certain problems. We show several examples of social, biological, ecological and technological systems where the use of complex networks gives very limited…
Deep learning has taken part in the competition since not long ago to learn and identify phase transitions in physical systems such as many body quantum systems, whose underlying lattice structures are generally regular as they're in…
Shape graphs are complex geometrical structures commonly found in biological and anatomical systems. A shape graph is a collection of nodes, some connected by curvilinear edges with arbitrary shapes. Their high complexity stems from the…
Providing an abstract representation of natural and human complex structures is a challenging problem. Accounting for the system heterogenous components while allowing for analytical tractability is a difficult balance. Here I introduce…
Simplicial neural networks (SNN) have recently emerged as the newest direction in graph learning which expands the idea of convolutional architectures from node space to simplicial complexes on graphs. Instead of pre-dominantly assessing…
We introduce a unified theoretical framework for the rigorous analysis and systematic construction of deep neural networks (DNNs). This framework addresses a gap in existing theory by explicitly modeling the structure of tensor operations…
Graph neural networks trained to predict observable dynamics can be used to decompose the temporal activity of complex heterogeneous systems into simple, interpretable representations. Here we apply this framework to simulated neural…
Modern communication networks are inherently complex in nature. First of all, they have a large number of heterogeneous components. Secondly, their connectivity is extremely dynamic. Nodes can come and go, links can be removed and added…
Graph Neural Networks (GNNs) are a framework for graph representation learning, where a model learns to generate low dimensional node embeddings that encapsulate structural and feature-related information. GNNs are usually trained in an…