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Brain networks exhibit complications such as noise, neuron failures, and partial synaptic connectivity. These can make it difficult to model and analyze their behavior. This paper describes a way to address this difficulty, namely, breaking…
Graph neural networks (GNNs) are a powerful tool to learn representations on graphs by iteratively aggregating features from node neighbourhoods. Many variant models have been proposed, but there is limited understanding on both how to…
Image recognition tasks that involve identifying parts of an object or the contents of a vessel can be viewed as a hierarchical problem, which can be solved by initial recognition of the main object, followed by recognition of its parts or…
Graph neural networks have emerged as a leading architecture for many graph-level tasks, such as graph classification and graph generation. As an essential component of the architecture, graph pooling is indispensable for obtaining a…
Recent advances in the integration of deep learning with automated theorem proving have centered around the representation of logical formulae as inputs to deep learning systems. In particular, there has been a growing interest in adapting…
Geometric trees are characterized by their tree-structured layout and spatially constrained nodes and edges, which significantly impacts their topological attributes. This inherent hierarchical structure plays a crucial role in domains such…
Deep neural networks achieve outstanding results in a large variety of tasks, often outperforming human experts. However, a known limitation of current neural architectures is the poor accessibility to understand and interpret the network…
Two architectures that generalize convolutional neural networks (CNNs) for the processing of signals supported on graphs are introduced. We start with the selection graph neural network (GNN), which replaces linear time invariant filters…
Current image processing methods usually operate on the finest-granularity unit; that is, the pixel, which leads to challenges in terms of efficiency, robustness, and understandability in deep learning models. We present an improved…
Graph Neural Networks (GNNs), which generalize deep neural networks to graph-structured data, have drawn considerable attention and achieved state-of-the-art performance in numerous graph related tasks. However, existing GNN models mainly…
We describe how hierarchical concepts can be represented in three types of layered neural networks. The aim is to support recognition of the concepts when partial information about the concepts is presented, and also when some of the…
In this work we study the problem of network morphism, an effective learning scheme to morph a well-trained neural network to a new one with the network function completely preserved. Different from existing work where basic morphing types…
Convolutional layers in graph neural networks are a fundamental type of layer which output a representation or embedding of each graph vertex. The representation typically encodes information about the vertex in question and its…
Graph Neural Networks (GNNs), neural network architectures targeted to learning representations of graphs, have become a popular learning model for prediction tasks on nodes, graphs and configurations of points, with wide success in…
We continue our study from Lynch and Mallmann-Trenn (Neural Networks, 2021), of how concepts that have hierarchical structure might be represented in brain-like neural networks, how these representations might be used to recognize the…
Network representation aims to represent the nodes in a network as continuous and compact vectors, and has attracted much attention in recent years due to its ability to capture complex structure relationships inside networks. However,…
The transformer is a neural network component that can be used to learn useful representations of sequences or sets of data-points. The transformer has driven recent advances in natural language processing, computer vision, and…
In this manuscript, we show that any neural network with any activation function can be represented as a decision tree. The representation is equivalence and not an approximation, thus keeping the accuracy of the neural network exactly as…
Reasoning, the ability to logically draw conclusions from existing knowledge, is a hallmark of human. Together with perception, they constitute the two major themes of artificial intelligence. While deep learning has pushed the limit of…
In many ways, graphs are the main modality of data we receive from nature. This is due to the fact that most of the patterns we see, both in natural and artificial systems, are elegantly representable using the language of graph structures.…