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The field of Graph Signal Processing (GSP) has proposed tools to generalize harmonic analysis to complex domains represented through graphs. Among these tools are translations, which are required to define many others. Most works propose to…

Classical tensors, the familiar mathematical objects denoted by symbols such as $t_{i}$, $t^{ij}$ and $t_{k}^{ij}$, are usually interpreted either as 'coordinatizable objects' with coordinates changing in a specific way under a change of…

Many modern data analytics applications on graphs operate on domains where graph topology is not known a priori, and hence its determination becomes part of the problem definition, rather than serving as prior knowledge which aids the…

Tensor decomposition methods are widely used for model compression and fast inference in convolutional neural networks (CNNs). Although many decompositions are conceivable, only CP decomposition and a few others have been applied in…

Rich semantic relations are important in a variety of visual recognition problems. As a concrete example, group activity recognition involves the interactions and relative spatial relations of a set of people in a scene. State of the art…

Tensor decomposition is an important technique for capturing the high-order interactions among multiway data. Multi-linear tensor composition methods, such as the Tucker decomposition and the CANDECOMP/PARAFAC (CP), assume that the complex…

Interpretability has emerged as a crucial aspect of building trust in machine learning systems, aimed at providing insights into the working of complex neural networks that are otherwise opaque to a user. There are a plethora of existing…

In mathematics, many notations have been invented for the concise representation of mathematical formulae. Tensor index notation is one of such notations and has been playing a crucial role in describing formulae in mathematical physics.…

Machine learning and data mining algorithms are becoming increasingly important in analyzing large volume, multi-relational and multi--modal datasets, which are often conveniently represented as multiway arrays or tensors. It is therefore…

We present a data-driven framework to automate the vectorization and machine interpretation of 2D engineering part drawings. In industrial settings, most manufacturing engineers still rely on manual reads to identify the topological and…

Graph Neural Networks (GNNs) are a powerful tool for machine learning on graphs.GNNs combine node feature information with the graph structure by recursively passing neural messages along edges of the input graph. However, incorporating…

We propose a method to construct the initial tensor representation of partition functions and observables for the tensor renormalization group (TRG). The TRG is a numerical calculation technique that utilizes a tensor network…

Recently, hetero-functional graph theory (HFGT) has developed as a means to mathematically model the structure of large-scale complex flexible engineering systems. It does so by fusing concepts from network science and model-based systems…

We propose neural-symbolic integration for abstract concept explanation and interactive learning. Neural-symbolic integration and explanation allow users and domain-experts to learn about the data-driven decision making process of large…

Graph convolutional networks (GCNs) aim at extending deep learning to arbitrary irregular domains, namely graphs. Their success is highly dependent on how the topology of input graphs is defined and most of the existing GCN architectures…

Graph neural networks form a class of deep learning architectures specifically designed to work with graph-structured data. As such, they share the inherent limitations and problems of deep learning, especially regarding the issues of…

Deep learning is currently the subject of intensive study. However, fundamental concepts such as representations are not formally defined -- researchers "know them when they see them" -- and there is no common language for describing and…

This paper reviews recent studies in understanding neural-network representations and learning neural networks with interpretable/disentangled middle-layer representations. Although deep neural networks have exhibited superior performance…

This study reports an unintuitive finding that positional encoding enhances learning of recurrent neural networks (RNNs). Positional encoding is a high-dimensional representation of time indices on input data. Most famously, positional…

Deep neural networks (DNNs) with high expressiveness have achieved state-of-the-art performance in many tasks. However, their distributed feature representations are difficult to interpret semantically. In this work, human-interpretable…