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We propose a general architecture that combines the coefficient learning scheme with a residual operator layer for learning mappings between continuous functions in the 3D Euclidean space. Our proposed model is guaranteed to achieve…
In representation learning on graph-structured data, many popular graph neural networks (GNNs) fail to capture long-range dependencies, leading to performance degradation. Furthermore, this weakness is magnified when the concerned graph is…
Interpreting graph neural networks (GNNs) is difficult because message passing mixes signals and internal channels rarely align with human concepts. We study superposition, the sharing of directions by multiple features, directly in the…
We present a novel approach to neural response prediction that incorporates higher-order operations directly within convolutional neural networks (CNNs). Our model extends traditional 3D CNNs by embedding higher-order operations within the…
In this study, we present the Graph Sub-Graph Network (GSN), a novel hybrid image classification model merging the strengths of Convolutional Neural Networks (CNNs) for feature extraction and Graph Neural Networks (GNNs) for structural…
Graph Neural Networks (GNNs) are characterized by their capacity of processing graph-structured data. However, due to the sparsity of labels under semi-supervised learning, they have been found to exhibit biased performance on specific…
Graph convolutional network (GCN) based approaches have achieved significant progress for solving complex, graph-structured problems. GCNs incorporate the graph structure information and the node (or edge) features through message passing…
Message-passing neural networks (MPNNs) have been successfully applied to representation learning on graphs in a variety of real-world applications. However, two fundamental weaknesses of MPNNs' aggregators limit their ability to represent…
Non-local self-similarity is well-known to be an effective prior for the image denoising problem. However, little work has been done to incorporate it in convolutional neural networks, which surpass non-local model-based methods despite…
Euclidean deep learning is often inadequate for addressing real-world signals where the representation space is irregular and curved with complex topologies. Interpreting the geometric properties of such feature spaces has become paramount…
Network representation learning has aroused widespread interests in recent years. While most of the existing methods deal with edges as pairwise relationships, only a few studies have been proposed for hyper-networks to capture more…
We study exceptional torsion in the integral cohomology of a family of p-groups associated to p-adic Lie algebras. A spectral sequence E_r^{*,*}[g] is defined for any Lie algebra g which models the Bockstein spectral sequence of the…
This paper presents an adaptive convolutional neural network (CNN) architecture that can automate diverse topology optimization (TO) problems having different underlying physics. The architecture uses the encoder-decoder networks with dense…
The translation equivariance of convolutional layers enables convolutional neural networks to generalize well on image problems. While translation equivariance provides a powerful inductive bias for images, we often additionally desire…
Convolutional neural networks are nowadays witnessing a major success in different pattern recognition problems. These learning models were basically designed to handle vectorial data such as images but their extension to non-vectorial and…
We present a logarithmic-scale efficient convolutional neural network architecture for edge devices, named WaveletNet. Our model is based on the well-known depthwise convolution, and on two new layers, which we introduce in this work: a…
We introduce the notion of an `inverse property' (IP) quandle C which we propose as the right notion of `Lie algebra' in the category of sets. To any IP quandle we construct an associated group G_C. For a class of IP quandles which we call…
The rapid progress of Artificial Intelligence research came with the development of increasingly complex deep learning models, leading to growing challenges in terms of computational complexity, energy efficiency and interpretability. In…
We present a new approach to 3D object representation where a neural network encodes the geometry of an object directly into the weights and biases of a second 'mapping' network. This mapping network can be used to reconstruct an object by…
In this paper, we introduce the notion of a (regular) Hom-Lie group. We associate a Hom-Lie algebra to a Hom-Lie group and show that every regular Hom-Lie algebra is integrable. Then, we define a Hom-exponential (Hexp) map from the Hom-Lie…