Related papers: Multilinear Operator Networks

Multimodal named entity recognition (MNER) requires to bridge the gap between language understanding and visual context. While many multimodal neural techniques have been proposed to incorporate images into the MNER task, the model's…

By contextualizing the kernel as global as possible, Modern ConvNets have shown great potential in computer vision tasks. However, recent progress on multi-order game-theoretic interaction within deep neural networks (DNNs) reveals the…

Operator learning trains a neural network to map functions to functions. An ideal operator learning framework should be mesh-free in the sense that the training does not require a particular choice of discretization for the input functions,…

Ophthalmic image segmentation serves as a critical foundation for ocular disease diagnosis. Although fully convolutional neural networks (CNNs) are commonly employed for segmentation, they are constrained by inductive biases and face…

Recent guided depth super-resolution methods are premised on the assumption of strict spatial alignment between depth and RGB, achieving high-quality depth reconstruction. However, in real-world scenarios, the acquisition of strictly…

Deep convolutional neural networks (CNN) have shown their promise as a universal representation for recognition. However, global CNN activations lack geometric invariance, which limits their robustness for classification and matching of…

Deep Operator Network (DeepONet) is a neural network framework for learning nonlinear operators such as those from ordinary differential equations (ODEs) describing complex systems. Multiple-input deep neural operators (MIONet) extended…

Operator learning provides methods to approximate mappings between infinite-dimensional function spaces. Deep operator networks (DeepONets) are a notable architecture in this field. Recently, an extension of DeepONet based on model…

This paper introduces a network architecture, called dynoNet, utilizing linear dynamical operators as elementary building blocks. Owing to the dynamical nature of these blocks, dynoNet networks are tailored for sequence modeling and system…

We introduce a deep multitask architecture to integrate multityped representations of multimodal objects. This multitype exposition is less abstract than the multimodal characterization, but more machine-friendly, and thus is more precise…

As an emerging paradigm in scientific machine learning, neural operators aim to learn operators, via neural networks, that map between infinite-dimensional function spaces. Several neural operators have been recently developed. However, all…

Predicting multiple real-world tasks in a single model often requires a particularly diverse feature space. Multimodal (MM) models aim to extract the synergistic predictive potential of multiple data types to create a shared feature space…

Neural operators have emerged as an efficient paradigm for solving PDEs, overcoming the limitations of traditional numerical methods and significantly improving computational efficiency. However, due to the diversity and complexity of PDE…

Transformer is a popularly used neural network architecture, especially for language understanding. We introduce an extended and unified architecture that can be used for tasks involving a variety of modalities like image, text, videos,…

Multilayer networks provide a powerful framework for modeling complex systems that capture different types of interactions between the same set of entities across multiple layers. Core-periphery detection involves partitioning the nodes of…

We introduce a new class of non-linear models for functional data based on neural networks. Deep learning has been very successful in non-linear modeling, but there has been little work done in the functional data setting. We propose two…

Network motifs can capture basic interaction patterns and inform the functional properties of networks. However, real-world complex systems often have multiple types of relationships, which cannot be represented by a monolayer network. The…

Feed-forward, fully-connected Artificial Neural Networks (ANNs) or the so-called Multi-Layer Perceptrons (MLPs) are well-known universal approximators. However, their learning performance varies significantly depending on the function or…

The study of complex networks has been historically based on simple graph data models representing relationships between individuals. However, often reality cannot be accurately captured by a flat graph model. This has led to the…

A Multilayer Network (MN) is a system consisting of several topological levels (i.e., layers) representing the interactions between the system's objects and the related interdependency. Therefore, it may be represented as a set of layers…