Related papers: Multilinear Operator Networks

Deep operator networks (DeepONets, DONs) offer a distinct advantage over traditional neural networks in their ability to be trained on multi-resolution data. This property becomes especially relevant in real-world scenarios where…

The information processing abilities of a multilayer neural network with a number of hidden units scaling as the input dimension are studied using statistical mechanics methods. The mapping from the input layer to the hidden units is…

Rich phenomena from complex systems have long intrigued researchers, and yet modeling system micro-dynamics and inferring the forms of interaction remain challenging for conventional data-driven approaches, being generally established by…

In this article we present new results on neural networks with linear threshold activation functions. We precisely characterize the class of functions that are representable by such neural networks and show that 2 hidden layers are…

The objective of this work is set-based face recognition, i.e. to decide if two sets of images of a face are of the same person or not. Conventionally, the set-wise feature descriptor is computed as an average of the descriptors from…

In recent years, deep neural networks (DNNs) achieved unprecedented performance in many low-level vision tasks. However, state-of-the-art results are typically achieved by very deep networks, which can reach tens of layers with tens of…

The recovery of magnetic resonance (MR) images from undersampled measurements is a key problem that has seen extensive research in recent years. Unrolled approaches, which rely on end-to-end training of convolutional neural network (CNN)…

In this paper, we propose a deep neural network architecture for object recognition based on recurrent neural networks. The proposed network, called ReNet, replaces the ubiquitous convolution+pooling layer of the deep convolutional neural…

In this paper, we propose a multiscale DeepONet to represent nonlinear operator between Banach spaces of highly oscillatory continuous functions. The multiscale deep neural network (DNN) utilizes a multiple scaling technique to convert high…

In this paper, an innovative multi-modal deep learning model is proposed to deeply integrate heterogeneous information from medical images and clinical reports. First, for medical images, convolutional neural networks were used to extract…

An important application of neural networks to scientific computing has been the learning of non-linear operators. In this framework, a neural network is trained to fit a non-linear map between two infinite dimensional spaces, for example,…

Recent NLP studies reveal that substantial linguistic information can be attributed to single neurons, i.e., individual dimensions of the representation vectors. We hypothesize that modeling strong interactions among neurons helps to better…

In this paper, we present a new kind of learning implementation to recognize the patterns using the concept of Mirroring Neural Network (MNN) which can extract information from distinct sensory input patterns and perform pattern recognition…

Singularly perturbed problems present inherent difficulty due to the presence of a thin boundary layer in its solution. To overcome this difficulty, we propose using deep operator networks (DeepONets), a method previously shown to be…

The optical neural network (ONN) is a promising hardware platform for next-generation neuromorphic computing due to its high parallelism, low latency, and low energy consumption. However, previous integrated photonic tensor cores (PTCs)…

Learning social media data embedding by deep models has attracted extensive research interest as well as boomed a lot of applications, such as link prediction, classification, and cross-modal search. However, for social images which contain…

Designing effective neural networks is fundamentally important in deep multimodal learning. Most existing works focus on a single task and design neural architectures manually, which are highly task-specific and hard to generalize to…

In this paper, we propose a new deep network that learns multi-level deep representations for image emotion classification (MldrNet). Image emotion can be recognized through image semantics, image aesthetics and low-level visual features…

The excellent performance of deep neural networks has enabled us to solve several automatization problems, opening an era of autonomous devices. However, current deep net architectures are heavy with millions of parameters and require…

Semantic segmentation of remote sensing images plays an important role in a wide range of applications including land resource management, biosphere monitoring and urban planning. Although the accuracy of semantic segmentation in remote…