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We describe the class of convexified convolutional neural networks (CCNNs), which capture the parameter sharing of convolutional neural networks in a convex manner. By representing the nonlinear convolutional filters as vectors in a…

Graph Convolutional Networks (GCNs), similarly to Convolutional Neural Networks (CNNs), are typically based on two main operations - spatial and point-wise convolutions. In the context of GCNs, differently from CNNs, a pre-determined…

Convolutional neural network (CNN) has achieved impressive success in computer vision during the past few decades. The image convolution operation helps CNNs to get good performance on image-related tasks. However, the image convolution has…

Convolutional neural networks (CNNs) have achieved breakthrough performances in a wide range of applications including image classification, semantic segmentation, and object detection. Previous research on characterizing the generalization…

Neural operators have recently become popular tools for designing solution maps between function spaces in the form of neural networks. Differently from classical scientific machine learning approaches that learn parameters of a known…

Despite their impressive performance, contemporary neural networks often lack structural safeguards that promote stable learning and interpretable behavior. In this work, we introduce a reformulation of layer-level transformations that…

Spectral graph convolutional neural networks (CNNs) require approximation to the convolution to alleviate the computational complexity, resulting in performance loss. This paper proposes the topology adaptive graph convolutional network…

Deep learning has established many new state of the art solutions in the last decade in areas such as object, scene and speech recognition. In particular Convolutional Neural Network (CNN) is a category of deep learning which obtains…

Convolutional Neural Networks (CNNs) are the state-of-the-art algorithms for the processing of images. However the configuration and training of these networks is a complex task requiring deep domain knowledge, experience and much trial and…

The hybrid architecture of convolution neural networks (CNN) and Transformer has been the most popular method for medical image segmentation. However, the existing networks based on the hybrid architecture suffer from two problems. First,…

This paper considers a convolutional neural network transformation that reduces computation complexity and thus speedups neural network processing. Usage of convolutional neural networks (CNN) is the standard approach to image recognition…

Inner product-based convolution has been a central component of convolutional neural networks (CNNs) and the key to learning visual representations. Inspired by the observation that CNN-learned features are naturally decoupled with the norm…

It has been repeatedly observed that convolutional architectures when applied to image understanding tasks learn oriented bandpass filters. A standard explanation of this result is that these filters reflect the structure of the images that…

Neural operators learn mappings between function spaces, which is practical for learning solution operators of PDEs and other scientific modeling applications. Among them, the Fourier neural operator (FNO) is a popular architecture that…

Algebraic neural networks (AlgNNs) are composed of a cascade of layers each one associated to and algebraic signal model, and information is mapped between layers by means of a nonlinearity function. AlgNNs provide a generalization of…

Computer vision systems in real-world applications need to be robust to partial occlusion while also being explainable. In this work, we show that black-box deep convolutional neural networks (DCNNs) have only limited robustness to partial…

Neural networks have been widely used, and most networks achieve excellent performance by stacking certain types of basic units. Compared to increasing the depth and width of the network, designing more effective basic units has become an…

Many different deep networks have been used to approximate, accelerate or improve traditional image operators, such as image smoothing, super-resolution and denoising. Among these traditional operators, many contain parameters which need to…

The majority of medical images, especially those that resemble cells, have similar characteristics. These images, which occur in a variety of shapes, often show abnormalities in the organ or cell region. The convolution operation possesses…

Vision transformers have become popular as a possible substitute to convolutional neural networks (CNNs) for a variety of computer vision applications. These transformers, with their ability to focus on global relationships in images, offer…