Related papers: Fully trainable Gaussian derivative convolutional …
Steerable convolutional neural networks (CNNs) provide a general framework for building neural networks equivariant to translations and transformations of an origin-preserving group $G$, such as reflections and rotations. They rely on…
Currently, increasingly deeper neural networks have been applied to improve their accuracy. In contrast, We propose a novel wider Convolutional Neural Networks (CNN) architecture, motivated by the Multi-column Deep Neural Networks and the…
This paper investigates the usage of kernel functions at the different layers in a convolutional neural network. We carry out extensive studies of their impact on convolutional, pooling and fully-connected layers. We notice that the linear…
Neural networks have achieved remarkable empirical performance, while the current theoretical analysis is not adequate for understanding their success, e.g., the Neural Tangent Kernel approach fails to capture their key feature learning…
Convolutional neural networks (CNNs) have demonstrated their capability to solve different kind of problems in a very huge number of applications. However, CNNs are limited for their computational and storage requirements. These limitations…
Neal (1996) proved that infinitely wide shallow Bayesian neural networks (BNN) converge to Gaussian processes (GP), when the network weights have bounded prior variance. Cho & Saul (2009) provided a useful recursive formula for deep kernel…
The Convolutional Neural Network (CNN) has been successfully applied in many fields during recent decades; however it lacks the ability to utilize prior domain knowledge when dealing with many realistic problems. We present a framework…
Convolutional Neural Networks (CNNs) achieve impressive performance in a wide variety of fields. Their success benefited from a massive boost when very deep CNN models were able to be reliably trained. Despite their merits, CNNs fail to…
Generative Adversarial Networks (GANs) have been very successful for synthesizing the images in a given dataset. The artificially generated images by GANs are very realistic. The GANs have shown potential usability in several computer…
It is a consensus in signal processing that the Gaussian kernel and its partial derivatives enable the development of robust algorithms for feature detection. Fourier analysis and convolution theory have central role in such development. In…
The convolutional layer and loss function are two fundamental components in deep learning. Because of the success of conventional deep learning kernels, the less versatile Gabor kernels become less popular despite the fact that they can…
Machine learning methods on graphs have proven useful in many applications due to their ability to handle generally structured data. The framework of Gaussian Markov Random Fields (GMRFs) provides a principled way to define Gaussian models…
Gaussian processes are flexible function approximators, with inductive biases controlled by a covariance kernel. Learning the kernel is the key to representation learning and strong predictive performance. In this paper, we develop…
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…
Gaussian Processes (GPs) are known to provide accurate predictions and uncertainty estimates even with small amounts of labeled data by capturing similarity between data points through their kernel function. However traditional GP kernels…
This paper investigates efficient deep neural networks (DNNs) to replace dense unstructured weight matrices with structured ones that possess desired properties. The challenge arises because the optimal weight matrix structure in popular…
Deep neural networks (DNN) and Gaussian processes (GP) are two powerful models with several theoretical connections relating them, but the relationship between their training methods is not well understood. In this paper, we show that…
In convolutional neural networks, the convolutions are conventionally performed using a square kernel with a fixed N $\times$ N receptive field (RF). However, what matters most to the network is the effective receptive field (ERF) that…
While kernel methods and Graph Neural Networks offer complementary strengths, integrating the two has posed challenges in efficiency and scalability. The Graph Neural Tangent Kernel provides a theoretical bridge by interpreting GNNs through…
A generative Bayesian model is developed for deep (multi-layer) convolutional dictionary learning. A novel probabilistic pooling operation is integrated into the deep model, yielding efficient bottom-up and top-down probabilistic learning.…