Related papers: Understanding Convolutional Neural Networks with I…
While initially devised for image categorization, convolutional neural networks (CNNs) are being increasingly used for the pixelwise semantic labeling of images. However, the proper nature of the most common CNN architectures makes them…
We propose a principled convolutional neural pyramid (CNP) framework for general low-level vision and image processing tasks. It is based on the essential finding that many applications require large receptive fields for structure…
Over the long history of machine learning, which dates back several decades, recurrent neural networks (RNNs) have been used mainly for sequential data and time series and generally with 1D information. Even in some rare studies on 2D…
We introduce the matrix-based Renyi's $\alpha$-order entropy functional to parameterize Tishby et al. information bottleneck (IB) principle with a neural network. We term our methodology Deep Deterministic Information Bottleneck (DIB), as…
Although standard Convolutional Neural Networks (CNNs) can be mathematically reinterpreted as Self-Explainable Models (SEMs), their built-in prototypes do not on their own accurately represent the data. Replacing the final linear layer with…
Motivated by the growing interest in representation learning approaches that uncover the latent structure of high-dimensional data, this work proposes new algorithms for reconstruction-based manifold learning within Reproducing-Kernel…
When optimizing convolutional neural networks (CNN) for a specific image-based task, specialists commonly overshoot the number of convolutional layers in their designs. By implication, these CNNs are unnecessarily resource intensive to…
Convolutional neural networks (CNNs) are able to attain better visual recognition performance than fully connected neural networks despite having much fewer parameters due to their parameter sharing principle. Modern architectures usually…
We study the sample complexity of learning one-hidden-layer convolutional neural networks (CNNs) with non-overlapping filters. We propose a novel algorithm called approximate gradient descent for training CNNs, and show that, with high…
Convolutional neural networks (CNNs) trained with cross-entropy loss have proven to be extremely successful in classifying images. In recent years, much work has been done to also improve the theoretical understanding of neural networks.…
This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…
Convolutional neural networks (CNNs) have shown exceptional performance for a range of medical imaging tasks. However, conventional CNNs are not able to explain their reasoning process, therefore limiting their adoption in clinical…
Kernel pruning methods have been proposed to speed up, simplify, and improve explanation of convolutional neural network (CNN) models. However, the effectiveness of a simplified model is often below the original one. In this letter, we…
We introduce a novel convolutional neural network architecture, termed the \emph{periodic CNN}, which incorporates periodic boundary conditions into the convolutional layers. Our main theoretical contribution is a rigorous approximation…
Convolutional Neural Networks (CNNs) are build specifically for computer vision tasks for which it is known that the input data is a hierarchical structure based on locally correlated elements. The question that naturally arises is what…
In the present study, the capabilities of a new Convolutional Neural Network (CNN) model are explored with the paramount objective of reconstructing the temperature field of wall-bounded flows based on a limited set of measurement points…
We introduce a divergence measure between data distributions based on operators in reproducing kernel Hilbert spaces defined by kernels. The empirical estimator of the divergence is computed using the eigenvalues of positive definite Gram…
This paper presents an unsupervised method to learn a neural network, namely an explainer, to interpret a pre-trained convolutional neural network (CNN), i.e., the explainer uses interpretable visual concepts to explain features in middle…
Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…
We introduce a class of convolutional neural networks (CNNs) that utilize recurrent neural networks (RNNs) as convolution filters. A convolution filter is typically implemented as a linear affine transformation followed by a non-linear…