Related papers: Expression of Fractals Through Neural Network Func…

In recent decades, digital image processing has gained enormous popularity. Consequently, a number of data compression strategies have been put forth, with the goal of minimizing the amount of information required to represent images. Among…

We present a physically-motivated topology of a deep neural network that can efficiently infer extensive parameters (such as energy, entropy, or number of particles) of arbitrarily large systems, doing so with O(N) scaling. We use a form of…

Modern deep neural networks have achieved impressive performance on tasks from image classification to natural language processing. Surprisingly, these complex systems with massive amounts of parameters exhibit the same structural…

Fractal analysis has been widely used in computer vision, especially in texture image processing and texture analysis. The key concept of fractal-based image model is the fractal dimension, which is invariant to bi-Lipschitz transformation…

Semi-structured networks (SSNs) merge the structures familiar from additive models with deep neural networks, allowing the modeling of interpretable partial feature effects while capturing higher-order non-linearities at the same time. A…

The interpretation of reasoning by Deep Neural Networks (DNN) is still challenging due to their perceived black-box nature. Therefore, deploying DNNs in several real-world tasks is restricted by the lack of transparency of these models. We…

Generating natural language descriptions for images is a challenging task. The traditional way is to use the convolutional neural network (CNN) to extract image features, followed by recurrent neural network (RNN) to generate sentences. In…

Humans are able to segment images effortlessly without supervision using perceptual grouping. Here, we propose a counter-intuitive computational approach to solving unsupervised perceptual grouping and segmentation: that they arise because…

Deep Neural Networks (DNNs) have already become a crucial computational approach to revealing the spatial patterns in the human brain; however, there are three major shortcomings in utilizing DNNs to detect the spatial patterns in…

Deep generative neural networks (DGNNs) have achieved realistic and high-quality data generation. In particular, the adversarial training scheme has been applied to many DGNNs and has exhibited powerful performance. Despite of recent…

We propose a novel perspective to understand deep neural networks in an interpretable disentanglement form. For each semantic class, we extract a class-specific functional subnetwork from the original full model, with compressed structure…

Feature propagation in Deep Neural Networks (DNNs) can be associated to nonlinear discrete dynamical systems. The novelty, in this paper, lies in letting the discretization parameter (time step-size) vary from layer to layer, which needs to…

We consider iterated function systems on the real line that consist of continuous, piecewise linear functions. Under a mild separation condition, we show that the Hausdorff and box dimensions of the attractor are equal to the minimum of 1…

Building discriminative representations for 3D data has been an important task in computer graphics and computer vision research. Convolutional Neural Networks (CNNs) have shown to operate on 2D images with great success for a variety of…

Deep neural networks have been widely applied in dichotomous medical image segmentation (DMIS) of many anatomical structures in several modalities, achieving promising performance. However, existing networks tend to struggle with…

Several fundamental properties of real complex networks, such as the small-world effect, the scale-free degree distribution, and recently discovered topological fractal structure, have presented the possibility of a unique growth mechanism…

We present an explicit construction for feedforward neural network (FNN), which provides a piecewise constant approximation for multivariate functions. The proposed FNN has two hidden layers, where the weights and thresholds are explicitly…

Deep learning has been extensively employed as a powerful function approximator for modeling physics-based problems described by partial differential equations (PDEs). Despite their popularity, standard deep learning models often demand…

DNNs have gained widespread adoption in feature interaction recommendation models. However, there has been a longstanding debate on their roles. On one hand, some works claim that DNNs possess the ability to implicitly capture high-order…

We describe a class of neuralized fermionic tensor network states (NN-fTNS) that introduce non-linearity into fermionic tensor networks through configuration-dependent neural network transformations of the local tensors. The construction…