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For the semantic segmentation of images, state-of-the-art deep neural networks (DNNs) achieve high segmentation accuracy if that task is restricted to a closed set of classes. However, as of now DNNs have limited ability to operate in an…

If the training dataset is not very large, image recognition is usually implemented with the transfer learning methods. In these methods the features are extracted using a deep convolutional neural network, which was preliminarily trained…

It is well established that spectral graph neural networks (GNNs) can universally approximate node signals; however, their expressive power remains bounded by the 1-dimensional Weisfeiler-Lehman test, which is mirrored in their lack of…

Fractal scaling--a power-law behavior of the number of boxes needed to tile a given network with respect to the lateral size of the box--is studied. We introduce a new box-covering algorithm that is a modified version of the original…

In an ever expanding set of research and application areas, deep neural networks (DNNs) set the bar for algorithm performance. However, depending upon additional constraints such as processing power and execution time limits, or…

Recent advances in deep learning have transformed many fields by introducing generic embedding spaces, capable of achieving great predictive performance with minimal labeling effort. The geology field has not yet met such success. In this…

Variational Bayesian neural networks (BNNs) perform variational inference over weights, but it is difficult to specify meaningful priors and approximate posteriors in a high-dimensional weight space. We introduce functional variational…

As neural networks are increasingly being applied to real-world applications, mechanisms to address distributional shift and sequential task learning without forgetting are critical. Methods incorporating network expansion have shown…

In the past decade, significant strides in deep learning have led to numerous groundbreaking applications. Despite these advancements, the understanding of the high generalizability of deep learning, especially in such an over-parametrized…

We study the family of functions that are represented by a linear convolutional neural network (LCN). These functions form a semi-algebraic subset of the set of linear maps from input space to output space. In contrast, the families of…

Natural Language Processing (NLP) provides highly effective tools for interpreting and handling human language, offering a broad spectrum of applications. In this paper, we address a classic combinatorial problem -- finding graph partitions…

We study the geometric properties of random neural networks by investigating the boundary volumes of their excursion sets for different activation functions, as the depth increases. More specifically, we show that, for activations which are…

We develop the hypothesis that the dynamics of a given system may lead to the activity being constricted to a subset of space, characterized by a fractal dimension smaller than the space dimension. We also address how the response function…

A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and…

The boundaries of central place models proved to be fractal lines, which compose fractal texture of central place networks. A textural fractal can be employed to explain the scale-free property of regional boundaries such as border lines,…

This paper addresses semantic image segmentation by incorporating rich information into Markov Random Field (MRF), including high-order relations and mixture of label contexts. Unlike previous works that optimized MRFs using iterative…

Fractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise…

Although the remarkable performance of deep neural networks (DNNs) in image classification, their vulnerability to adversarial attacks remains a critical challenge. Most existing detection methods rely on complex and poorly interpretable…

Explaining the prediction of deep neural networks (DNNs) and semantic image compression are two active research areas of deep learning with a numerous of applications in decision-critical systems, such as surveillance cameras, drones and…

Implicit neural representations (INRs) mark a fundamental shift in signal modeling, moving from discrete sampled data to continuous functional representations. By parameterizing signals as neural networks, INRs provide a unified framework…