Related papers: Characterization of topological structures in diff…
In this thesis, we develop various techniques for working with sets in machine learning. Each input or output is not an image or a sequence, but a set: an unordered collection of multiple objects, each object described by a feature vector.…
One of the main drawbacks of the practical use of neural networks is the long time required in the training process. Such a training process consists of an iterative change of parameters trying to minimize a loss function. These changes are…
Vision Transformer (ViT) is emerging as the state-of-the-art architecture for image recognition. While recent studies suggest that ViTs are more robust than their convolutional counterparts, our experiments find that ViTs trained on…
Deep learning network training is usually computationally expensive and intuitively complex. We present a novel network architecture for custom training and weight evaluations. We reformulate the layers as ResNet-similar blocks with certain…
Topological Data Analysis (TDA) has recently gained significant attention in the field of financial prediction. However, the choice of point cloud construction methods, topological feature representations, and classification models has a…
We present the application of topological data analysis (TDA) to study unweighted complex networks via their persistent homology. By endowing appropriate weights that capture the inherent topological characteristics of such a network, we…
Texture, a significant visual attribute in images, has been extensively investigated across various image recognition applications. Convolutional Neural Networks (CNNs), which have been successful in many computer vision tasks, are…
Vision transformers (ViTs) have been successfully applied in image classification tasks recently. In this paper, we show that, unlike convolution neural networks (CNNs)that can be improved by stacking more convolutional layers, the…
We present a new distributed representation in deep neural nets wherein the information is represented in native form as a matrix. This differs from current neural architectures that rely on vector representations. We consider matrices as…
This work begins by establishing a mathematical formalization between different geometrical interpretations of Neural Networks, providing a first contribution. From this starting point, a new interpretation is explored, using the idea of…
We perform topological data analysis on the internal states of convolutional deep neural networks to develop an understanding of the computations that they perform. We apply this understanding to modify the computations so as to (a) speed…
With the wide and deep adoption of deep learning models in real applications, there is an increasing need to model and learn the representations of the neural networks themselves. These models can be used to estimate attributes of different…
Deep neural networks proved to be a very useful and powerful tool with many practical applications. They especially excel at learning from large data sets with labeled samples. However, in order to achieve good learning results, the network…
With the widespread use of information technologies, information networks are becoming increasingly popular to capture complex relationships across various disciplines, such as social networks, citation networks, telecommunication networks,…
Combinatorial and topological structures, such as graphs, simplicial complexes, and cell complexes, form the foundation of geometric and topological deep learning (GDL and TDL) architectures. These models aggregate signals over such…
The paper aims to investigate relevant computational issues of deep neural network architectures with an eye to the interaction between the optimization algorithm and the classification performance. In particular, we aim to analyze the…
Topological Data Analysis (TDA) can broadly be described as a collection of data analysis methods that find structure in data. This includes: clustering, manifold estimation, nonlinear dimension reduction, mode estimation, ridge estimation…
Topological Data Analysis (TDA) provides powerful tools to explore the shape and structure of data through topological features such as clusters, loops, and voids. Persistence diagrams are a cornerstone of TDA, capturing the evolution of…
Deep Neural Networks (DNN) have shown great promise in many classification applications, yet are widely known to have poorly calibrated predictions when they are over-parametrized. Improving DNN calibration without comprising on model…
Discovering a suitable neural network architecture for modeling complex dynamical systems poses a formidable challenge, often involving extensive trial and error and navigation through a high-dimensional hyper-parameter space. In this…