Related papers: Persformer: A Transformer Architecture for Topolog…

A persistence diagram provides a compact summary of persistent homology, which captures the topological features of a space at different scales. However, due to its nature as a set, incorporating it as a feature into a machine learning…

To improve persistence diagram representation learning, we propose Multiset Transformer. This is the first neural network that utilizes attention mechanisms specifically designed for multisets as inputs and offers rigorous theoretical…

Topological Data Analysis (TDA) is a novel statistical technique, particularly powerful for the analysis of large and high dimensional data sets. Much of TDA is based on the tool of persistent homology, represented visually via persistence…

Topological data analysis (TDA) provides insight into data shape. The summaries obtained by these methods are principled global descriptions of multi-dimensional data whilst exhibiting stable properties such as robustness to deformation and…

TDA (topological data analysis) is a relatively new area of research related to importing classical ideas from topology into the realm of data analysis. Under the umbrella term TDA, there falls, in particular, the notion of persistent…

Topological Data Analysis (TDA) is a rising field of computational topology in which the topological structure of a data set can be observed by persistent homology. By considering a sequence of sublevel sets, one obtains a filtration that…

Despite significant advances in the field of deep learning in ap-plications to various areas, an explanation of the learning pro-cess of neural network models remains an important open ques-tion. The purpose of this paper is a comprehensive…

Recurrent Neural Networks were, until recently, one of the best ways to capture the timely dependencies in sequences. However, with the introduction of the Transformer, it has been proven that an architecture with only attention-mechanisms…

While convolutional neural networks have shown a tremendous impact on various computer vision tasks, they generally demonstrate limitations in explicitly modeling long-range dependencies due to the intrinsic locality of the convolution…

Topological data analysis (TDA) delivers invaluable and complementary information on the intrinsic properties of data inaccessible to conventional methods. However, high computational costs remain the primary roadblock hindering the…

Conventional machine learning algorithms have traditionally been designed under the assumption that input data follows a vector-based format, with an emphasis on vector-centric paradigms. However, as the demand for tasks involving set-based…

Topological data analysis (TDA) is a branch of computational mathematics, bridging algebraic topology and data science, that provides compact, noise-robust representations of complex structures. Deep neural networks (DNNs) learn millions of…

Topological methods for data analysis present opportunities for enforcing certain invariances of broad interest in computer vision, including view-point in activity analysis, articulation in shape analysis, and measurement invariance in…

The transformer is a neural network component that can be used to learn useful representations of sequences or sets of data-points. The transformer has driven recent advances in natural language processing, computer vision, and…

Topological data analysis uses tools from topology -- the mathematical area that studies shapes -- to create representations of data. In particular, in persistent homology, one studies one-parameter families of spaces associated with data,…

Under the banner of `Big Data', the detection and classification of structure in extremely large, high dimensional, data sets, is, one of the central statistical challenges of our times. Among the most intriguing approaches to this…

Retentive Network (RetNet) represents a significant advancement in neural network architecture, offering an efficient alternative to the Transformer. While Transformers rely on self-attention to model dependencies, they suffer from high…

In many real-world scenarios, data to train machine learning models become available over time. However, neural network models struggle to continually learn new concepts without forgetting what has been learnt in the past. This phenomenon…

Topological Data Analysis (TDA) provides tools to describe the shape of data, but integrating topological features into deep learning pipelines remains challenging, especially when preserving local geometric structure rather than…

Topological data analysis (TDA) provides a set of data analysis tools for extracting embedded topological structures from complex high-dimensional datasets. In recent years, TDA has been a rapidly growing field which has found success in a…