Related papers: From trees to barcodes and back again: theoretical…

Modern deep neural networks have shown remarkable performance in medical image classification. However, such networks either emphasize pixel-intensity features instead of fundamental anatomical structures (e.g., those encoded by topological…

The inner representation of deep neural networks (DNNs) is indecipherable, which makes it difficult to tune DNN models, control their training process, and interpret their outputs. In this paper, we propose a novel approach to investigate…

Data representation remains a fundamental challenge in machine learning, particularly when adapting sequence-based architectures like Transformers and Large Language Models (LLMs) for structured tabular data. Existing methods often fail to…

Parts of the brain that carry sensory tasks are organized topographically: nearby neurons are responsive to the same properties of input signals. Thus, in this work, inspired by the neuroscience literature, we proposed a new topographic…

Tensor network decomposition, originated from quantum physics to model entangled many-particle quantum systems, turns out to be a promising mathematical technique to efficiently represent and process big data in parsimonious manner. In this…

Grouping the nodes of a graph into clusters is a standard technique for studying networks. We study a problem where we are given a directed network and are asked to partition the graph into a sequence of coherent groups. We assume that…

In this work, we introduce and study what we believe is an intriguing and, to the best of our knowledge, previously unknown connection between two areas in computational topology, topological data analysis (TDA) and knot theory. Given a…

Knowledge graphs serve as critical resources supporting intelligent systems, but they can be noisy due to imperfect automatic generation processes. Existing approaches to noise detection often rely on external facts, logical rule…

Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…

High-dimensional data arise naturally in many areas of science and engineering, including machine learning, signal processing, computational physics, and statistics. Such data are often represented as tensors, multi-dimensional…

In the domain of sequence modelling, Recurrent Neural Networks (RNN) have been capable of achieving impressive results in a variety of application areas including visual question answering, part-of-speech tagging and machine translation.…

We propose to study neural networks' loss surfaces by methods of topological data analysis. We suggest to apply barcodes of Morse complexes to explore topology of loss surfaces. An algorithm for calculations of the loss function's barcodes…

The aim of applied topology is to use and develop topological methods for applied mathematics, science and engineering. One of the main tools is persistent homology, an adaptation of classical homology, which assigns a barcode, i.e. a…

Triplet loss is widely used for learning local descriptors from image patch. However, triplet loss only minimizes the Euclidean distance between matching descriptors and maximizes that between the non-matching descriptors, which neglects…

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…

This paper proposes a new topology optimization method that applies a convolutional neural network (CNN), which is one deep learning technique for topology optimization problems. Using this method, we acquire a structure with a little…

Convolutional neural networks (CNNs) are a standard tool for computer vision tasks such as image classification. However, typical model architectures may result in the loss of topological information. In specific domains such as…

Graph encoders in AMR-to-text generation models often rely on neighborhood convolutions or global vertex attention. While these approaches apply to general graphs, AMRs may be amenable to encoders that target their tree-like structure. By…

Tree-like structures, such as blood vessels, often express complexity at very fine scales, requiring high-resolution grids to adequately describe their shape. Such sparse morphology can alternately be represented by locations of centreline…

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…