Related papers: Homological Convolutional Neural Networks
This paper presents a mathematically rigorous framework for brain-inspired representation learning founded on the interplay between persistent topological structures and cohomological flows. Neural computation is reformulated as the…
Topology optimization is computationally demanding that requires the assembly and solution to a finite element problem for each material distribution hypothesis. As a complementary alternative to the traditional physics-based topology…
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…
Due to object detection's close relationship with video analysis and image understanding, it has attracted much research attention in recent years. Traditional object detection methods are built on handcrafted features and shallow trainable…
Topological data analysis (TDA) is a rapidly evolving field in applied mathematics and data science that leverages tools from topology to uncover robust, shape-driven insights in complex datasets. The main workhorse is persistent homology,…
While Deep Learning excels in structured data as encountered in vision and natural language processing, it failed to meet its expectations on tabular data. For tabular data, Support Vector Machines (SVMs), Random Forests, and Gradient…
Convolutional Neural Networks (CNNs) have proven to be highly effective in solving a broad spectrum of computer vision tasks, such as classification, identification, and segmentation. These methods can be deployed in both centralized and…
Topological learning is a wide research area aiming at uncovering the mutual spatial relationships between the elements of a set. Some of the most common and oldest approaches involve the use of unsupervised competitive neural networks.…
A large amount of research on Convolutional Neural Networks has focused on flat Classification in the multi-class domain. In the real world, many problems are naturally expressed as problems of hierarchical classification, in which the…
Homography estimation is an important task in computer vision applications, such as image stitching, video stabilization, and camera calibration. Traditional homography estimation methods heavily depend on the quantity and distribution of…
Deep learning has shown great potential for automated medical image segmentation to improve the precision and speed of disease diagnostics. However, the task presents significant difficulties due to variations in the scale, shape, texture,…
Despite the ubiquity of tabular data in high-stakes domains, traditional deep learning architectures often struggle to match the performance of gradient-boosted decision trees while maintaining scientific interpretability. Standard neural…
Mathematical morphology is a theory and technique to collect features like geometric and topological structures in digital images. Given a target image, determining suitable morphological operations and structuring elements is a cumbersome…
Graph neural networks (GNNs) have emerged as a powerful tool for graph classification and representation learning. However, GNNs tend to suffer from over-smoothing problems and are vulnerable to graph perturbations. To address these…
Recently, topological deep learning (TDL), which integrates algebraic topology with deep neural networks, has achieved tremendous success in processing point-cloud data, emerging as a promising paradigm in data science. However, TDL has not…
This overview article makes the case for how topological concepts can enrich research in machine learning. Using the Euler Characteristic Transform (ECT), a geometrical-topological invariant, as a running example, I present different use…
Deep Neural networks are efficient and flexible models that perform well for a variety of tasks such as image, speech recognition and natural language understanding. In particular, convolutional neural networks (CNN) generate a keen…
Deep convolutional neural networks, assisted by architectural design strategies, make extensive use of data augmentation techniques and layers with a high number of feature maps to embed object transformations. That is highly inefficient…
Convolutional neural networks (CNNs) have been established as the main workhorse in image data processing; nonetheless, they require large amounts of data to train, often produce overconfident predictions, and frequently lack the ability to…
Additive manufacturing methods together with topology optimization have enabled the creation of multiscale structures with controlled spatially-varying material microstructure. However, topology optimization or inverse design of such…