Simplicial Complex

Simplicial complexes are mathematical structures that generalize graphs by representing higher-order relationships among data points, going beyond simple pairwise connections. Current research focuses on developing neural network architectures, such as simplicial convolutional neural networks and those based on state-space models and random walks, to effectively process and learn from data represented as simplicial complexes. These advancements are driving progress in topological deep learning and enabling applications in diverse fields, including data analysis, classification, and network modeling, by offering more expressive representations of complex systems. The development of large-scale benchmark datasets and improved algorithms for computing topological features from simplicial complexes are also key areas of ongoing investigation.