Positional Encodings for Simplicial Complex Transformers

In this work, the application of transformer neural networks for classification of nodes in simplicial complexes is considered, which represents an important direction in the analysis of complex network structures. The study focuses on the investigation and comparison of the effectiveness of traditional and positional features calculated based on graph and simplicial data. The main goal of the work is to develop a transformer model capable of effectively processing various features and performing classification with high accuracy. In the course of the study, the following tasks were completed: - Development and implementation of methods for extracting and processing data from simplicial complexes; - Extraction and analysis of traditional (one-hot encoding) and positional features (centrality, triangles, pyramids); - Modeling and training a neural network transformer based on the selected features; - Evaluation of the model's effectiveness based on a comparative analysis of different types of features. The results of the work show that the use of positional features in transformer models significantly improves the quality of classification compared to traditional methods, making this approach promising for analyzing complex networks in various scientific and applied fields. The work contains 44 pages, 24 illustrations, 10 sources of literature, 1 table. Keywords: transformers, neural networks, simplicial complexes, node classification, positional features, machine learning, network analysis.