A Deep Autoregressive Model for Dynamic Combinatorial Complexes
Ata Tuna
TL;DR
This work introduces DAMCC, the first deep autoregressive model designed to generate dynamic combinatorial complexes (CCs), addressing the gap in modeling temporal evolution and higher-order interactions beyond static graphs. It proposes a CC-specific encoder–decoder framework built on a higher-order attention backbone (HOAN) and a row-wise permutation-invariant loss (RWPL) to enable CC-time-series generation via incidence/co-incidence representations. Key contributions include novel CC loss functions, an autoregressive generation scheme over CCs, and comprehensive experiments on real and synthetic datasets that demonstrate the model’s ability to capture temporal and higher-order dependencies, along with a frank discussion of training challenges. The work lays a foundational framework for dynamic topological learning with CCs and points to future directions for scalability, richer temporal modeling, and datasets that inherently require CC representations.
Abstract
We introduce DAMCC (Deep Autoregressive Model for Dynamic Combinatorial Complexes), the first deep learning model designed to generate dynamic combinatorial complexes (CCs). Unlike traditional graph-based models, CCs capture higher-order interactions, making them ideal for representing social networks, biological systems, and evolving infrastructures. While existing models primarily focus on static graphs, DAMCC addresses the challenge of modeling temporal dynamics and higher-order structures in dynamic networks. DAMCC employs an autoregressive framework to predict the evolution of CCs over time. Through comprehensive experiments on real-world and synthetic datasets, we demonstrate its ability to capture both temporal and higher-order dependencies. As the first model of its kind, DAMCC lays the foundation for future advancements in dynamic combinatorial complex modeling, with opportunities for improved scalability and efficiency on larger networks.