Ordered Topological Deep Learning: a Network Modeling Case Study

TL;DR

This work reframes network modeling as an ordered Topological Deep Learning problem, introducing ordered TDL and the OrdGCCN framework to encode higher-order interactions in discrete topological spaces. It shows that RouteNet, a leading network-modeling model, is naturally an instance of OrdGCCN, providing a theoretical bridge between practical network modeling and TDL principles. Through extensive simulations and real-world testbeds, the authors demonstrate that order-aware, topology-driven message passing yields superior accuracy and generalization compared to traditional models and non-ordered GNNs, even in unseen routings and large-scale topologies. The study thus establishes ordered TDL as a potent, real-world tool for scalable, high-fidelity network performance prediction and paves the way for broader ordered and directed TDL applications. The mathematical backbone relies on combinatorial complexes $(\mathcal{V}, \mathcal{C}, \mathrm{rk})$ and flows $\mathcal{F}$, queues $\mathcal{Q}$, and links $\mathcal{L}$, where flows induce an ordered structure over their constituent elements, enabling face-dependent and history-aware aggregations within OrdGCCNs.

Abstract

Computer networks are the foundation of modern digital infrastructure, facilitating global communication and data exchange. As demand for reliable high-bandwidth connectivity grows, advanced network modeling techniques become increasingly essential to optimize performance and predict network behavior. Traditional modeling methods, such as packet-level simulators and queueing theory, have notable limitations --either being computationally expensive or relying on restrictive assumptions that reduce accuracy. In this context, the deep learning-based RouteNet family of models has recently redefined network modeling by showing an unprecedented cost-performance trade-off. In this work, we revisit RouteNet's sophisticated design and uncover its hidden connection to Topological Deep Learning (TDL), an emerging field that models higher-order interactions beyond standard graph-based methods. We demonstrate that, although originally formulated as a heterogeneous Graph Neural Network, RouteNet serves as the first instantiation of a new form of TDL. More specifically, this paper presents OrdGCCN, a novel TDL framework that introduces the notion of ordered neighbors in arbitrary discrete topological spaces, and shows that RouteNet's architecture can be naturally described as an ordered topological neural network. To the best of our knowledge, this marks the first successful real-world application of state-of-the-art TDL principles --which we confirm through extensive testbed experiments--, laying the foundation for the next generation of ordered TDL-driven applications.

Figures (6)

• Figure 1: Comparison of RouteNet against traditional network modeling. A. Inference times for simulating 1 second of network operation in a fixed topology depending on the amount of traffic found in the network. B. Delay prediction performance (Mean Absolute Percentage Error (MAPE), lower is better) obtained by each of the methods with both simulated and real traffic data.
• Figure 2: Domains of Topological Deep Learning encoding higher-order relations (cells in light and dark pink) between elements (nodes in blue). Figure adapted from papillon2023architectures.
• Figure 3: Neighborhoods. Given a complex $\mathcal{C}$ (left), we illustrate three examples of augmented Hasse graphs $\mathcal{G}_\mathcal{N}$ corresponding to a given neighborhood $\mathcal{N}$, listed at the bottom.
• Figure 4: Topological representation of a computer network where relationships naturally form higher-order topological structures. A. Routers can be seen as a set of queues. B. Analogously, links can be devised as the collection of queues that inject traffic to them. C. Flow paths can admit several (combinatorial) interpretations, potentially encompassing the routers, queues and links they traverse.
• Figure 5: RouteNet's internal representation of a flow path as a set of links, depicted as an ordered combinatorial complex. Each flow link on the physical network (left, white arrows) is visualized as a 1-cell containing all queues that inject traffic into it (middle). The generic EoF queue simply marks the end of the flow.

Theorems & Definitions (4)

• Proposition 5.1
• Proposition 5.2
• Definition C.1: CC-Homomorphism induced by $(\mathcal{N}_1, \mathcal{N}_2)$ papillon2024topotune
• Definition C.2: CC-Isomorphism induced by $(\mathcal{N}_1, \mathcal{N}_2)$