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From GNNs to Symbolic Surrogates via Kolmogorov-Arnold Networks for Delay Prediction

Sami Marouani, Kamal Singh, Baptiste Jeudy, Amaury Habrard

TL;DR

This paper addresses the challenge of predicting per-flow delay in complex networks, where traditional analytical models and DES are impractical and data-driven GNNs suffer from large parameter counts and limited transparency. It introduces FlowKANet, a GNN where all transformations are implemented with Kolmogorov-Arnold Network (KAN) layers and KAMP-Attn for integrated transformation and attention, plus a symbolic distillation step that yields a fully analytical, graph-aware surrogate. The contributions include a strong heterogeneous GNN baseline, a compact KAN-based FlowKANet with competitive accuracy, and a progressive symbolic surrogate pipeline that preserves graph structure while eliminating trainable weights. The results highlight a clear efficiency–transparency trade-off: FlowKANet approaches the neural baseline in predictive power with significantly fewer parameters, while the symbolic surrogates enable lightweight and transparent deployment suitable for resource-constrained or safety-critical environments.

Abstract

Accurate prediction of flow delay is essential for optimizing and managing modern communication networks. We investigate three levels of modeling for this task. First, we implement a heterogeneous GNN with attention-based message passing, establishing a strong neural baseline. Second, we propose FlowKANet in which Kolmogorov-Arnold Networks replace standard MLP layers, reducing trainable parameters while maintaining competitive predictive performance. FlowKANet integrates KAMP-Attn (Kolmogorov-Arnold Message Passing with Attention), embedding KAN operators directly into message-passing and attention computation. Finally, we distill the model into symbolic surrogate models using block-wise regression, producing closed-form equations that eliminate trainable weights while preserving graph-structured dependencies. The results show that KAN layers provide a favorable trade-off between efficiency and accuracy and that symbolic surrogates emphasize the potential for lightweight deployment and enhanced transparency.

From GNNs to Symbolic Surrogates via Kolmogorov-Arnold Networks for Delay Prediction

TL;DR

This paper addresses the challenge of predicting per-flow delay in complex networks, where traditional analytical models and DES are impractical and data-driven GNNs suffer from large parameter counts and limited transparency. It introduces FlowKANet, a GNN where all transformations are implemented with Kolmogorov-Arnold Network (KAN) layers and KAMP-Attn for integrated transformation and attention, plus a symbolic distillation step that yields a fully analytical, graph-aware surrogate. The contributions include a strong heterogeneous GNN baseline, a compact KAN-based FlowKANet with competitive accuracy, and a progressive symbolic surrogate pipeline that preserves graph structure while eliminating trainable weights. The results highlight a clear efficiency–transparency trade-off: FlowKANet approaches the neural baseline in predictive power with significantly fewer parameters, while the symbolic surrogates enable lightweight and transparent deployment suitable for resource-constrained or safety-critical environments.

Abstract

Accurate prediction of flow delay is essential for optimizing and managing modern communication networks. We investigate three levels of modeling for this task. First, we implement a heterogeneous GNN with attention-based message passing, establishing a strong neural baseline. Second, we propose FlowKANet in which Kolmogorov-Arnold Networks replace standard MLP layers, reducing trainable parameters while maintaining competitive predictive performance. FlowKANet integrates KAMP-Attn (Kolmogorov-Arnold Message Passing with Attention), embedding KAN operators directly into message-passing and attention computation. Finally, we distill the model into symbolic surrogate models using block-wise regression, producing closed-form equations that eliminate trainable weights while preserving graph-structured dependencies. The results show that KAN layers provide a favorable trade-off between efficiency and accuracy and that symbolic surrogates emphasize the potential for lightweight deployment and enhanced transparency.
Paper Structure (21 sections, 11 equations, 3 figures, 6 tables, 2 algorithms)

This paper contains 21 sections, 11 equations, 3 figures, 6 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Traditional Network Modeling
  4. Machine Learning for Networking
  5. GNN-based Models
  6. Kolmogorov--Arnold Networks (KANs)
  7. Framework for Flow Delay Prediction
  8. Graph Construction
  9. Feature Selection
  10. Baseline GNN Model Architecture
  11. FlowKANet Model Architecture
  12. Symbolic Surrogate Models
  13. Sequential block-wise search
  14. Final surrogate pipeline.
  15. Performance Evaluation
  16. ...and 6 more sections

Figures (3)

  • Figure 1: Baseline GNN architecture with heterogeneous message passing, attention, and GRU refinement.
  • Figure 2: Predicted vs. true per-flow delay on the test set (878 graphs, containing 13,704 flows).
  • Figure 3: Progressive-hybrid full-dataset MSE as blocks are symbolized in sequence (lower is better). L0-L2 denote message-passing layers; f2l and l2f refer to flow-to-link and link-to-flow directions.