Author: Denis Avetisyan
Researchers are leveraging the power of neural networks and symbolic regression to not only predict communication delays but also to distill those predictions into human-readable formulas.
This work demonstrates how Kolmogorov-Arnold Networks integrated with Graph Neural Networks enable accurate, compact, and interpretable flow delay prediction, even achieving fully symbolic model distillation for heterogeneous graphs.
Accurate network delay prediction remains a critical challenge despite advances in machine learning. This paper, ‘From GNNs to Symbolic Surrogates via Kolmogorov-Arnold Networks for Delay Prediction’, investigates a novel approach to flow delay prediction by integrating Kolmogorov-Arnold Networks (KANs) within Graph Neural Network architectures. The resulting framework achieves a compelling balance of predictive accuracy, model compactness, and interpretability, culminating in fully symbolic surrogate models devoid of trainable parameters. Could this distillation into closed-form equations unlock truly lightweight and transparent network management solutions?
The Ebb and Flow of Prediction: Limitations of Traditional Network Models
The predictive power of established network performance tools, such as Queueing Models and Discrete Event Simulation (DES), diminishes rapidly when confronted with the intricacies of contemporary networks. These techniques often necessitate a series of simplifying assumptions – treating traffic as uniform, ignoring correlation between flows, or limiting the scope of network topology considered – to render the problem computationally tractable. While useful in idealized scenarios, these abstractions introduce significant inaccuracies when applied to real-world networks characterized by heterogeneous traffic patterns, dynamic routing, and complex interdependencies. Consequently, predictions generated by these traditional methods can deviate substantially from actual network behavior, hindering effective resource allocation and potentially compromising Quality of Service (QoS) guarantees. The inherent limitations stem from the difficulty in faithfully capturing the stochastic and multifaceted nature of modern network environments within the constraints of analytical or simulation-based approaches.
Traditional network performance prediction techniques, such as analytical modeling and discrete event simulation, frequently encounter limitations when applied to contemporary network environments. These methods often demand significant computational resources, becoming increasingly impractical as network scale and complexity grow; the time required for accurate analysis can quickly become prohibitive. More critically, these approaches frequently struggle with generalization, meaning a model meticulously calibrated for one specific network topology or traffic pattern may perform poorly when faced with even minor deviations. This lack of adaptability stems from their reliance on pre-defined parameters and assumptions that rarely hold true across diverse, real-world network configurations, hindering their effectiveness in dynamic and evolving environments and necessitating costly re-calibration with each change.
The efficacy of modern network management hinges significantly on the ability to accurately predict flow delay; this prediction is not merely a technical detail, but a foundational requirement for both Traffic Engineering (TE) and Quality of Service (QoS) guarantees. Effective TE relies on proactively routing traffic to minimize congestion and latency, a process impossible without anticipating potential delays across various network paths. Similarly, delivering consistent QoS – ensuring applications receive the necessary bandwidth and experience minimal interruption – demands precise delay prediction to allocate resources appropriately and prevent performance degradation. Consequently, limitations in current predictive capabilities directly translate to suboptimal network performance, increased operational costs, and a diminished user experience, underscoring the urgent need for more robust and adaptable solutions capable of navigating the complexities of contemporary network environments.
A Network Observed: Graph Neural Networks as a Paradigm Shift
Graph Neural Networks (GNNs) provide a distinct methodology for network performance prediction by shifting from feature-based approaches to directly incorporating network structure and traffic patterns into the model. Traditional methods often rely on hand-engineered features representing node and link characteristics, requiring significant domain expertise and potentially overlooking crucial relationships. GNNs, however, operate on the graph itself, learning node embeddings that encode both topological information-such as node degree and path lengths-and dynamic flow data-like traffic volume and source-destination pairs. This direct modeling of network topology and flow dynamics allows GNNs to capture complex dependencies and non-linear interactions, leading to improved accuracy in predicting metrics like latency, throughput, and packet loss compared to feature-based or statistical models.
Representing networks as bipartite graphs within Graph Neural Networks (GNNs) facilitates the learning of relationships between network flows and the links that carry them. In this structure, nodes represent both network flows and network links, with edges connecting flows to the links they utilize. This explicit representation allows the GNN to directly model the interaction between flow characteristics and link capacity/utilization. By considering both entities simultaneously, the model can better infer how specific flow attributes impact link performance and vice versa, leading to improved accuracy in network performance prediction tasks such as estimating latency or bandwidth availability. The bipartite formulation enables the GNN to capture complex dependencies that would be difficult to discern with traditional network modeling approaches.
RouteNet and Heterogeneous Graph Neural Networks (HGNNs) represent specific implementations demonstrating the efficacy of GNNs in network performance estimation. RouteNet utilizes a GNN architecture to predict network-level metrics based on source-destination pairs, focusing on routing-related data. HGNNs extend this capability by explicitly modeling heterogeneous network elements – different node and edge types representing diverse network components and their relationships – to improve prediction accuracy for metrics like flow delay. Evaluations of these models have shown they can achieve lower prediction errors compared to traditional methods that rely on feature engineering or statistical modeling, particularly in dynamic network conditions where topology and traffic patterns change frequently. These results indicate GNNs can effectively learn and generalize from network structure and traffic data to estimate key performance indicators.
FlowKANet: Distilling Efficiency Through Kolmogorov-Arnold Networks
FlowKANet introduces a Graph Neural Network (GNN) architecture predicated on the use of Kolmogorov-Arnold Networks (KANs). KANs are a class of neural networks capable of representing complex functions with a limited number of parameters, contributing to FlowKANet’s efficiency. This approach allows for a substantial reduction in model size without sacrificing predictive power, and also facilitates interpretability by providing a more compact and understandable representation of learned features. The utilization of KAN operators within the network enables the transformation of input features and the calculation of attention coefficients, forming the basis of the KAMP-Attn mechanism and ultimately contributing to both performance and clarity in the model’s operation.
The KAMP-Attn mechanism within FlowKANet implements Kolmogorov-Arnold Networks (KANs) as core components for both feature transformation and attention coefficient calculation. Specifically, KAN operators are utilized to map input features to a different space prior to attention weighting, and subsequently, to compute the attention coefficients themselves. This approach replaces traditional linear layers commonly used in attention mechanisms with the non-linear, compact representation offered by KANs. By leveraging the properties of KANs – namely their universal approximation capability with a limited number of parameters – KAMP-Attn aims to improve both the performance and efficiency of the attention process within the GNN architecture.
FlowKANet demonstrates significant model compression by reducing the number of trainable parameters to approximately 20,000. This represents a nearly five-fold decrease compared to the baseline Graph Neural Network (GNN), which utilized 98,000 parameters. Critically, this reduction in model size was achieved without a corresponding decrease in predictive accuracy, indicating improved parameter efficiency and a more compact model representation. This efficiency is a key benefit for deployment on resource-constrained devices or in applications requiring faster inference times.
The Calculus of Understanding: Symbolic Regression and Network Insight
FlowKANet, a complex neural network designed to predict flow delay, often operates as a ‘black box’ – providing accurate results without revealing how those results are derived. Symbolic distillation, employing tools such as PySR, addresses this limitation by constructing compact analytical surrogates directly from the trained neural network. This process doesn’t simply approximate the network’s output; it actively seeks mathematical equations that faithfully replicate the network’s behavior. The resulting symbolic model, built from fundamental mathematical operations, offers a transparent and interpretable alternative, effectively distilling the knowledge embedded within the neural network into a human-readable form. These equations can then be analyzed to pinpoint the key variables and relationships governing flow delay, providing insights unattainable from the original neural network itself.
The transformation of a complex neural network into symbolic equations offers a pathway to demystify the factors governing flow delay. Rather than simply predicting outcomes, techniques like symbolic regression extract underlying mathematical relationships from the network’s learned behavior. This distillation process yields concise, human-readable formulas – for example, delay = a <i> bandwidth + b </i> packet\_size – that explicitly define how variables such as bandwidth and packet size influence network performance. Consequently, researchers gain a clear, interpretable understanding of why the network behaves as it does, moving beyond correlation to establish causal links and pinpoint critical parameters driving delay, which is often obscured within the ‘black box’ of traditional neural network models.
The culmination of symbolic regression applied to network analysis yields models distinguished by their complete lack of trainable parameters. This represents a significant departure from conventional neural networks, where performance hinges on adjusting numerous weights and biases. By distilling complex relationships into concise, mathematical equations – often involving fundamental physical principles – the resulting models offer unparalleled interpretability. This efficiency isn’t merely academic; it translates to dramatically reduced computational cost for prediction and analysis. Researchers can readily discern the precise factors influencing network behavior, and the models themselves are easily deployable on resource-constrained platforms, fostering a deeper, more accessible understanding of complex systems without sacrificing predictive power. y = ax + b represents a simple example of such a distilled model, highlighting the direct relationship between input x and output y without any hidden layers or adjustable components.
The pursuit of model compactness, as demonstrated by distilling Graph Neural Networks into symbolic equations, echoes a fundamental principle of resilient systems. This work acknowledges that any improvement, even in predictive accuracy, ages faster than expected, necessitating a continual re-evaluation of model complexity. As Linus Torvalds famously stated, “Talk is cheap. Show me the code.” This sentiment aligns perfectly with the paper’s emphasis on deriving explicit, interpretable symbolic representations-moving beyond opaque neural networks to reveal the underlying mechanisms driving flow delay prediction. The resulting equations aren’t merely a demonstration of technique, but a pathway toward understanding and maintaining these systems over time, ensuring they age gracefully rather than succumbing to the inevitable decay of complexity.
What’s Next?
The pursuit of predictive accuracy in network flows invariably encounters the entropic reality of change. This work, by distilling complexity into symbolic surrogates, offers a temporary reprieve, a localized minimum in the decay of predictive power. Yet, the true challenge isn’t simply modeling delay, but acknowledging its inevitable drift. The elegance of a closed-form equation is appealing, but such forms presume stationarity-a fiction maintained only within limited observation windows.
Future iterations must address the lifespan of these symbolic representations. How readily can these models adapt to shifts in network topology, traffic patterns, or even the underlying physics of data transmission? The transition from point predictions to probability distributions, reflecting inherent uncertainty, seems less a refinement and more an honest reckoning. Uptime, after all, is merely a temporary alignment of variables.
Moreover, the heterogeneity inherent in modern networks-the layering of protocols, diverse hardware, and unpredictable user behavior-introduces further latency. The tax every request must pay. Extending these techniques to encompass not just what delays occur, but where and why-mapping delay signatures to specific network components-represents a logical, if ambitious, progression. Stability is an illusion cached by time, and the quest for perfect prediction, a perpetual asymptotic approach.
Original article: https://arxiv.org/pdf/2512.20885.pdf
Contact the author: https://www.linkedin.com/in/avetisyan/
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2025-12-26 06:31