Going with the Flow: Approximating Banzhaf Values via Graph Neural Networks

• URL: http://arxiv.org/abs/2510.13391v2
• Date: Mon, 20 Oct 2025 10:08:41 GMT
• Title: Going with the Flow: Approximating Banzhaf Values via Graph Neural Networks
• Authors: Benjamin Kempinski, Tal Kachman,
• Abstract summary: We present a novel learning-based approach using Graph Neural Networks (GNNs) to approximate Banzhaf values in cardinal network flow games.<n>We show that trained GNN models achieve high-fidelity Banzhaf value approximation with order-of-magnitude speedups.<n>This work establishes GNNs as a practical tool for scalable cooperative game-theoretic analysis of complex networked systems.
• Score: 1.8047694351309207
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Computing the Banzhaf value in network flow games is fundamental for quantifying agent influence in multi-agent systems, with applications ranging from cybersecurity to infrastructure planning. However, exact computation is intractable for systems with more than $\sim20$ agents due to exponential complexity $\mathcal{O}(2^m)$. While Monte Carlo sampling methods provide statistical estimates, they suffer from high sample complexity and cannot transfer knowledge across different network configurations, making them impractical for large-scale or dynamic systems. We present a novel learning-based approach using Graph Neural Networks (GNNs) to approximate Banzhaf values in cardinal network flow games. By framing the problem as a graph-level prediction task, our method learns generalisable patterns of agent influence directly from network topology and control structure. We conduct a comprehensive empirical study comparing three state-of-the-art GNN architectures-Graph Attention Networks (GAT), Graph Isomorphism Networks with Edge features (GINE), and EdgeConv-on a large-scale synthetic dataset of 200,000 graphs per configuration, varying in size (20-100 nodes), agent count (5-20), and edge probability (0.5-1.0). Our results demonstrate that trained GNN models achieve high-fidelity Banzhaf value approximation with order-of-magnitude speedups compared to exact and sampling-based methods. Most significantly, we show strong zero-shot generalisation: models trained on graphs of a specific size and topology accurately predict Banzhaf values for entirely new networks with different structural properties, without requiring retraining. This work establishes GNNs as a practical tool for scalable cooperative game-theoretic analysis of complex networked systems.

Related papers

• Exact Computation of Any-Order Shapley Interactions for Graph Neural Networks [53.10674067060148]
  Shapley Interactions (SIs) quantify node contributions and interactions among multiple nodes.<n>By exploiting the GNN architecture, we show that the structure of interactions in node embeddings are preserved for graph prediction.<n>We introduce GraphSHAP-IQ, an efficient approach to compute any-order SIs exactly.
  arXiv  Detail & Related papers  (2025-01-28T13:37:44Z)
• DeltaGNN: Graph Neural Network with Information Flow Control [5.563171090433323]
  Graph Neural Networks (GNNs) are designed to process graph-structured data through neighborhood aggregations in the message passing process.<n>Message-passing enables GNNs to understand short-range spatial interactions, but also causes them to suffer from over-smoothing and over-squashing.<n>We propose a mechanism called emph information flow control to address over-smoothing and over-squashing with linear computational overhead.<n>We benchmark our model across 10 real-world datasets, including graphs with varying sizes, topologies, densities, and homophilic ratios, showing superior performance
  arXiv  Detail & Related papers  (2025-01-10T14:34:20Z)
• BLIS-Net: Classifying and Analyzing Signals on Graphs [20.345611294709244]
  Graph neural networks (GNNs) have emerged as a powerful tool for tasks such as node classification and graph classification. We introduce the BLIS-Net (Bi-Lipschitz Scattering Net), a novel GNN that builds on the previously introduced geometric scattering transform. We show that BLIS-Net achieves superior performance on both synthetic and real-world data sets based on traffic flow and fMRI data.
  arXiv  Detail & Related papers  (2023-10-26T17:03:14Z)
• Dynamic Graph Message Passing Networks for Visual Recognition [112.49513303433606]
  Modelling long-range dependencies is critical for scene understanding tasks in computer vision. A fully-connected graph is beneficial for such modelling, but its computational overhead is prohibitive. We propose a dynamic graph message passing network, that significantly reduces the computational complexity.
  arXiv  Detail & Related papers  (2022-09-20T14:41:37Z)
• Lipschitz Bound Analysis of Neural Networks [0.0]
  Lipschitz Bound Estimation is an effective method of regularizing deep neural networks to make them robust against adversarial attacks. In this paper, we highlight the significant gap in obtaining a non-trivial Lipschitz bound certificate for Convolutional Neural Networks (CNNs) We also show that unrolling Convolutional layers or Toeplitz matrices can be employed to convert Convolutional Neural Networks (CNNs) to a Fully Connected Network.
  arXiv  Detail & Related papers  (2022-07-14T23:40:22Z)
• Deep Architecture Connectivity Matters for Its Convergence: A Fine-Grained Analysis [94.64007376939735]
  We theoretically characterize the impact of connectivity patterns on the convergence of deep neural networks (DNNs) under gradient descent training. We show that by a simple filtration on "unpromising" connectivity patterns, we can trim down the number of models to evaluate.
  arXiv  Detail & Related papers  (2022-05-11T17:43:54Z)
• Breaking the Limit of Graph Neural Networks by Improving the Assortativity of Graphs with Local Mixing Patterns [19.346133577539394]
  Graph neural networks (GNNs) have achieved tremendous success on multiple graph-based learning tasks. We focus on transforming the input graph into a computation graph which contains both proximity and structural information. We show that adaptively choosing between structure and proximity leads to improved performance under diverse mixing.
  arXiv  Detail & Related papers  (2021-06-11T19:18:34Z)
• Analyzing the Performance of Graph Neural Networks with Pipe Parallelism [2.269587850533721]
  We focus on Graph Neural Networks (GNNs) that have found great success in tasks such as node or edge classification and link prediction. New approaches for processing larger networks are needed to advance graph techniques. We study how GNNs could be parallelized using existing tools and frameworks that are known to be successful in the deep learning community.
  arXiv  Detail & Related papers  (2020-12-20T04:20:38Z)
• Dynamic Graph: Learning Instance-aware Connectivity for Neural Networks [78.65792427542672]
  Dynamic Graph Network (DG-Net) is a complete directed acyclic graph, where the nodes represent convolutional blocks and the edges represent connection paths. Instead of using the same path of the network, DG-Net aggregates features dynamically in each node, which allows the network to have more representation ability.
  arXiv  Detail & Related papers  (2020-10-02T16:50:26Z)
• Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networks [183.97265247061847]
  We leverage graph signal processing to characterize the representation space of graph neural networks (GNNs) We discuss the role of graph convolutional filters in GNNs and show that any architecture built with such filters has the fundamental properties of permutation equivariance and stability to changes in the topology. We also study the use of GNNs in recommender systems and learning decentralized controllers for robot swarms.
  arXiv  Detail & Related papers  (2020-03-08T13:02:15Z)
• Analyzing Neural Networks Based on Random Graphs [77.34726150561087]
  We perform a massive evaluation of neural networks with architectures corresponding to random graphs of various types. We find that none of the classical numerical graph invariants by itself allows to single out the best networks. We also find that networks with primarily short-range connections perform better than networks which allow for many long-range connections.
  arXiv  Detail & Related papers  (2020-02-19T11:04:49Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.