AI-Driven Consensus: Modeling Multi-Agent Networks with Long-Range Interactions through path-Laplacian Matrices

TL;DR

The paper addresses predicting the final consensus in multi-agent networks by extending the classical Laplacian framework to $k$-path Laplacians $L_k$ to capture long-range interactions. It combines this path-based formalism with a suite of ML models (LSTM, xLSTM, Transformer, XGBoost, ConvLSTM) to predict consensus across directed and undirected graphs (ER, WS, BA), demonstrating that multi-hop interactions improve predictive accuracy. Key findings show that exponential multi-hop weighting accelerates diffusion and enhances prediction quality, with topology and network size influencing performance; the study also compares computational trade-offs among models. The proposed framework offers a scalable, data-driven tool for analyzing and designing robust, fast-reaching consensus in real-world multi-agent systems such as autonomous networks and distributed sensing.

Abstract

Extended connectivity in graphs can be analyzed through k-path Laplacian matrices, which permit the capture of long-range interactions in various real-world networked systems such as social, transportation, and multi-agent networks. In this work, we present several alternative methods based on machine learning methods (LSTM, xLSTM, Transformer, XGBoost, and ConvLSTM) to predict the final consensus value based on directed networks (Erdös-Renyi, Watts-Strogatz, and Barabási-Albert) and on the initial state. We highlight how different k-hop interactions affect the performance of the tested methods. This framework opens new avenues for analyzing multi-scale diffusion processes in large-scale, complex networks.

Figures (4)

• Figure 1: Comparison of RMSE values for five models (ConvLSTM, LSTM, Extended-LSTM, Transformer, XGBoost) in both base and exponential scenarios across three network topologies (Barabási–Albert, Erdős–Rényi, Watts–Strogatz) and varying node sizes.
• Figure 2: Mean Absolute Percentage Error (MAPE) for consensus predictions across network sizes for Barabási–Albert, Erdős–Rényi, and Watts–Strogatz models.
• Figure 3: Box-and-whisker plots of MAPE for ConvLSTM, LSTM, Extended-LSTM, Transformer, and XGBoost at different network sizes.
• Figure 4: Prediction time comparison for ConvLSTM, LSTM, Extended-LSTM, Transformer, and XGBoost across various network sizes.