How to build weighted gossip network matrices?
Constructing Stochastic Matrices for Weighted Averaging in Gossip Networks
February 28, 2025
https://arxiv.org/pdf/2502.19821This paper addresses the challenge of designing communication rules (stochastic matrices) for distributed averaging in multi-agent systems, specifically in gossip networks. It introduces an algorithm that guarantees the network converges to a pre-defined consensus state, where groups of agents (consensus clusters) reach agreement on values based on assigned weights.
Key points for LLM-based multi-agent systems:
- Controlled Consensus: The algorithm provides fine-grained control over which agents reach consensus and the influence each agent has on the final agreed-upon value. This is relevant for LLMs where different agents might have different expertise or levels of trustworthiness.
- Dynamic Network Topologies: The research considers gossip networks, where communication links can change dynamically. This is analogous to LLM agents interacting in evolving conversational contexts or online environments.
- Formal Guarantees: The algorithm offers provable convergence to the desired consensus state, essential for reliable and predictable behavior in LLM-based multi-agent applications.
- Scalability: The distributed nature of gossip protocols is well-suited for scaling multi-agent LLM applications to a large number of agents.
- Decentralized Control: The gossip process is inherently decentralized, aligning with the distributed nature of many LLM-based multi-agent scenarios. This eliminates the need for a central controller.
- Weighted Averaging: The algorithm explicitly incorporates weights, allowing developers to define the relative importance of different LLM agents' outputs. This is valuable when combining insights from diverse LLMs or dealing with varying levels of agent reliability.
- Admissible Partitions: The concept of admissible partitions allows for flexible grouping of agents based on desired consensus structures, relevant for modular or hierarchical LLM agent systems.