Heterogeneous Swarms: Jointly Optimizing Model Roles and Weights for Multi-LLM Systems

We propose Heterogeneous Swarms, an algorithm to discover and adapt multi-LLM systems by jointly optimizing model roles and weights. Given a pool of LLM experts and a utility function, Heterogeneous Swarms employs two iterative steps: role-step and weight-step. For role-step, we interpret model roles as input-output relationships and optimize the directed acyclic graph (DAG) of LLMs representing a multi-LLM system. Starting from a swarm of randomly initialized continuous adjacency matrices, we decode them into discrete DAGs, call the LLMs in topological order with message passing, evaluate on the utility function, and optimize the adjacency matrices with swarm intelligence based on the utility score. For weight-step, we define JFK-score to evaluate the contribution of individual LLMs in the best-found DAG of the role-step, then optimize model weights with swarm intelligence based on the JFK-score. Extensive experiments demonstrate that Heterogeneous Swarms outperforms 15 baselines spanning role-based and weight-based approaches by 18.5% on average across 12 tasks and contexts. Further analysis reveals that Heterogeneous Swarms discovers multi-LLM systems with heterogeneous model roles and substantial collaborative gains, and benefits from the diversity of initial LLMs.