Great paper on designing multi-agent systems.

How many distinct communication topologies does an LLM multi-agent system actually need?

This works claims that it's about six.

Technical summary:

Researchers grew the codebook capacity from 8 to 64 and the topologies that survived a reward filter kept collapsing to roughly the same six.

Two further findings undercut the standard formulation. Edge count correlates negatively with measured token consumption at r about -0.4, so sparsifying the agent graph makes inference more expensive.

And a message-passing scorer over agent-profile nodes is adjacency-invariant whenever agents share a profile, which is the default configuration in published benchmarks, so it cannot rank candidates at all in that regime.

Codebook Agent drops the search entirely. A vector-quantized autoencoder compresses successful topologies into a query-independent 16-entry codebook, a reward-weighted MLP maps the query embedding to a distribution over codes, and an MLP proxy reading the flattened adjacency reranks the top decoded candidates in one batched forward pass.

It emits a topology in 2.4 ms, leads all six benchmarks at 84.6 average against 83.0 for the strongest prior designer, and uses 21.9 to 33.2% fewer LLM tokens.

Paper: https://arxiv.org/abs/2609.02264

Chat with Paper: https://academy.dair.ai/papers/codebook-agent-amortized-topology-design-for-llm-multi-agent-systems-2609.02264