# Codebook Agent: Amortized Topology Design for LLM Multi-Agent Systems

arXiv: https://arxiv.org/abs/2609.02264 · HTML: https://mlsanity.com/paper/2609.02264/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in General LLM agent frameworks and benchmarks, one of 16 directions in LLM agents and tool use.
- Builds on 23 of its 43 references that are in the map.
- First posted on arXiv 2 Sep 2026.

## Placed in

- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)

## Builds on (most cited first, 23 of 23)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation](https://mlsanity.com/paper/2308.08155/) (2023)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [ChatDev: Communicative Agents for Software Development](https://mlsanity.com/paper/2307.07924/) (2023)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [Why Do Multi-Agent LLM Systems Fail?](https://mlsanity.com/paper/2503.13657/) (2025)
- [LLM-Blender: Ensembling Large Language Models with Pairwise Ranking and Generative Fusion](https://mlsanity.com/paper/2306.02561/) (2023)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [Solving General Arithmetic Word Problems](https://mlsanity.com/paper/1608.01413/) (2016)
- [Should we be going MAD? A Look at Multi-Agent Debate Strategies for LLMs](https://mlsanity.com/paper/2311.17371/) (2023)
- [Assemble Your Crew: Automatic Multi-agent Communication Topology Design via Autoregressive Graph Generation](https://mlsanity.com/paper/2507.18224/) (2025)
- [VQGraph: Rethinking Graph Representation Space for Bridging GNNs and MLPs](https://mlsanity.com/paper/2308.02117/) (2023)
- [Unifying Generation and Prediction on Graphs with Latent Graph Diffusion](https://mlsanity.com/paper/2402.02518/) (2024)

## Built on by (most cited first, 1 of 1)

- [CollabFlow: Recursive Self-Improvement of Agent Collaboration](https://mlsanity.com/paper/2609.38662/) (2026)

## Abstract (arXiv)

Adapting the communication topology of an LLM multi-agent system to each query improves both accuracy and efficiency, yet current designers treat this as conditional graph generation: a variational, autoregressive, or diffusion decoder searches the N × N adjacency space, and a graph-network proxy trained on utility and a structural cost such as edge count ranks the sampled candidates. We argue that this formulation is misaligned with the problem. Empirically, topologies that survive a reward filter collapse to about six distinct graphs even when the codebook capacity grows from 8 to 64; edge count is negatively correlated with measured token consumption (Pearson r ≈ -0.4), so sparsifying the graph makes inference more expensive; and a message-passing scorer over agent-profile nodes is adjacency-invariant whenever agents share a profile---the default configuration of published benchmarks---so it cannot rank candidates at all in that regime. These three facts motivate Codebook Agent: 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 that reads the flattened adjacency, regressed on measured utility and per-task normalized token cost, reranks the top decoded candidates in a single batched forward pass. With no iterative search and no message passing at test time, Codebook Agent is the most accurate method on all six benchmarks we compare (84.6 average against 83.0 for the strongest prior designer), emits a topology in 2.4 ms, and uses 21.9--33.2% fewer LLM tokens.