# Predictive Maps of Multi-Agent Reasoning: A Successor-Representation Spectrum for LLM Communication Topologies

arXiv: https://arxiv.org/abs/2605.11453 · HTML: https://mlsanity.com/paper/2605.11453/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 6 of its 51 references that are in the map.
- First posted on arXiv 12 May 2026.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)
- 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, 6 of 6)

- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [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)
- [Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate](https://mlsanity.com/paper/2305.19118/) (2023)
- [Large Language Model based Multi-Agents: A Survey of Progress and Challenges](https://mlsanity.com/paper/2402.01680/) (2024)
- [ChatEval: Towards Better LLM-based Evaluators through Multi-Agent Debate](https://mlsanity.com/paper/2308.07201/) (2023)

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

- [ProvenAI: Provenance-Native Traces of Evidence in Generated Answers](https://mlsanity.com/paper/2606.26449/) (2026)

## Abstract (arXiv)

Practitioners deploying multi-agent large language model (LLM) systems must currently choose between communication topologies such as chain, star, mesh, and richer variants without any pre-inference diagnostic for which topology will amplify drift, converge to consensus, or remain robust under perturbation. Existing evaluation answers these questions only post hoc and only for the task measured. We introduce a structural diagnostic for multi-agent LLM communication graphs based on the successor representation M = (I - γ P)-1 of the row-stochastic communication operator, and we connect three of its spectral quantities, the spectral radius ρ(M), the spectral gap Delta(M), and the condition number kappa(M), to three distinct failure modes. We derive closed-form spectra for the chain, star, and mesh under row-stochastic normalization, and validate the predictions on a 12-step structured state-tracking task with Qwen2.5-7B-Instruct over 100 independent trials. The condition number is a perfect rank-order predictor of empirical perturbation robustness (rs = 1.0); the spectral gap partially predicts consensus dynamics (rs = 0.5); and the spectral radius is perfectly inverted with respect to cumulative error (rs = -1.0). We trace this inversion to a regime in which linear spectra are blind to non-contracting bias drift, and we propose an affine-noise extension of the predictive map that recovers the empirical ordering. We read this as a first step toward representational, drift-aware structural diagnostics for multi-agent LLM systems, sitting alongside classical spectral and consensus theory.