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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2601.17311 |
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| _version_ | 1866917269049704448 |
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| author | Liu, Bang Kong, Linglong Pei, Jian |
| author_facet | Liu, Bang Kong, Linglong Pei, Jian |
| contents | Multi-agent systems can improve reliability, yet under a fixed inference budget they often help, saturate, or even collapse. We develop a minimal and calibratable theory that predicts these regimes from three binding constraints of modern agent stacks: finite context windows, lossy inter-agent communication, and shared failures among similar agents. Each leaf agent is summarized by a compute-performance scaling exponent $β$; communication is captured by a message-length fidelity curve $γ(m)$; dependence is captured by an effective shared-error correlation $ρ$; and a context window $W$ imposes hard fan-in limits that make hierarchy necessary. For binary success/failure tasks with majority aggregation, we prove a sharp phase transition for deep $b$-ary trees with correlated inputs and lossy communication: a single scalar $α_ρ$ (combining $γ(m)$, $ρ$, and fan-in $b$) determines whether weak signal is amplified to a nontrivial fixed point or washed out to chance. In the amplifying regime, we derive an organization exponent $s$ and show that budgeted synergy, i.e., outperforming the best single agent under the same total budget, occurs exactly when $s>β$, yielding closed-form compute allocation rules and explicit budget thresholds. We further characterize saturation via a mixing depth and provide a conservative clipped predictor that remains accurate across growth and saturation. A continuous-performance warm-up gives closed-form risks for star, chain, and tree organizations, making correlation- and communication-induced floors explicit and exposing the core design trade-offs in a smooth setting. Finally, we validate the predicted phase boundaries in controlled synthetic simulations and show how the same mechanisms explain the dominant bottlenecks reported in recent large-scale matched-budget studies of LLM agent-system scaling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_17311 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Phase Transition for Budgeted Multi-Agent Synergy Liu, Bang Kong, Linglong Pei, Jian Artificial Intelligence Multi-agent systems can improve reliability, yet under a fixed inference budget they often help, saturate, or even collapse. We develop a minimal and calibratable theory that predicts these regimes from three binding constraints of modern agent stacks: finite context windows, lossy inter-agent communication, and shared failures among similar agents. Each leaf agent is summarized by a compute-performance scaling exponent $β$; communication is captured by a message-length fidelity curve $γ(m)$; dependence is captured by an effective shared-error correlation $ρ$; and a context window $W$ imposes hard fan-in limits that make hierarchy necessary. For binary success/failure tasks with majority aggregation, we prove a sharp phase transition for deep $b$-ary trees with correlated inputs and lossy communication: a single scalar $α_ρ$ (combining $γ(m)$, $ρ$, and fan-in $b$) determines whether weak signal is amplified to a nontrivial fixed point or washed out to chance. In the amplifying regime, we derive an organization exponent $s$ and show that budgeted synergy, i.e., outperforming the best single agent under the same total budget, occurs exactly when $s>β$, yielding closed-form compute allocation rules and explicit budget thresholds. We further characterize saturation via a mixing depth and provide a conservative clipped predictor that remains accurate across growth and saturation. A continuous-performance warm-up gives closed-form risks for star, chain, and tree organizations, making correlation- and communication-induced floors explicit and exposing the core design trade-offs in a smooth setting. Finally, we validate the predicted phase boundaries in controlled synthetic simulations and show how the same mechanisms explain the dominant bottlenecks reported in recent large-scale matched-budget studies of LLM agent-system scaling. |
| title | Phase Transition for Budgeted Multi-Agent Synergy |
| topic | Artificial Intelligence |
| url | https://arxiv.org/abs/2601.17311 |