Every Response Counts: Quantifying Uncertainty of LLM-based Multi-Agent Systems through Tensor Decomposition
Organizations: Arizona State University · University of California, Riverside
Abstract
While Large Language Model-based Multi-Agent Systems (MAS) consistently outperform single-agent systems on complex tasks, their intricate interactions introduce critical reliability challenges arising from communication dynamics and role dependencies. Existing Uncertainty Quantification methods, typically designed for single-turn outputs, fail to address the unique complexities of the MAS. Specifically, these methods struggle with three distinct challenges: the cascading uncertainty in multi-step reasoning, the variability of inter-agent communication paths, and the diversity of communication topologies. To bridge this gap, we introduce MATU, a novel framework that quantifies uncertainty through tensor decomposition. MATU moves beyond analyzing final text outputs by representing entire reasoning trajectories as embedding matrices and organizing multiple execution runs into a higher-order tensor. By applying tensor decomposition, we disentangle and quantify distinct sources of uncertainty, offering a comprehensive reliability measure that is generalizable across different agent structures. We provide comprehensive experiments to show that MATU effectively estimates holistic and robust uncertainty across diverse tasks and communication topologies.
Figures & tables
| Methods | GPT-4o | Qwen2.5-7B | Llama3.1-8B | |||
|---|---|---|---|---|---|---|
| AUROC | AUARC | AUROC | AUARC | AUROC | AUARC | |
| Dataset: MATH | ||||||
| Eigv(Agre)-final | 0.6359 | 0.6133 | 0.6506 | 0.8212 | 0.6340 | 0.6059 |
| Eigv(Agre)-Whole | 0.6308 | 0.6115 | 0.6314 | 0.8081 | 0.6215 | 0.5953 |
| P(true) | 0.6226 | 0.6070 | 0.6602 | 0.8291 | 0.6581 | 0.6225 |
| SAUP-Single | - | - | 0.6261 | 0.7982 | 0.6339 | 0.6008 |
| Method | AUROC ( ) |
|---|---|
| SAUP-Single | 0.5930 |
| SAUP-Multiple | 0.6201 |
| Eigv(Agre)-final | 0.6355 |
| MATU | 0.6770 |
Appendix figures & tables1 asset
Supplementary material from the paper’s appendix.
Appendix
| Case Info | Agent Reasoning Trajectories (Key Steps Only) | Uncertainty Quantification |
|---|---|---|
| Problem: Find the distance between intersections of and . True Answer: System Accuracy: 100% (10/10 runs correct) | Trajectory Type A: Direct & Concise Determine intersection coordinates Calculate distance Assessment: Ideal path, minimal token generation. | SAUP (Baseline): 0.88 (High) Issue: High cumulative entropy from verbose steps. Eigv-Whole (Baseline): 0.35 (Medium) Issue: Long contexts dilute NLI entailment accuracy. MATU (Ours): 0.05 (Low) Result: Correctly aligns semantic intent across diverse paths. |
| Trajectory Type B: Self-Correction Determine coordinates Correct y-axis calculation error Get correct coordinates Calculate distance Assessment: Agent successfully recovers from an error. | ||
| Trajectory Type C: Verbose (High Step Count) Determine coordinates Get coordinates … (intermediate steps) … Calculate distance Assessment: Logically identical to Type A, but higher step count increases cumulative entropy. |
Uncertainty Quantification
Uncertainty quantification estimates how reliable predictions and scientific inferences are, and how uncertainty propagates into decisions.
See all 649 papers