# QUIVER: A Formal Framework for Quantifying Perturbation Propagation and Bifurcation in Compound AI Systems

arXiv: https://arxiv.org/abs/2605.23956 · HTML: https://mlsanity.com/paper/2605.23956/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 24 references that are in the map.
- First posted on arXiv 11 May 2026.

## Builds on (most cited first, 22 of 22)

- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [DSPy: Compiling Declarative Language Model Calls into Self-Improving Pipelines](https://mlsanity.com/paper/2310.03714/) (2023)
- [ColBERTv2: Effective and Efficient Retrieval via Lightweight Late Interaction](https://mlsanity.com/paper/2112.01488/) (2021)
- [Ragas: Automated Evaluation of Retrieval Augmented Generation](https://mlsanity.com/paper/2309.15217/) (2023)
- [TextGrad: Automatic "Differentiation" via Text](https://mlsanity.com/paper/2406.07496/) (2024)
- [Assisting in Writing Wikipedia-like Articles From Scratch with Large Language Models](https://mlsanity.com/paper/2402.14207/) (2024)
- [Towards a Science of Scaling Agent Systems](https://mlsanity.com/paper/2512.08296/) (2025)
- [AgenTracer: Who Is Inducing Failure in the LLM Agentic Systems?](https://mlsanity.com/paper/2509.03312/) (2025)
- [Trace is the Next AutoDiff: Generative Optimization with Rich Feedback, Execution Traces, and LLMs](https://mlsanity.com/paper/2406.16218/) (2024)
- [Understanding the Information Propagation Effects of Communication Topologies in LLM-based Multi-Agent Systems](https://mlsanity.com/paper/2505.23352/) (2025)
- [UProp: Investigating the Uncertainty Propagation of LLMs in Multi-Step Agentic Decision-Making](https://mlsanity.com/paper/2506.17419/) (2025)
- [LLM-AutoDiff: Auto-Differentiate Any LLM Workflow](https://mlsanity.com/paper/2501.16673/) (2025)
- [RAFFLES: Reasoning-based Attribution of Faults for LLM Systems](https://mlsanity.com/paper/2509.06822/) (2025)
- [From Spark to Fire: Modeling and Mitigating Error Cascades in LLM-Based Multi-Agent Collaboration](https://mlsanity.com/paper/2603.04474/) (2026)
- [An Information Theoretic Perspective on Agentic System Design](https://mlsanity.com/paper/2512.21720/) (2025)
- [Compound AI Systems Optimization: A Survey of Methods, Challenges, and Future Directions](https://mlsanity.com/paper/2506.08234/) (2025)
- [Geometric Dynamics of Agentic Loops in Large Language Models](https://mlsanity.com/paper/2512.10350/) (2025)
- [ValueFlow: Measuring the Propagation of Value Perturbations in Multi-Agent LLM Systems](https://mlsanity.com/paper/2602.08567/) (2026)
- [A Control-Theoretic Foundation for Agentic Systems](https://mlsanity.com/paper/2603.10779/) (2026)
- [TextResNet: Decoupling and Routing Optimization Signals in Compound AI Systems via Deep Residual Tuning](https://mlsanity.com/paper/2602.08306/) (2026)
- [Textual Equilibrium Propagation for Deep Compound AI Systems](https://mlsanity.com/paper/2601.21064/) (2026)

## Built on by (most cited first, 2 of 2)

- [Detection Without Correction: A Two-Parameter Decomposition of Multi-Stage LLM Pipelines](https://mlsanity.com/paper/2605.27559/) (2026)
- [CAFE: A Compound-AI Factorial Evaluation Framework](https://mlsanity.com/paper/2607.10380/) (2026)

## Abstract (arXiv)

Compound AI systems that chain multiple LLM calls into directed computation graphs are now the dominant architecture for production AI. Although these architectures leverage heterogeneous nodes with mixed-mode outputs, no existing framework quantifies how perturbations propagate through such pipelines, where nodes are stochastic and execution paths can diverge structurally. We introduce QUIVER, a formal framework for measuring perturbation propagation in graph-structured LLM pipelines. The framework defines: (1) a sensitivity matrix with type-dispatched distance metrics that classifies edges as amplifiers, absorbers, or threshold-sensitive, complemented by occurrence-lift; (2) trajectory divergence decomposing variation into value drift, structural path divergence, and iteration count divergence; (3) bifurcation thresholds identifying the smallest perturbation that causes structural execution path changes; and (4) distribution faithfulness, quantifying when per node evaluation datasets diverge from production distributions. We validate on two production enterprise pipelines and a public DSPy multihop QA pipeline, three structurally distinct architectures. Across 8,200+ instrumented traces (32,000+ pair comparisons), we demonstrate that QUIVER reveals distinct sensitivity profiles across architectures, distinguishes mechanistically different cascade patterns producing identical divergence rates, predicts nodes prone to trajectory bifurcation from observational data alone, and localizes stale evaluation artifacts to specific node-field categories that aggregate metrics cannot surface.