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

Computer Science > Artificial Intelligence [Submitted on 11 May 2026] QUIVER: A Formal Framework for Quantifying Perturbation Propagation and Bifurcation in Compound AI Systems Prashanti Nilayam, Sankalp Nayak 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. Subjects: Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Multiagent Systems (cs.MA) Cite as: arXiv:2605.23956 [cs.AI]   (or arXiv:2605.23956v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2605.23956 Focus to learn more Submission history From: Prashanti Nilayam [view email] [v1] Mon, 11 May 2026 18:42:38 UTC (196 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-05 Change to browse by: cs cs.LG cs.MA References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)