arXiv cs.AITuesday · May 26, 2026FREE

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

QUIVER, introduced in a new arXiv preprint (2605.23956v1), provides a formal framework for measuring how perturbations propagate through compound AI systems that chain multiple LLM calls into directed computation graphs. The framework defines four key components: (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 causing structural execution path changes; and (4) distribution faithfulness, quantifying when per-node evaluation datasets diverge from production distributions. The authors validate QUIVER on two production enterprise pipelines and a public DSPy multihop QA pipeline, demonstrating its applicability to real-world systems. This work addresses a critical gap: no existing framework quantifies perturbation propagation in stochastic, graph-structured pipelines where execution paths can diverge structurally. By providing formal metrics, QUIVER enables developers to systematically analyze robustness, identify fragile components, and understand how small input changes can cascade through complex AI systems.