arXiv cs.AIMonday · May 25, 2026FREE

BOHM: Zero-Cost Hierarchical Attribution for Compound AI Systems

BOHM, detailed in a new arXiv preprint (2605.22866), offers a method for hierarchical attribution in compound AI systems that incurs zero marginal cost. Unlike Shapley-based methods like SHAP, which require evaluating the system on arbitrary component subsets—often impossible with third-party APIs or opaque endpoints—BOHM extracts an attribution tree directly from the routing weights that systems already maintain. Leaf attribution is computed as the path product of root-to-leaf routing weights, while level-k attribution is the induced distribution over depth-k nodes. This provides multi-resolution attribution at every level simultaneously, a capability flat methods cannot offer at any evaluation budget. BOHM and SHAP answer different questions but converge when the deployed router routes near-optimally. The method was evaluated on 18 LLMs in a 3-level hierarchy over 880 LiveCodeBench problems, yielding key insights into component contributions without additional computational cost.