BOHM: Zero-Cost Hierarchical Attribution for Compound AI Systems
This paper introduces BOHM, a method to extract hierarchical attribution trees from routing weights in compound AI systems, requiring zero marginal cost and no access to component internals, providing multi-resolution attribution that correlates highly with SHAP but at a fraction of the cost.
Article intelligence
Key points
- BOHM leverages existing routing weights to build attribution trees at zero marginal cost.
- On benchmarks, BOHM achieves Kendall tau up to 0.928 vs SHAP's 0.980 but needs 9000x fewer evaluations.
- BOHM satisfies efficiency, monotonicity, symmetry, and weak suppression, but not Shapley additivity.
Why it matters
This matters because BOHM leverages existing routing weights to build attribution trees at zero marginal cost.
Technical impact
May affect model selection, inference cost, product capability, and evaluation benchmarks.
[2605.22866] BOHM: Zero-Cost Hierarchical Attribution for Compound AI Systems
[Submitted on 19 May 2026]
Title:BOHM: Zero-Cost Hierarchical Attribution for Compound AI Systems
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Abstract:Compound AI systems route tasks through hierarchies of specialised components. Attribution is dominated by Shapley-based methods (SHAP), which decompose a coalition value function into per-component marginal contributions and require evaluation of the system on arbitrary component subsets. That requirement fails for third-party APIs, opaque endpoints, and agentic orchestrators that concentrate routing on a few tools, leaving most coalitions un-evaluable from the deployed orchestrator. We introduce BOHM, which extracts a hierarchical attribution tree directly from the routing weights such systems already maintain: leaf attribution is the path product of root-to-leaf routing weights; level-k attribution is the induced distribution over depth-k nodes. The method has zero marginal cost, requires no access to component internals, and provides multi-resolution attribution at every level simultaneously, which flat methods cannot offer at any evaluation budget. BOHM and SHAP answer different questions and converge when the deployed router routes near-optimally. On 18 LLMs in a 3-level hierarchy over 880 LiveCodeBench problems, BOHM yields Kendall tau=0.928; SHAP reaches tau=0.980 at 9,000x more coalition evaluations per seed. On a 5-driver, 7-benchmark agentic study (35 cells, complete coverage), drivers concentrate routing on a single tool (top-share median 0.65), and cell-level tau(BOHM,SHAP) is predicted by whether the driver's top pick is the empirically best tool (mean +0.22 vs ~+0.01). On a US Census hierarchy (475 leaves, 4 levels), BOHM recovers ground-truth rankings at every level (tau up to 0.722). BOHM satisfies efficiency, monotonicity, symmetry, and weak suppression but not Shapley's additivity. It is best understood as a complementary primitive: a multi-resolution decomposition computable wherever routing state exists, whose disagreement with Shapley is itself diagnostic.
Comments: 35 pages, 10 figures, 20 tables
Subjects:
Artificial Intelligence (cs.AI); Machine Learning (cs.LG)
Cite as: arXiv:2605.22866 [cs.AI]
(or arXiv:2605.22866v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2605.22866
arXiv-issued DOI via DataCite
Submission history
From: Joss Armstrong [view email] [v1] Tue, 19 May 2026 19:38:14 UTC (354 KB)
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