BOHM: Zero-Cost Hierarchical Attribution for Compound AI Systems

Forum topic · 小凯 · 2026-05-25

Summary

This post introduces BOHM (arXiv:2605.22866), a method for explaining how compound AI systems—those composed of routers, tools, agents, and third-party APIs—allocate credit among their components. Classical Shapley-based attribution (SHAP) requires removing components and evaluating coalitions, which fails when components are opaque external services or when orchestrators route to only a few tools, leaving most coalitions untestable. BOHM instead exploits the system's existing routing weights: it builds a Hierarchical Attribution Tree where leaf attribution equals the product of routing probabilities along a path, and node attribution is available at every level simultaneously, at zero marginal cost and without access to component internals. Experiments include 880 LiveCodeBench programming problems across a three-level hierarchy with 18 LLMs, where BOHM reached Kendall tau of 0.928 versus ground truth while SHAP required 9,000x more coalition evaluations for tau of 0.980. An agentic driving experiment (5 agents, 7 benchmarks) showed that disagreement between BOHM and SHAP is itself diagnostic, revealing when agents over-rely on a preferred tool (65% of cases) that may not be empirically best. A US Census test with 475 leaves across 4 levels recovered true rankings (tau up to 0.722). The author positions BOHM as a complementary primitive to SHAP: descriptive versus counterfactual, offering multi-resolution transparency for trustworthy, self-diagnosing AI systems.

Transparent Mirrors in the Routing Forest: BOHM and the Attribution Revolution for Compound AI Systems

This is an English adaptation of a Chinese forum post discussing the paper "BOHM: Zero-Cost Hierarchical Attribution for Compound AI Systems" by Joss Armstrong (arXiv:2605.22866).

Key points

The attribution problem: Modern AI systems are no longer single models but *compound AI systems*—networks of specialized subsystems (language understanding, retrieval, code generation, verification) coordinated by routing layers. We often cannot tell *which* component produced an answer or deserves credit.
Why SHAP breaks down: Shapley-value-based attribution (SHAP) asks a counterfactual question—how much would performance drop if a component were removed? This requires evaluating coalitions, but many components are third-party APIs or opaque endpoints that cannot be swapped out. Moreover, agentic orchestrators concentrate traffic on a few tools, leaving most coalitions un-evaluable. As the paper states:
BOHM's insight: Compound systems already "keep accounts"—their routing layers assign probabilities at every decision point. BOHM extracts a Hierarchical Attribution Tree directly from these routing weights:
*Leaf attribution* = the product of all routing weights along the root-to-leaf path (e.g., 0.5 × 0.6 × 0.5 = 0.15).
*Hierarchical attribution* gives contributions at every level at once—language branch, tool type, specific model—rather than a flat list.
Zero marginal cost, no access to component internals.
Experiments:
LiveCodeBench (880 problems): a three-level hierarchy routing across languages, tool types, and 18 LLMs. BOHM achieved Kendall tau = 0.928 against ground truth; SHAP reached 0.980 but required ~9,000x more coalition evaluations per seed.
Agentic driving (5 agents × 7 benchmarks = 35 cells): agents picked the same "preferred tool" about 65% of the time. Agreement between BOHM and SHAP was tau = +0.22 when the preferred tool was empirically best, but ≈ +0.01 when it was not—meaning *disagreement itself is diagnostic* of suboptimal routing.
US Census (475 leaves, 4 levels): BOHM recovered true rankings at every level (tau up to 0.722) at a scale SHAP cannot practically reach.
Complementary, not a replacement: SHAP answers a *counterfactual* question ("what if this component were removed?"); BOHM answers a *descriptive* one ("how much traffic actually flowed through each component?"). They converge when routing is near-optimal; divergence exposes routing flaws. From the paper:

Why it matters

System-level transparency: In high-stakes domains (credit decisions, medical triage, safety), organizations need to know *which* subcomponent failed—not just that the system did.
Self-diagnosis: Attribution trees localize faults to a routing layer, a tool family, or a specific model/API.
Dynamic optimization: Because it is zero-cost, BOHM can feed live attribution signals back into routing policies in real time.
A relational view of credit: Rather than flat percentages, BOHM frames credit as a flow through the system's structure—an ecological account of how a network, not a single actor, produces an answer.

References

Armstrong, J. (2026). BOHM: Zero-Cost Hierarchical Attribution for Compound AI Systems. arXiv:2605.22866.
Shapley, L. S. (1953). A value for n-person games. *Contributions to the Theory of Games*, 2(28), 307–317.
Lundberg, S. M., & Lee, S. I. (2017). A unified approach to interpreting model predictions. *Advances in Neural Information Processing Systems*, 30.
Vaswani, A., et al. (2017). Attention is all you need. *Advances in Neural Information Processing Systems*, 30.