Proposition 1. Assume the robust loss function is non-decreasing in [0, 1 ], (0) = 0 and The proof of Proposition 1 is mainly adapted from the proof in Kim & Scott ( 2012). For any given function: R! We first introduce a few notations that are useful for stating this result. B> (2 +) |O| where is the failure probability. By adapting Lemma 1 in Nguyen et al. ( 2022c) to uniform concentration bound, ImageNet We use the full ImageNet dataset that contains 1 .

ML models call for an equitable model valuation method to price them. In particular, we investigate the black-box access setting which allows querying a model (to observe predictions) without disclosing model-specific information (e.g., architecture and parameters). By exploiting a Dirichlet abstraction of a model's predictions, we propose a novel and equitable model valuation method called

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The key feature of circuits is that they enable one to precisely characterize tractability conditions (structural properties of the circuit) under which a given inference query can be computed exactly and efficiently. One can then enforce these circuit properties when compiling or learning a model to enable tractable inference.