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Yet ML-as-a-Service reveals little about what actually ran or whether returned outputs faithfully reflect the intended inputs. Users lack recourse against service downgrades (model swaps, quantization, graph rewrites, or discrepancies like altered ad embeddings). Verifying outputs is hard because floating-point(FP) execution on heterogeneous accelerators is inherently nondeterministic. Existing approaches are either impractical for real FP neural networks or reintroduce vendor trust. We present TAO: a Tolerance Aware Optimistic verification protocol that accepts outputs within principled operator-level acceptance regions rather than requiring bitwise equality. TAO combines two error models: (i) sound per-operator IEEE-754 worst-case bounds and (ii) tight empirical percentile profiles calibrated across hardware. 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