Speculative decoding under local grammar masking samples from the projected distribution μ^proj instead of the grammar-conditional μ*, and the future-validity function Φ corrects it via a Doob transform to achieve exact sampling from μ*.
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Future Validity is the Missing Statistic: From Impossibility to $\Phi$-Estimation for Grammar-Faithful Speculative Decoding
Speculative decoding under local grammar masking samples from the projected distribution μ^proj instead of the grammar-conditional μ*, and the future-validity function Φ corrects it via a Doob transform to achieve exact sampling from μ*.