Future Validity is the Missing Statistic: From Impossibility to Phi-Estimation for Grammar-Faithful Speculative Decoding

arXiv:2605.07698v1 Announce Type: new Abstract: Grammar-constrained generation is often combined with local vocabulary masking and speculative decoding, but the resulting sampling law is not the grammar-conditional distribution users usually intend. We show that any speculative decoder with local mask access, Leviathan rejection, and rollback soundness samples from the locally projected distribution mu^{proj} rather than the grammar-conditional distribution mu^star. This extends the GAD impossibility result to speculative decoding; on Dyck grammars with Qwen3-8B, the total-variation gap can reach 0.996. We identify the future-validity function Phi_t(y)=Pr_p[valid completionmid y] as the missing correction statistic. The target distribution is a Doob transform of the base model with h=Phi, while local masking corresponds to setting h to one. With exact Phi, our oracle decoder FVO-Spec samples exactly from mu^star; with approximate Phi, we bound the resulting total-variation error. Because exact future validity is hard for general context-free grammars, we evaluate estimator hierarchies on tractable Dyck and finite JSON languages. OneStep reduces Dyck TV by 14% with under 1% throughput overhead, exact dynamic programming reduces it by 97%, and finite-language correction closes JSON gaps to numerical precision. All fidelity claims are scoped to enumerable grammars and token tries.

Source: arXiv cs.LG | 2026-05-11