Future Validity is the Missing Statistic: From Impossibility to $Φ$-Estimation for Grammar-Faithful Speculative Decoding
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915993419251712 |
|---|---|
| author | Nie, Wenhua Meng, Zijie Zou, Kun Lin, Zheng Li, Ziwei Zheng, Haoran Jang, Jyh-Shing Roger Zhang, Hao |
| author_facet | Nie, Wenhua Meng, Zijie Zou, Kun Lin, Zheng Li, Ziwei Zheng, Haoran Jang, Jyh-Shing Roger Zhang, Hao |
| contents | 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 $μ^{\mathrm{proj}}$ rather than the grammar-conditional distribution $μ^\star$. 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 $Φ_t(y)=\Pr_p[\mathrm{valid\ completion}\mid y]$ as the missing correction statistic. The target distribution is a Doob transform of the base model with $h=Φ$, while local masking corresponds to setting $h$ to one. With exact $Φ$, our oracle decoder FVO-Spec samples exactly from $μ^\star$; with approximate $Φ$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_07698 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Future Validity is the Missing Statistic: From Impossibility to $Φ$-Estimation for Grammar-Faithful Speculative Decoding Nie, Wenhua Meng, Zijie Zou, Kun Lin, Zheng Li, Ziwei Zheng, Haoran Jang, Jyh-Shing Roger Zhang, Hao Machine Learning Information Theory 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 $μ^{\mathrm{proj}}$ rather than the grammar-conditional distribution $μ^\star$. 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 $Φ_t(y)=\Pr_p[\mathrm{valid\ completion}\mid y]$ as the missing correction statistic. The target distribution is a Doob transform of the base model with $h=Φ$, while local masking corresponds to setting $h$ to one. With exact $Φ$, our oracle decoder FVO-Spec samples exactly from $μ^\star$; with approximate $Φ$, 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. |
| title | Future Validity is the Missing Statistic: From Impossibility to $Φ$-Estimation for Grammar-Faithful Speculative Decoding |
| topic | Machine Learning Information Theory |
| url | https://arxiv.org/abs/2605.07698 |