Prefix parsing asks whether an input prefix can be extended to a complete string generated by a given grammar. In the weighted setting, it also provides prefix probabilities, which are central to context-free language modeling, psycholinguistic analysis, and syntactically constrained generation from large language models. We introduce the prefix grammar transformation, an efficient reduction of prefix parsing to ordinary parsing. Given a grammar, our method constructs another grammar that generates exactly the prefixes of its original strings. Prefix parsing is then solved by applying any ordinary parsing algorithm on the transformed grammar without modification. The reduction is both elegant and practical: the transformed grammar is only a small factor larger than the input, and any optimized implementation can be used directly, eliminating the need for bespoke prefix-parsing algorithms. We also present a strategy-based on algorithmic differentiation-for computing the next-token weight vector, i.e., the prefix weights of all one-token extensions, enabling efficient prediction of the next token. Together, these contributions yield a simple, general, and efficient framework for prefix parsing.
Reasoning prefixes shape the future trajectory of LLM problem solving, yet existing process reward models usually evaluate them through local step correctness. We argue that correctness is a useful but indirect proxy for the effect we ultimately care about: whether a prefix increases the probability of successful completion. We define this effect as prefix gain, the solve-rate improvement induced by conditioning lightweight student model group on a prefix, and use it to train a Prefix Utility Model (PUM) with a simple pairwise ranking objective. PUM learns outcome-grounded prefix utility and can score both complete trajectories and partial reasoning prefixes. Across Best-of-N selection, beam search, and reinforcement learning on mathematical reasoning, PUM provides a strong prefix-level supervision signal, especially when candidate pools are large, search budgets increase, or rule-based rewards are sparse. We release all data, models, and code at https://zhiqix.github.io/pum-project-page.
We introduce PARSE (PArallel pRefix Speculative Engine), a speculative generation framework that accelerates large language model (LLM) inference by parallelizing prefix verification on a semantic level. Existing speculative decoding methods are fundamentally limited by token-level equivalence: the target model must verify each token, leading to short acceptance lengths and modest speedups. Moving to semantic or segment-level verification can substantially increase acceptance granularity, but prior approaches rely on sequential verification, introducing significant overhead and limiting practical gains. PARSE introduces parallel prefix verification, enabling semantic-level verification without sequential checks. Given a full draft from a draft model, the target model evaluates correctness across multiple prefixes in a single forward pass using a custom attention mask, directly identifying the maximal valid prefix. This eliminates sequential segment verification, and makes verification compute-efficient. PARSE is orthogonal to token-level speculative decoding and can be composed with it for additional gains. Across models and benchmarks, PARSE delivers 1.25× to 4.3× throughput gain over the target model, and 1.6× to 4.5× when composed with EAGLE-3, all with negligible accuracy degradation. This demonstrates parallel prefix verification as an effective, general approach to accelerating LLM inference.
We revisit punctuation-aware tree binarization for constituency parsing and ask whether dependency-induced headedness improves binary parser supervision. Although learned heads substantially outperform rule-based heads in intrinsic head prediction, they do not yield consistent parsing gains after debinarization. In particular, punctuation-conditioned evaluation shows that learned headedness underperforms rule-based binarization in macro-average punctuation-sensitive F1, despite a small overall gain on CTB. Similar instability appears under cross-treebank transfer. These results suggest that \ycc{linguistically grounded} headedness is not necessarily parser-optimal when used as a binarization control signal. The paper presents a negative result: better head prediction does not imply better punctuation-sensitive constituency parsing.