LLM Decoding and Grammar Constraints: An In-Depth Analysis

A new study explores the decoding process of large language models (LLMs) when it is constrained by formal grammars. The research focuses on the interaction between the autoregressive distribution of the next tokens and a reachability oracle based on a pushdown system compiled from a context-free grammar (CFG).

Oracle Invariance and Ambiguity Costs

The researchers demonstrate an oracle invariance theorem: language-equivalent grammars induce identical sets of admissible next tokens for every prefix, and therefore identical logit masks. However, these grammars can lead to significantly different compiled state spaces and online ambiguity costs. A left-to-right structural ambiguity cost (SAC) is introduced, measuring the incremental growth of the packed-parse-forest per token.

Lower Bounds and Grammar Optimization

The study establishes engine-independent lower bounds: any sound, retrieval-efficient, and parse-preserving online masking engine must incur ฮฉ(t^2) work per token on a specific constant-size CFG family. Decoding-cost equivalence classes of grammars are defined, and the existence of minimal-SAC representatives within bounded rewrite families is demonstrated.

Integration with Modern Architectures

The results are integrated with Transformer and Mixture-of-Experts architectures, deriving latency envelopes in terms of vocabulary size, active state sets, and beam width. SAC is linked to instrumentation-based predictive performance models and automated grammar optimization.

For those evaluating on-premise deployments, there are trade-offs to consider. AI-RADAR offers analytical frameworks on /llm-onpremise to evaluate these aspects.