Compiling Autoregressive LLM Control into Policy-Exact Parallel Inference for Hierarchical RAG

arXiv:2610.30664v1 Announce Type: new Abstract: Large language models increasingly act as controllers in structured decision pipelines, yet their decisions are still executed by autoregressive text decoding. Hierarchical RAG is one such setting: at each frontier of a document tree, an LLM commits to $b$ of $k$ sections under an input-dependent action grammar, executed as either failure-prone free-form JSON or reliable but strictly serial grammar-constrained generation. We show that this serialization is unnecessary for bounded-horizon control: the reachable future forms a shallow action-prefix tree, which we compile --- one root prefill plus one tree-causal probe evaluate every prefix-conditioned action distribution with serial decoding's tokens, positions, and causal ancestry. A prefix-state lemma makes compiled control policy-exact in exact arithmetic: the same policy with a two-forward critical path and zero output tokens. One further probe pass certifies the exact order-marginalized MAP set. Across four document-disjoint splits and two scales on the primary MetaX device, compiled control matches the serial policy on $84$--$89%$ of questions --- every instrumented divergence a floating-point near-tie --- and cuts control latency by $35$--$47%$ versus token-wise serial decoding and $6$--$7%$ versus an idealized chunked engine; an H800 repetition preserves the ordering.