Constraint-Lattice Decoding with Posterior Certificates for Auditable Long-Context Autoregressive Reasoning

Abstract

Large autoregressive models are increasingly used to produce long-form reasoning and structured outputs in settings where reliability must be assessed, not merely assumed. In practical deployments, failures often arise from subtle inconsistencies that accumulate across many generated tokens: entity bindings drift, quantitative relations become incompatible with earlier commitments, and local fluency masks global constraint violations. This paper introduces a constraint-lattice decoding framework that treats generation as inference over a latent lattice of semantic commitments, enabling both improved constraint adherence and explicit posterior certificates of residual risk. The core contribution is a semiring-valued lattice transducer that couples token likelihood with constraint energies defined over evolving symbolic states, yielding a tractable dynamic program for selecting continuations that optimize a calibrated tradeoff between probability and constraint satisfaction. We formalize constraint extraction as a differentiable map from prefix representations to stochastic constraint factors, and we integrate these factors into decoding through an energy-tilted posterior that supports confidence reporting. A certificate is produced by bounding the posterior mass of all lattice paths whose constraint violation exceeds a threshold, which yields a principled abstention and verification mechanism without requiring external tools. The approach is compatible with standard cache-based decoding and can operate in streaming mode, updating certificates online as tokens arrive. We analyze identifiability of constraint states under partial observability, derive stability guarantees under prefix perturbations, and describe evaluation protocols that separate local perplexity gains from global consistency improvements.