Fast Controlled Generation from Language Models with Adaptive Weighted
  Rejection Sampling
Authors: name: Benjamin Lipkin, name: Benjamin LeBrun, name: Jacob Hoover Vigly, name: João Loula, name: David R. MacIver, name: Li Du, name: Jason Eisner, name: Ryan Cotterell, name: Vikash Mansinghka, name: Timothy J. O'Donnell, name: Alexander K. Lew, name: Tim Vieira

The dominant approach to generating from language models subject to some
constraint is locally constrained decoding (LCD), incrementally sampling tokens
at each time step such that the constraint is never violated. Typically, this
is achieved through token masking: looping over the vocabulary and excluding
non-conforming tokens. There are two important problems with this approach. (i)
Evaluating the constraint on every token can be prohibitively expensive -- LM
vocabularies often exceed 100,000 tokens. (ii) LCD can distort the global
distribution over strings, sampling tokens based only on local information,
even if they lead down dead-end paths. This work introduces a new algorithm
that addresses both these problems. First, to avoid evaluating a constraint on
the full vocabulary at each step of generation, we propose an adaptive
rejection sampling algorithm that typically requires orders of magnitude fewer
constraint evaluations. Second, we show how this algorithm can be extended to
produce low-variance, unbiased estimates of importance weights at a very small
additional cost -- estimates that can be soundly used within previously
proposed sequential Monte Carlo algorithms to correct for the myopic behavior
of local constraint enforcement. Through extensive empirical evaluation in
text-to-SQL, molecular synthesis, goal inference, pattern matching, and JSON
domains, we show that our approach is superior to state-of-the-art baselines,
supporting a broader class of constraints and improving both runtime and
performance. Additional theoretical and empirical analyses show that our
method's runtime efficiency is driven by its dynamic use of computation,
scaling with the divergence between the unconstrained and constrained LM, and
as a consequence, runtime improvements are greater for better models.