On the Query Complexity of Verifier-Assisted Language Generation

TL;DR

This paper develops a mathematical framework to understand how verifiers can improve the efficiency and quality of constrained language generation, showing that even simple algorithms benefit significantly from verifier access.

Contribution

It introduces a formal framework for verifier-assisted generation and demonstrates that simple algorithms can become tractable and more effective with verifier integration.

Findings

Verifier access can make intractable problems tractable.

Backtracking in rejection sampling improves efficiency and diversity.

Verifier-assisted algorithms outperform baseline methods.

Abstract

Recently, a plethora of works have proposed inference-time algorithms (e.g. best-of-n), which incorporate verifiers to assist the generation process. Their quality-efficiency trade-offs have been empirically benchmarked on a variety of constrained generation tasks, but the algorithmic design landscape is still largely poorly understood. In this paper, we develop a mathematical framework for reasoning about constrained generation using a pre-trained language model generator oracle and a process verifier--which can decide whether a prefix can be extended to a string which satisfies the constraints of choice. We show that even in very simple settings, access to a verifier can render an intractable problem (information-theoretically or computationally) to a tractable one. In fact, we show even simple algorithms, like tokenwise rejection sampling, can enjoy significant benefits from access to a verifier. Empirically, we show that a natural modification of tokenwise rejection sampling, in which the sampler is allowed to "backtrack" (i.e., erase the final few generated tokens) has robust and substantive benefits over natural baselines (e.g. (blockwise) rejection sampling, nucleus sampling)--both in terms of computational efficiency, accuracy and diversity.