Title: Taming Imperfect Process Verifiers: A Sampling Perspective on Backtracking
Primary area: learning theory
Keywords: theory, reinforcement learning, sampling, process verifier, process reward, language model, LLM, value function, markov chain

Abstract: Test-time algorithms that combine the *generative* power of language models with *process verifiers* that assess the quality of partial generations offer a promising lever for eliciting new reasoning capabilities, but the algorithmic design space and computational scaling properties of such approaches are still opaque, and their benefits are far from apparent when one accounts for the cost of learning a high-quality verifier. Our starting point is the observation that seemingly benign errors in a learned verifier can lead to catastrophic failures for standard decoding techniques due to *error amplification* during the course of generation. We then ask: can this be improved with more sophisticated decoding strategies?

We introduce a new process-guided test-time sampling algorithm, VGB, which uses theoretically grounded *backtracking* to achieve *provably* better robustness to verifier errors. VGB interprets autoregressive generation as a random walk on a tree of partial completions, with transition probabilities guided by the process verifier and base model; crucially, backtracking occurs probabilistically. This process generalizes the seminal *Sinclair-Jerrum random walk* (Sinclair & Jerrum, 1989) from the literature on approximate counting and sampling in theoretical computer science, and a conceptual contribution of our work is to highlight parallels with this literature. Empirically, we demonstrate on both synthetic and real language modeling tasks that VGB outperforms baselines on a variety of metrics.

TL;DR: We give an algorithm for value-guided generation that provably avoids error amplification with an imperfect process verifier.