OpenNovelty.org

Taming Imperfect Process Verifiers: A Sampling Perspective on Backtracking

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.5Download Report PDF
theoryreinforcement learningsamplingprocess verifierprocess rewardlanguage modelLLMvalue functionmarkov 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.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
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Overview

Overall Novelty Assessment

The paper introduces VGB, a value-guided sampling algorithm with stochastic backtracking designed to mitigate error amplification from imperfect process verifiers during autoregressive generation. Within the taxonomy, it occupies the 'Backtracking-Based Sampling for Verifier Robustness' leaf under 'Test-Time Decoding with Process Guidance'. Notably, this leaf contains only the original paper itself, with no sibling papers identified in the taxonomy. This suggests the specific focus on probabilistic backtracking for verifier robustness represents a relatively sparse research direction within the broader field of process-guided generation.

The taxonomy reveals that neighboring work primarily addresses verifier training (Process Reward Model Training, Uncertainty-Aware Value Modeling) and post-training optimization (Adversarial Critic-Based RL), rather than test-time decoding strategies. The closest related direction is 'Uncertainty-Aware Value Modeling', which tackles verifier imperfection through uncertainty quantification in value functions, whereas VGB addresses the same challenge through inference-time backtracking. Domain-specific applications (video QA, code generation) apply process guidance to specialized tasks but do not focus on the core algorithmic robustness question that VGB targets.

Among the three contributions analyzed, none were clearly refuted by the fourteen candidates examined. The VGB algorithm itself was compared against four candidates with no refutations found. The theoretical analysis of error amplification examined one candidate, and the connection to approximate sampling theory examined nine candidates, both without finding overlapping prior work. These statistics suggest that within the limited search scope—top-K semantic matches plus citation expansion—the paper's contributions appear distinct from existing literature, though the small candidate pool (fourteen total) means this assessment is necessarily preliminary.

Based on the limited literature search, the work appears to occupy a novel position at the intersection of test-time decoding and verifier robustness. The absence of sibling papers in its taxonomy leaf and the lack of refutations across fourteen candidates suggest originality, though a more exhaustive search covering broader decoding strategies and approximate sampling methods would strengthen this assessment. The taxonomy structure indicates the paper addresses a gap between verifier training methods and their deployment at inference time.

Taxonomy

Core-task Taxonomy Papers
5
3
Claimed Contributions
14
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: process-guided language model generation with imperfect verifiers. The field addresses how to leverage intermediate verification signals—often noisy or unreliable—to steer language model outputs toward correct solutions. The taxonomy organizes work into several main branches: Process Verification and Value Modeling focuses on learning step-level reward or value functions that assess partial reasoning traces; Test-Time Decoding with Process Guidance explores inference-time strategies such as search and sampling that use these verifiers to select or refine outputs; Post-Training Optimization with Imperfect Feedback examines how to train models using noisy process signals; and Domain-Specific Applications of Imperfect Verification applies these techniques to specialized settings like mathematical reasoning or visual question answering. Representative works such as ReasVQA[1] and InstructFlow[2] illustrate how process supervision can be integrated into both training pipelines and domain-specific architectures, while methods like RLAC[3] and Rewarding Progress[5] highlight different strategies for handling imperfect feedback during optimization. A central theme across these branches is the tension between exploiting verifier guidance and mitigating verifier errors. Many studies explore how to make decoding robust when step-level scores are unreliable, for instance by incorporating uncertainty estimates as in Robust Search Uncertainty[4] or by designing search procedures that can recover from incorrect intermediate assessments. Taming Imperfect Verifiers[0] sits within the Test-Time Decoding branch, specifically addressing backtracking-based sampling for verifier robustness. Its emphasis on allowing the generation process to revisit and correct earlier steps aligns closely with the broader goal of making search resilient to noisy signals, a concern shared by works like Robust Search Uncertainty[4]. Compared to approaches that primarily refine verifier training or aggregate multiple signals, Taming Imperfect Verifiers[0] focuses on the inference-time mechanism itself, offering a complementary perspective on how to navigate imperfect guidance without requiring perfect step-level supervision.

Claimed Contributions

VGB: Value-Guided Sampling with Stochastic Backtracking algorithm

The authors propose VGB, a novel algorithm that interprets autoregressive generation as a random walk on a tree of partial generations with probabilistic backtracking. The algorithm generalizes the Sinclair-Jerrum random walk and provides theoretical guarantees for robustness to value function errors during guided generation.

4 retrieved papers
Theoretical analysis of error amplification in action-level sampling

The authors provide theoretical examples showing that standard action-level rejection sampling catastrophically amplifies seemingly benign errors in learned value functions across long generation horizons, motivating the need for more sophisticated decoding strategies.

1 retrieved paper
Connection between value-guided inference and approximate sampling theory

The authors establish conceptual connections between value-guided language model inference and classical approximate counting and sampling techniques from theoretical computer science, particularly the Sinclair-Jerrum random walk, opening avenues for transferring ideas between these areas.

9 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Within the taxonomy built over the current TopK core-task papers, the original paper is assigned to a leaf with no direct siblings and no cousin branches under the same grandparent topic. In this retrieved landscape, it appears structurally isolated, which is one partial signal of novelty, but still constrained by search coverage and taxonomy granularity.

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

VGB: Value-Guided Sampling with Stochastic Backtracking algorithm

The authors propose VGB, a novel algorithm that interprets autoregressive generation as a random walk on a tree of partial generations with probabilistic backtracking. The algorithm generalizes the Sinclair-Jerrum random walk and provides theoretical guarantees for robustness to value function errors during guided generation.

Contribution

Theoretical analysis of error amplification in action-level sampling

The authors provide theoretical examples showing that standard action-level rejection sampling catastrophically amplifies seemingly benign errors in learned value functions across long generation horizons, motivating the need for more sophisticated decoding strategies.

Contribution

Connection between value-guided inference and approximate sampling theory

The authors establish conceptual connections between value-guided language model inference and classical approximate counting and sampling techniques from theoretical computer science, particularly the Sinclair-Jerrum random walk, opening avenues for transferring ideas between these areas.

Table of Contents