Deductive Beam Search: Decoding Deducible Rationale for Chain-of-Thought Reasoning

TL;DR

Addressing the problem of error accumulation in chain-of-thought reasoning, this paper introduces Deductive Beam Search (DBS), a framework that couples step-wise beam search with a deductive verifier to select deducible reasoning steps. A scalable two-stage data construction method trains the verifier to detect grounding and logic errors, enabling robust pruning of non-deducible steps across models from 7B to ChatGPT on eight diverse datasets. Empirical results show DBS boosts accuracy across arithmetic, commonsense, and symbolic tasks, while also reducing token costs and exposing diverse reasoning errors for better reliability. The work advances practical, deducible reasoning in LLMs and offers a model-agnostic, verification-driven decoding paradigm with broad applicability.

Abstract

Recent advancements have significantly augmented the reasoning capabilities of Large Language Models (LLMs) through various methodologies, especially chain-of-thought (CoT) reasoning. However, previous methods fail to address reasoning errors in intermediate steps, leading to accumulative errors. In this paper, we propose Deductive Beam Search (DBS), which seamlessly integrates CoT and deductive reasoning with step-wise beam search for LLMs. Our approach deploys a verifier, verifying the deducibility of a reasoning step and its premises, thus alleviating the error accumulation. Furthermore, we introduce a scalable and labor-free data construction method to amplify our model's verification capabilities. Extensive experiments demonstrate that our approach significantly enhances the base performance of LLMs of various scales (7B, 13B, 70B, and ChatGPT) across 8 reasoning datasets from 3 diverse reasoning genres, including arithmetic, commonsense, and symbolic. Moreover, our analysis proves DBS's capability of detecting diverse and subtle reasoning errors and robustness on different model scales.

Figures (6)

• Figure 1: Example of error in an intermediate step leading to accumulative error from Llama2-7b. The dependency on intermediate steps introduces accumulative errors in the reasoning process.
• Figure 2: Overview of Deductive Beam Search. We illustrate the process under the configuration of beam size 2 and sampling times 2.
• Figure 3: Distributions of language model and verifier scores on reasoning paths.
• Figure 4: Accuracy under different beam sizes on different models.
• Figure 5: Accuracy under different deductive score thresholds on greedy decoding results.