Order Doesn't Matter, But Reasoning Does: Training LLMs with Order-Centric Augmentation

TL;DR

This paper proposes an order-centric data augmentation method based on logical commutativity to improve large language models' reasoning flexibility and generalization across logical transformations.

Contribution

It introduces a novel augmentation framework that leverages logical commutativity and DAG modeling to enhance LLM reasoning capabilities.

Findings

Significant performance improvements on logical reasoning benchmarks.

Enhanced model robustness to order variations in reasoning steps.

Better generalization to logically equivalent transformations.

Abstract

Logical reasoning is essential for large language models (LLMs) to ensure accurate and coherent inference. However, LLMs struggle with reasoning order variations and fail to generalize across logically equivalent transformations. LLMs often rely on fixed sequential patterns rather than true logical understanding. To address this issue, we introduce an order-centric data augmentation framework based on commutativity in logical reasoning. We first randomly shuffle independent premises to introduce condition order augmentation. For reasoning steps, we construct a directed acyclic graph (DAG) to model dependencies between steps, which allows us to identify valid reorderings of steps while preserving logical correctness. By leveraging order-centric augmentations, models can develop a more flexible and generalized reasoning process. Finally, we conduct extensive experiments across multiple logical reasoning benchmarks, demonstrating that our method significantly enhances LLMs' reasoning performance and adaptability to diverse logical structures. We release our codes and augmented data in https://github.com/qianxiHe147/Order-Centric-Data-Augmentation.