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

TL;DR

This work tackles the sensitivity of LLMs to reasoning order by introducing order-centric data augmentation that enforces logical commutativity. It combines condition-order augmentation (shuffling independent premises) with answer-order augmentation (DAG-guided, topologically valid step reorderings) to expose models to multiple, equivalent reasoning paths. The method leverages DAGs to model dependencies among reasoning steps and uses LLMs to generate step-by-step solutions, from which augmented sequences are derived. Across benchmarks like FOLIO, RuleTaker, and LogicNLI, the approach improves reasoning performance and generalizes to other reasoning tasks (e.g., GSM8K, MATH), with DAG-dependency and augmentation frequency analyses providing guidance on when and how to apply the perturbations.

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.

Figures (6)

• Figure 1: A logical reasoning example. Independent premises can be freely reordered, while reasoning steps must be reordered without violating dependencies.
• Figure 2: The framework of order-centric data augmentation method. First, we apply condition augmentation by randomly reordering independent premises. Then, we enhance reasoning step order through a directed acyclic graph (DAG) to identify step dependencies and reorder them while preserving logical correctness.
• Figure 3: An example of generating a specific solution from data containing only labels and constructing a Directed Acyclic Graph (DAG) to represent the dependencies between steps. Due to space limitations, we only list the conclusions of each step without showing the detailed content.
• Figure 4: The performance of training efficiency across different training steps in condition order augmentation.
• Figure 5: The distribution of TFI index across different intervals in the training sets of FOLIO, RuleTaker, and LogicNLI. Since none of the datasets contain data in the [0.6-0.9) interval, this portion is omitted from the presentation.