Your Language Model May Think Too Rigidly: Achieving Reasoning Consistency with Symmetry-Enhanced Training (2025)

Abstract: Large Language Models (LLMs) have demonstrated strong reasoning capabilities across various tasks. However, even minor variations in query phrasing, despite preserving the underlying semantic meaning, can significantly affect their performance. To address this, we focus on enhancing LLMs’ awareness of symmetry in query variations and propose syMmetry-ENhanceD (MEND) data augmentation, a data-centric approach that improves the model’s ability to extract useful information from context. Unlike existing methods that emphasize reasoning chain augmentation, our approach improves model robustness at the knowledge extraction stage through query augmentation, enabling more data-efficient training and stronger generalization to Out-of-Distribution (OOD) settings. Extensive experiments on both logical and arithmetic reasoning tasks show that MEND enhances reasoning performance across diverse query variations, providing new insights into improving LLM robustness through structured dataset curation.

## introduction large language models (llms) have demonstrated superior performance across various reasoning tasks, including mathematical reasoning @xcite @xcite @xcite , code generation @xcite @xcite , and autonomous system decision-making @xcite @xcite . despite their ability to handle complex reasoning tasks, llms exhibit naive failure modes. for instance, they suffer from premise order sensitivity @xcite , the reverse-curse phenomenon @xcite , and distractibility @xcite , making them vulnerable to variations in the natural language description of a query, even when the underlying semantic meaning remains unchanged. a reasoning problem can be structurally decomposed into two layers @xcite : the underlying layer represents the semantic meaning, which includes the structure of reasoning chains and the knowledge required for logical deduction, while the upper layer consists of the surface form, referring to the natural language description of the problem @xcite . the inability of llms to maintain consistent performance across different surface forms highlights the need for reasoning consistency, which we define as the model's ability to generate consistent and correct answers from different query transformations of a problem with the same semantic meaning. in this work, we explore the question: how to improve llms' reasoning consistency across varying surface forms. our key insight is that llm reasoning problems maintain certain underlying structures, such as description symmetry, which describes transformations of the query description that preserve its semantic meaning. existing llm post-training methods typically focus on improving the quality of training data for reasoning chains, such as using bootstrapping to enhance reasoning diversity @xcite . however, these methods overlook the description symmetry in reasoning tasks, which naturally exists in surface form variations. as a result, they often suffer from overfitting and inconsistent reasoning with respect to different surface forms as shown in figure 1 . to address this issue, we propose symmetry-enhanced (mend) data augmentation for llm post-training. our method augments the dataset with the symmetry information, enforcing the model's capability to better capture semantic meanings in different query variations, thereby improving post-training data efficiency and enhancing ood generalization. the main contributions of this work are: ## mend data augmentation in this section, we first analyze the surface form and its transformations and reveal the symmetry in description queries. we then discuss llms' capability for reasoning consistency. lastly, we introduce the data augmentation method to improve reasoning consistency and a probing tool for capability verification. ## experiments in the experiments, we are going to answer the following research questions. (rq-1) how do current llms perform in terms of reasoning consistency? (rq-2) how does mend benefit reasoning consistency? (rq-3) why does mend improve reasoning consistency? to answer these questions, we make the following experiment setup.