Large language models (LLMs) have achieved significant success in reasoning tasks, including mathematical reasoning and logical deduction. Among these reasoning tasks, graph problems stand out due to their complexity and unique structural characteristics, attracting considerable attention from researchers. Previous studies have explored LLMs’ graph reasoning abilities through various techniques, such as different encoding methods for graph structures and the use of carefully designed prompts. However, a critical factor has been mostly overlooked: the prompt sequential order in which graph descriptions are presented to the models. In this study, we present the first comprehensive analysis of how the order of graph descriptions impacts LLM performance. Specifically, we comprehensively evaluate four graph description orders across six graph problems using six mainstream LLMs. The results reveal that: (1) ordered graph descriptions significantly improve LLMs’ comprehension of graph structures; (2) the robustness of LLMs to graph description order varies across different tasks; and (3) the impact of graph order on performance is closely related to the inherent characteristics of tasks. This study provides a critical advancement in the application of LLMs for solving graph-related problems, paving the way for future research to optimize model performance through strategic graph description ordering.

Language models (LMs) are indispensable tools for natural language processing tasks, but their vulnerability to adversarial attacks remains a concern. While current research has explored adversarial training techniques, their improvements to defend against word-level attacks have been limited. In this work, we propose a novel approach called Semantic Robust Defence (SemRoDe), a Macro Adversarial Training strategy to enhance the robustness of LMs. Drawing inspiration from recent studies in the image domain, we investigate and later confirm that in a discrete data setting such as language, adversarial samples generated via word substitutions do indeed belong to an adversarial domain exhibiting a high Wasserstein distance from the base domain. Our method learns a robust representation that bridges these two domains. We hypothesize that if samples were not projected into an adversarial domain, but instead to a domain with minimal shift, it would improve attack robustness. We align the domains by incorporating a new distance-based objective. With this, our model is able to learn more generalized representations by aligning the model’s high-level output features and therefore better handling unseen adversarial samples. This method can be generalized across word embeddings, even when they share minimal overlap at both vocabulary and word-substitution levels. To evaluate the effectiveness of our approach, we conduct experiments on BERT and RoBERTa models on three datasets. The results demonstrate promising state-of-the-art robustness.