Improving the Robustness of Scene-Aware Neuro-Symbolic Solving for Arithmetic Word Problems Under Input Perturbations

Robust Arithmetic Word Problem (AWP) solving is important for applying mathematical reasoning systems in educational scenarios, where problem statements may contain changed numerical values, paraphrased descriptions, or irrelevant distracting information. Although Large Language Models (LLMs) have shown strong potential in solving AWPs, their reasoning processes may still be sensitive to surface-form variations and perturbation-induced noise. To address this issue, this paper proposes a Scene-Aware Neuro-Symbolic solver designed to improve the robustness of AWP solving under perturbations. The proposed method extends the existing scene-aware framework by introducing perturbation-oriented mechanisms at the scene, relation, and symbolic-solving levels. A Chain-of-Scene (CoS) prompting strategy first generates candidate scenes, after which goal-guided filtering retains target-related and bridge scenes while removing distractor-induced scenes. The retained scenes are then processed by the Scene-Aware Syntax-Semantics ($S^2$) method to extract explicit and implicit relations, and relation consistency checking is applied to remove locally plausible but globally irrelevant relations. Finally, the symbolic solver performs iterative equation-based reasoning over the filtered relation sets, with fallback recovery activated when standard solving does not produce a target-compatible answer. Experiments on AGG, MAWPS, and GSM8K show an average accuracy of 92.8% on clean datasets. On GSM-Perturb and AWP-Perturb, the solver achieves perturbed accuracies of 80.8% and 87.5%, with robustness drops of 8.3% and 6.8%, respectively. Ablation results show that scene filtering and relation consistency checking are the main contributors to reducing perturbation-induced errors. These findings suggest that combining LLM-based scene understanding with symbolic relation reasoning is a promising direction for improving the robustness and interpretability of AWP solvers in the evaluated perturbation settings.