A multi-view graph learning model with dual strategies for solving math word problems

TL;DR

• 提出多视图图学习到树的 MWP 求解模型 MVG-DS-T，同时建模语义与数量关系两种图视图。
• 用“结构重构”获得更适配下游任务的表示，用“跨视图对齐”提升多视图一致性。
• 在 Math23K 与 MAWPS 上达到与 SOTA Graph2Tree 类方法相当的性能。

论文信息

• Venue: (2024)
• DOI: 10.1016/j.neucom.2024.127674
• Keywords: Math word problem, Natural language processing, Text mining, Multi-view graph learning

问题与动机

• 任务：数学应用题（Math Word Problem, MWP）从文本生成可执行的方程/表达式。
• 现有图方法常依赖先验知识图/手工构图：构图噪声与偏差会影响鲁棒性；多图视图学习容易“各学各的”，缺少统一表示。

方法概览（MVG-DS-T）

flowchart LR
  T[MWP 文本] --> SDP[语义依存解析]
  SDP --> SG[语义图 (Semantic Graph)]
  T --> Q[数量/量词抽取]
  Q --> QG[数量图 (Quantitative Graph)]
  SG --> ENC[多视图图编码器\n(重构 + 对齐)]
  QG --> ENC
  ENC --> DEC[树结构解码器\n(Graph2Tree)]
  DEC --> EQ[方程/表达式]
  EQ --> A[答案]
  ENC -->|输出表示| R[MVG-DS-T]

图视图构建

• 语义图：基于语义依存分析（semantic dependency parsing）构建词/实体关系。
• 数量图：强调数量、单位、比较等与数值推理相关的边与结构。

双策略多视图学习

• 重构（Reconstruction）：对基准图结构进行重构学习，提取更适配下游表达式生成的表示。
• 对齐（Alignment）：跨视图约束语义/数量嵌入的一致性，缓解独立视图表示不统一的问题。

解码与训练细节

• 解码：树结构解码器（Graph2Tree 风格）自顶向下生成表达式。
• 损失：引入自适应长度归一化的平衡项，缓解不同表达式长度带来的训练偏置。

主要贡献（论文原文归纳）

• To our knowledge, this is the first instance of employing se- mantic dependency parsing within the realm of MWP, presenting a groundbreaking solution for constructing semantic graphs in mathematical problem-solving.
• A novel multi-view graph learning encoder is introduced, which utilizes reconstruction and alignment strategies to generate adap- tive and consistent representations from multiple graph views, providing rich semantic information for precise reasoning of mathematical expressions.
• Experiments are conducted on two widely-used MWP-solving datasets, MAWPS and Math23K. Experimental results demon- strate that the proposed approach is comparable to state-of-the-art graph-based methods.

实验与结果（高层总结）

• 数据集：MAWPS, Math23K
• 结论：作者报告 MVG-DS-T 的整体效果与当前主流 Graph2Tree 类图方法“可比/相当”，并通过消融/对比展示各模块有效性（详见论文实验章节）。

局限与展望（来自结论与个人解读）

• 仍依赖解析/构图质量：语义依存与数量抽取的误差会向下传递。
• 多视图策略的收益可能与数据集/题型分布相关；在更复杂的多步推理题上仍需验证。
• 未来方向：结合预训练模型、更强的图结构学习与外部知识整合（论文结论亦提及）。

mindmap
  root((MVG-DS-T))
    任务
      "数学应用题 (MWP)"
      "生成解题表达式"
    图构建
      "语义依存图"
      "数量关系图"
    学习策略
      "结构重构 (adaptive)"
      "跨视图对齐 (consistent)"
    解码
      "树解码 (Graph2Tree)"
      "长度归一化损失"
    实验
      (MAWPS)
      (Math23K)

摘要（原文提取）

Recently, graph-based deep learning models have exhibited remarkable performance in generating solution expressions for the math word problem (MWP). However, most of these models have not taken into account the limitations and errors in constructing prior knowledge graphs, which may affect their accuracy and reliability in practical applications. In addition, during graph learning, they focus on extracting information from each given graph, while neglecting the adaptability and unification of graph representation learning. In this paper, we propose a novel multi-view graph learning-to-tree model with dual-strategy (MVG-DS-T), in which it performs adaptive and consistent multi-view representation learning through two benchmark graphs. Specifically, we construct benchmark graphs via semantic dependency parsing of MWP text, considering both semantic and quantitative aspects, i.e., semantic graph and quantitative graph. Then, the reconstruction strategy is employed to reconstruct the structure of the benchmark graphs to capture the adaptive representation information suitable for downstream tasks, while the alignment strategy is utilized to overcome the limitation of independent view representations by unifying the semantic and quantity embedding information through graph structure. Also, an adaptive length normalized loss balancing term for the tree-based decoder is introduced to control the model focus on label length during training, resulting in better equation generation. Extensive experiments demonstrate the effectiveness of the proposed approach on the MWP task. The empirical results show that MVG-DS-T achieves performance comparable to that of the state-of-the-art graph-based models in the existing literature.

参考

• PDF 元数据来源：本地 PDF（Elsevier / ScienceDirect 导出）