Developing automatic Math Word Problem (MWP) solvers is a challenging task that demands the ability of understanding and mathematical reasoning over the natural language. Recent neural-based approaches mainly encode the problem text using a language model and decode a mathematical expression over quantities and operators iteratively. Note the problem text of a MWP consists of a context part and a question part, a recent work finds these neural solvers may only perform shallow pattern matching between the context text and the golden expression, where question text is not well used. Meanwhile, existing decoding processes fail to enforce the mathematical laws into the design, where the representations for mathematical equivalent expressions are different. To address these two issues, we propose a new encoder-decoder architecture that fully leverages the question text and preserves step-wise commutative law. Besides generating quantity embeddings, our encoder further encodes the question text and uses it to guide the decoding process. At each step, our decoder uses Deep Sets to compute expression representations so that these embeddings are invariant under any permutation of quantities. Experiments on four established benchmarks demonstrate that our framework outperforms state-of-the-art neural MWP solvers, showing the effectiveness of our techniques. We also conduct a detailed analysis of the results to show the limitations of our approach and further discuss the potential future work. Code is available at https://github.com/sophistz/Question-Aware-Deductive-MWP.
翻译:开发自动数学文字问题解答器是一项具有挑战性的任务,需要具备理解和数学推理自然语言的能力。最近基于神经的处理办法主要是使用语言模型对问题文本进行编码,并用数量和操作员的数学表达方式进行迭代。注意到一个数学解码器的问题文本由上下文部分和问题部分组成,最近的一项工作发现这些神经解析器可能只能对上下文文字和金色表达式进行浅色的匹配,因为问题文本没有得到很好的使用。与此同时,现有的解码过程未能在数学表达式不同的设计中执行数学法律。为了解决这两个问题,我们建议了一个新的编码解码器-解码器结构,以充分利用问题文本,并保存了分步的通法。除了生成内容嵌入部分和问题部分外,我们的编码器进一步编码器进一步编码了问题文本,并用来指导解码过程。我们的解码器在每一个步骤中都使用深层表达表达式表达式表达式表达式,因此这些嵌入在数学等式表达式的表达式中都是不相同的。在四个既定的基准下进行实验,在充分利用问题解解码-解解解解码-解解解码结构分析我们未来框架, 显示我们未来框架的系统/变码分析结果的系统分析, 显示我们未来的分析结果,我们未来的分析,我们未来的分析是显示的系统分析。我们未来的分析。我们未来的分析。我们未来的框架的系统,我们未来的分析,我们未来的分析是显示法的方法,显示法。