Math word problem (MWP) solving aims to understand the descriptive math
problem and calculate the result, for which previous efforts are mostly devoted
to upgrade different technical modules. This paper brings a different
perspective of \textit{reexamination process} during training by introducing a
pseudo-dual task to enhance the MWP solving. We propose a pseudo-dual (PseDual)
learning scheme to model such process, which is model-agnostic thus can be
adapted to any existing MWP solvers. The pseudo-dual task is specifically
defined as filling the numbers in the expression back into the original word
problem with numbers masked. To facilitate the effective joint learning of the
two tasks, we further design a scheduled fusion strategy for the number
infilling task, which smoothly switches the input from the ground-truth math
expressions to the predicted ones. Our pseudo-dual learning scheme has been
tested and proven effective when being equipped in several representative MWP
solvers through empirical studies. \textit{The codes and trained models are
available at:} https://github.com/steven640pixel/PsedualMWP.
\end{abstract}

通过引入伪双任务来增强数学单词问题求解的研究，该研究在训练期间提出了一种重新审视过程的不同视角，并以模型不可知的方式模拟了该过程。通过实证研究，证明该伪双任务学习方案在几种代表性数学单词问题求解器上的有效性。

使用复查法解决数学应用题

Solving Math Word Problems with Reexamination

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 this https URL.

该研究提出了一种基于编码器 - 解码器的模型，完全利用问题文本并保留逐步的交换律，以产生无论数量的排列方式如何都具有不变性的表达式嵌入，并进一步对问题文本进行编码以指导解码过程，可以提高数学问题自动求解程序的性能。

提升神经数学问题求解器的技术

Techniques to Improve Neural Math Word Problem Solvers

Developing automatic Math Word Problem (MWP) solvers has been an interest of
NLP researchers since the 1960s. Over the last few years, there are a growing
number of datasets and deep learning-based methods proposed for effectively
solving MWPs. However, most existing methods are benchmarked soly on one or two
datasets, varying in different configurations, which leads to a lack of
unified, standardized, fair, and comprehensive comparison between methods. This
paper presents MWPToolkit, the first open-source framework for solving MWPs. In
MWPToolkit, we decompose the procedure of existing MWP solvers into multiple
core components and decouple their models into highly reusable modules. We also
provide a hyper-parameter search function to boost the performance. In total,
we implement and compare 17 MWP solvers on 4 widely-used single equation
generation benchmarks and 2 multiple equations generation benchmarks. These
features enable our MWPToolkit to be suitable for researchers to reproduce
advanced baseline models and develop new MWP solvers quickly. Code and
documents are available at this https URL

本文介绍了 MWPToolkit，这是第一个解决 MWPs 的开源框架，其中将现有 MWP 求解器的过程分解为多个核心组件，并将它们的模型解耦为可重用的模块，提供了一个超参数搜索功能来提高性能，并在 4 个广泛使用的单方程产生基准和 2 个多方程产生基准上，实现并比较了 17 个 MWP 求解器，这些功能使得 MWPToolkit 适合研究人员快速复现先进的基线模型并开发新的 MWP 求解器。