Automatically answer math word problems is a challenging task in artificial intelligence.Previous solvers constructed mathematical expressions in sequence or binary tree.However,these approaches may suffer from the fo...Automatically answer math word problems is a challenging task in artificial intelligence.Previous solvers constructed mathematical expressions in sequence or binary tree.However,these approaches may suffer from the following issues:Models relying on such structures exhibit fixed-order reasoning(e.g.,left-to-right),limiting flexibility and increasing error susceptibility;prior models rely on autoregressive reasoning in a single pass,accumulating minor errors(e.g.,incorrect math symbols)during generation,resulting in reduced accuracy.To address the above issues,we emulate the human“check and modify”process in reasoning and propose a unified M-tree self-correction solver(UTSCSolver)by iterative inference with self-correction mechanism.First,we use an iterative,non-autoregressive process for generating mathematical expressions,free from fixed generation orders to handle complex and diverse problems.Additionally,we design a self-correction mechanism based on alternating execution between a generator and a discriminator.This module iteratively detects and rectifies errors in generated expressions,leveraging previous iteration information for subsequent generation guidance.Experimental results show that our UTSC-Solver outperforms traditional models in accuracy on two popular datasets,while it improves the interpretability of mathematical reasoning.展开更多
Math word problem uses a real word story to present basic arithmetic operations using textual narration. It is used to develop student’s comprehension skill in conjunction with the ability to generate a solution that...Math word problem uses a real word story to present basic arithmetic operations using textual narration. It is used to develop student’s comprehension skill in conjunction with the ability to generate a solution that agrees with the story given in the problem. To master math word problem solving, students need to be given fresh and enormous amount of problems, which normal textbooks as well as teachers fail to provide most of the time. To fill the gap, a few research works have been proposed on techniques to automatically generate math word problems and equations mainly for English speaking community. Amharic is a Semitic language spoken by more than hundred million Ethiopians and is a language of instruction in elementary schools in Ethiopia. And yet it belongs to one of a less resourced language in the field of linguistics and natural language processing (NLP). Hence, in this paper, a strategy for automatic generation of Amharic Math Word (AMW) problem and equation is proposed, which is a first attempt to introduce the use template based shallow NLP approach to generate math word problem for Amharic language as a step towards enabling comprehension and learning problem solving in mathematics for primary school students. The proposed novel technique accepts a sample AMW problem as user input to form a template. A template provides AMW problem with placeholders, type of problem and equation template. It is used as a pattern to generate semantically equivalent AMW problems with their equations. To validate the reality of the proposed approach, a prototype was developed and used as a testing platform. Experimental results have shown 93.84% overall efficiency on the core task of forming templates from a given corpus containing AMW problems collected from elementary school mathematics textbooks and other school worksheets. Human judges have also found generated AMW problem and equation as solvable as the textbook problems.展开更多
基金supported by the National Natural Science Foundation of China(62106244)the Fundamental Research Funds for the Central Universities(WK2150110021)the University Synergy Innovation Program of Anhui Province(GXXT-2022-042).
文摘Automatically answer math word problems is a challenging task in artificial intelligence.Previous solvers constructed mathematical expressions in sequence or binary tree.However,these approaches may suffer from the following issues:Models relying on such structures exhibit fixed-order reasoning(e.g.,left-to-right),limiting flexibility and increasing error susceptibility;prior models rely on autoregressive reasoning in a single pass,accumulating minor errors(e.g.,incorrect math symbols)during generation,resulting in reduced accuracy.To address the above issues,we emulate the human“check and modify”process in reasoning and propose a unified M-tree self-correction solver(UTSCSolver)by iterative inference with self-correction mechanism.First,we use an iterative,non-autoregressive process for generating mathematical expressions,free from fixed generation orders to handle complex and diverse problems.Additionally,we design a self-correction mechanism based on alternating execution between a generator and a discriminator.This module iteratively detects and rectifies errors in generated expressions,leveraging previous iteration information for subsequent generation guidance.Experimental results show that our UTSC-Solver outperforms traditional models in accuracy on two popular datasets,while it improves the interpretability of mathematical reasoning.
文摘Math word problem uses a real word story to present basic arithmetic operations using textual narration. It is used to develop student’s comprehension skill in conjunction with the ability to generate a solution that agrees with the story given in the problem. To master math word problem solving, students need to be given fresh and enormous amount of problems, which normal textbooks as well as teachers fail to provide most of the time. To fill the gap, a few research works have been proposed on techniques to automatically generate math word problems and equations mainly for English speaking community. Amharic is a Semitic language spoken by more than hundred million Ethiopians and is a language of instruction in elementary schools in Ethiopia. And yet it belongs to one of a less resourced language in the field of linguistics and natural language processing (NLP). Hence, in this paper, a strategy for automatic generation of Amharic Math Word (AMW) problem and equation is proposed, which is a first attempt to introduce the use template based shallow NLP approach to generate math word problem for Amharic language as a step towards enabling comprehension and learning problem solving in mathematics for primary school students. The proposed novel technique accepts a sample AMW problem as user input to form a template. A template provides AMW problem with placeholders, type of problem and equation template. It is used as a pattern to generate semantically equivalent AMW problems with their equations. To validate the reality of the proposed approach, a prototype was developed and used as a testing platform. Experimental results have shown 93.84% overall efficiency on the core task of forming templates from a given corpus containing AMW problems collected from elementary school mathematics textbooks and other school worksheets. Human judges have also found generated AMW problem and equation as solvable as the textbook problems.
