Key Points
1. The paper discusses various mathematical datasets such as Dolphin1878, Math23k, GSM8K, HMWP, and others which provide word problems in mathematics, structured equations, and answers.
2. The research explores the creation of fine-grained annotations of reasoning processes to enhance the comprehensibility and precision of intricate reasoning.
3. The authors introduce the DRAW-1K dataset featuring 1,000 general algebra word problems, each annotated with answer options, rationale, and correct option label.
4. The paper identifies challenges in the application of mathematical language models, including data scarcity, faithfulness, multi-modality, uncertainty, and evaluation.
5. The authors highlight the potential application of mathematical language models in educational settings, emphasizing the need to address challenges related to mathematical proficiency and pedagogy.
6. The article discusses the importance of data in advancing mathematical research and presents a systematic framework for understanding the intricacies of language model-based methodologies.
7. The survey provides a taxonomical delineation of mathematical tasks and methods, distinguishing arithmetic calculation, mathematical reasoning, and algorithmic approaches employed in language models.
8. The paper highlights the challenges and future directions in the development of mathematical language models, including theorem creation, data scarcity, multi-modal information processing, and evaluation.
9. The research paper also discusses studies focusing on the hallucination phenomena in language models, and the need to enhance the trustworthiness and utility of mathematical language models in practical applications and scholarly pursuits.
Summary
The paper introduces a new large-scale dataset of math word problems called MathQA and a neural math problem solver. The paper systematically categorizes pivotal research endeavors in leveraging language models (LMs) within the domain of mathematics. It emphasizes the landscape of proposed mathematical LLMs and over 60 mathematical datasets, including training datasets, benchmark datasets, and augmented datasets. The paper addresses the main traditional solutions to math word problems, outlining machine learning techniques alongside semantic parsing methods. The paper addresses the evolution of deep learning technologies and their employ in crafting neural networks capable of resolving mathematical problems. It demonstrates how PLMs and large-scale language models (LLMs) have assumed a central role in reshaping the landscape of mathematical exploration and practical applications, and has a comprehensive categorization of extant research and implicative results. Additionally, the paper categorizes mathematical tasks and their existing algorithms. It discusses the recent advent of LLMs and their catalyzation of an unforeseen surge in innovation, highlighting the multifaceted potential of AI within the domain of mathematics. The research aims to provide a thorough overview of extant research in the field of mathematical language models, systematically summarizing the diverse range of studies and innovations in this field. It ultimately aims to inspire and inform researchers to harness the power of language models to revolutionize mathematics and its myriad applications.
The paper introduces a new large-scale dataset of math word problems called MathQA and a neural math problem solver that aims to resolve challenges of previous datasets in this domain. The MathQA dataset consists of 37,000 English multiple-choice math word problems covering various mathematical domains. The authors address the challenges of previous datasets by leveraging a new representation language for each math problem, improving the interpretability of the learned models, and enhancing performance. The new dataset includes fine-grained annotations, rationale, answer options, and correct option labels, which make the models more interpretable.
Improved Neural Math Problem Solver and Future Challenges
The authors propose a neural math problem solver that learns to map problems to operation programs using the new MathQA dataset. They introduce a new representation language for each math problem, which aims to improve the interpretability of the learned models. Using this representation language, their new dataset includes fine-grained annotations, rationale, answer options, and correct option labels. The experimental results show that their approach outperforms previous models in terms of interpretability and performance. Additionally, the paper poses new challenges for future research by introducing a new dataset with improved interpretability and performance. It also emphasizes the need for better evaluation metrics and approaches to address challenges such as faithfulness, multi-modality, uncertainty, and the creation of novel theorems. The authors provide a comprehensive overview of the current state-of-the-art, the challenges, and the opportunities for future research in the domain of mathematical language models.
The paper introduces a new large-scale dataset of math word problems called MathQA and a neural math problem solver. The paper addresses the challenges of previous datasets in this domain by providing a diverse range of math problems and incorporating solutions written in a domain-specific programming language. The improvements brought by MathQA include better performance and interpretability of the learned models. Experimental results demonstrate that the neural math problem solver achieves higher accuracy and model interpretability compared to baseline models on MathQA. The paper also discusses the new challenges posed by the MathQA dataset for future research, such as the need to develop models that can perform multi-step reasoning and handle complex mathematical concepts. This work represents a significant contribution to the field of math problem solving and opens up new opportunities for advancing the development of AI systems that can reason and solve complex math problems.
Reference: https://arxiv.org/abs/2312.07622