A Survey of Deep Learning for Mathematical Reasoning

By Pan Lu, Liang Qiu, Wenhao Yu, Sean Welleck, Kai-Wei Chang. 2022

204 citations recorded by the source corpus.

Mathematical reasoning is a fundamental aspect of human intelligence and is applicable in various fields, including science, engineering, finance, and everyday life. The development of artificial intelligence (AI) systems capable of solving math problems and proving theorems in language has garnered significant interest in the fields of machine learning and natural language processing. For example, mathematics serves as a testbed for aspects of reasoning that are challenging for powerful deep learning models, driving new algorithmic and modeling advances. On the other hand, recent advances in large-scale neural language models have opened up new benchmarks and opportunities to use deep learning for mathematical reasoning. In this survey paper, we review the key tasks, datasets, and methods at the intersection of mathematical reasoning and deep learning over the past decade. We also evaluate existing benchmarks and methods, and discuss future research directions in this domain.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Computer Science Applications, Prompting & Reasoning

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Citations in the corpus

Llemma: An Open Language Model For Mathematics (2023, methodology): “Second, mathematical reasoning is in itself a central AI task, its study dating back to at least Gelernter (1959) and Wang (1960) and continuing to today (Lu et al., 2023).”
Multimodal Chain-of-Thought Reasoning in Language Models (2023, neutral): “(A) hospital”
SciBench: Evaluating College-Level Scientific Problem-Solving Abilities of Large Language Models (2023, background): “Additionally, other strategies propose to enable LLMs to utilize external tools (Lu et al., 2023b; Schick et al., 2023) that improve the numerical computation capability.”
Dynamic Prompt Learning via Policy Gradient for Semi-structured Mathematical Reasoning (2022, background): “However, recent studies show that few-shot GPT-3 highly depends on the selection of in-context examples and could be unstable, varying from the near chance to near state-of-the-art performance (Zhao et al., 2021; Liu et al., 2022a; Lu et al., 2022b).”
WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct (2023, unknown): “Figure 4 illustrates that the evolution process does not yield higher similarity scores.”
MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts (2023, background): “Our analysis highlights that hallucination is a major source of errors in the generative foundation models (Lu et al., 2023c; Ji et al., 2023).”
Mathematical Capabilities of ChatGPT (2023, background): “An up-to-date survey on mathematical datasets and performance of various LLMs can be found in [23].”
OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems (2024, background): “Consequently, a challenging multimodal benchmark is essential for advancing scientific reasoning tasks(Zhang et al., 2024a; Lu et al., 2023).”
Large Language Models for Mathematical Reasoning: Progresses and Challenges (2024, background): “Diverse mathematical problem types pose a formidable challenge, exacerbated by the varied evaluation metrics, datasets, and settings employed in the assessment of LLM-oriented techniques (Testolin, 2023; Lu et al., 2023c).”
Chameleon: Plug-and-Play Compositional Reasoning with Large Language Models (2023, background): “3 Tool-Augmented Language Models Despite impressive performance of LLMs, they suffer from inherent limitations, such as the inability to access up-to-date information [21], utilize external tools [43], or perform precise mathematical reasoning [38, 30].”
A Survey of Large Language Models (2023, unknown): “Besides, it has been revealed that there might also exist inconsistency between tasks with similar inputs, where small changes in the task description may cause the model to produce different results [49, 245].”