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The paper discusses the capacities and limitations of current artificial intelligence (AI) technology to solve word problems that combine elementary mathematics with commonsense reasoning. No existing AI systems can solve these reliably. We review three approaches that have been developed, using AI natural language technology: outputting the answer directly, outputting a computer program that solves the problem, and outputting a formalized representation that can be input to an automated theorem verifier. We review some benchmarks that have been developed to evaluate these systems and some experimental studies. We discuss the limitations of the existing technology at solving these kinds of problems. We argue that it is not clear whether these kinds of limitations will be important in developing AI technology for pure mathematical research, but that they will be important in applications of mathematics, and may well be important in developing programs capable of reading and understanding mathematical content written by humans.
This paper highlights the current state of AI technology in solving mathematical word problems (MWPs), particularly those requiring a combination of elementary knowledge and commonsense reasoning. The central argument is that despite significant advancements in AI, no existing AI system can reliably solve these types of problems.
Key innovations and findings discussed in the paper:
Limitations of Current AI: The paper emphasizes that AI systems, even with recent advances, struggle with elementary commonsense word problems (CSWs). This is despite success in other AI domains.
Approaches Reviewed: The paper reviews three main approaches for using Large Language Models (LLMs) to solve MWPs:
Benchmark Analysis: It examines various benchmarks like SVAMP and LILA and experimental studies that evaluate AI systems' performance on these tasks, pointing out limitations and flaws in current technology.
Artifacts in Training Data: The paper discusses the problem of "artifacts," where AI systems learn superficial regularities in the training data rather than the underlying characteristics of the problem.
Untested Abilities: It notes that many benchmark tests for AI math abilities are designed for humans and assume certain basic abilities that AI systems may lack.
The main prior ingredients needed to understand this paper are:
Basic understanding of AI and Machine Learning (ML): Including concepts like corpus-based machine learning, neural networks, and deep learning.
Familiarity with Large Language Models (LLMs): Knowing how LLMs work, including text generation, training sets, and language modeling.
Knowledge of Natural Language Processing (NLP): Understanding the challenges of processing and understanding natural language.
Awareness of Automated Theorem Proving: Knowing about systems used for formally verifying mathematical proofs.
General Knowledge of Mathematics: Including elementary arithmetic, solid geometry, and mathematical notation.