Limitations of Language Models in Arithmetic and Symbolic Induction

By Jingu Qian, Hong Wang, Zekun Li, SHIYANG LI, Xifeng Yan. 2022

92 citations recorded by the source corpus.

Recent work has shown that large pretrained Language Models (LMs) can not only perform remarkably well on a range of Natural Language Processing (NLP) tasks but also start improving on reasoning tasks such as arithmetic induction, symbolic manipulation, and commonsense reasoning with increasing size of models. However, it is still unclear what the underlying capabilities of these LMs are. Surprisingly, we find that these models have limitations on certain basic symbolic manipulation tasks such as copy, reverse, and addition. When the total number of symbols or repeating symbols increases, the model performance drops quickly. We investigate the potential causes behind this phenomenon and examine a set of possible methods, including explicit positional markers, fine-grained computation steps, and LMs with callable programs. Experimental results show that none of these techniques can solve the simplest addition induction problem completely. In the end, we introduce LMs with tutor, which demonstrates every single step of teaching. LMs with tutor is able to deliver 100% accuracy in situations of OOD and repeating symbols, shedding new insights on the boundary of large LMs in induction.

Subfields: Artificial Intelligence, Information Systems, Large Language Models, Natural Language Processing

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Citations in the corpus

Augmented Language Models: a Survey (2023, background): “This leads to many avoidable mistakes, for example in the context of arithmetics (Qian et al., 2022) or within a reasoning chain (Wei et al.”
PAL: Program-aided Language Models (2022, background): “…decompose natural language problems into steps and perform simple arithmetic operations, their performance falls dramatically when dealing with complex arithmetic (Hendrycks et al., 2021; Madaan & Yazdanbakhsh, 2022) or large numbers (Geva et al., 2020; Nogueira et al., 2021; Qian et al., 2022).”
A Survey on Knowledge Distillation of Large Language Models (2024, background): “While recent LLMs have shown proficiency in solving various tasks, they still tend to make mistakes when handling large numerical values or executing intricate mathematical calculations (Qian et al., 2022; She et al., 2023; Manikandan et al., 2023; Liang et al., 2023b; Mialon et al., 2023).”
A Survey of Large Language Models (2023, unknown): “To solve this issue, existing studies incorporate scratchpad [326, 367] and tutor [368] strategies to help LLMs better manipulate symbolic operations, for generating”
Large Language Model (LLM) for Telecommunications: A Comprehensive Survey on Principles, Key Techniques, and Opportunities (2024, background): “3) Planning for complex task solving : While ICL and CoT prompting provide a straightforward approach for task solving, they often fall short in complex scenarios like mathematical reasoning and multi-hop question answering [75].”
ToolQA: A Dataset for LLM Question Answering with External Tools (2023, background): “Additionally, they exhibit weaknesses in numerical reasoning, an essential skill in numerous real-life applications [14, 36, 41, 28, 51, 13].”
A Comprehensive Evaluation of Tool-Assisted Generation Strategies (2023, background): “Augmenting language models (LMs) with tools has been proposed to overcome LMs’ inherent weaknesses (Mialon et al., 2023; Qian et al., 2022), such as the lack of grounding to reliable or updated sources (Jiang et al.”
Faithful Chain-of-Thought Reasoning (2023, background): “…CoT (Wang et al., 2022), Minerva (Lewkowycz et al., 2022), and DI-VERSE (Li et al., 2022), which differ mainly in the voting granularity and the underlying LM. Modu-larized methods break down Q into subproblems and then conquer them individually (Jung et al., 2022; Qian et al., 2022, i.a.).”