Limitations of Language Models in Arithmetic and Symbolic Induction

Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics Volume 1: Long Papers, pages 9285–9298 July 9-14, 2023 ©2023 Association for Computational Linguistics Limitations of Language Models in Arithmetic and Symbolic Induction Jing Qian∗, Hong Wang∗, Zekun Li, Shiyang Li, Xifeng Yan University of California, Santa Barbara {jing_qian, hongwang600, zekunli, shiyangli, xyan}@cs.ucsb.edu Abstract Recent work has shown that large pretrained Language Models (LMs) can not only perform remarkably well on a range of Natural Lan- guage Processing (NLP) tasks but also start improving on reasoning tasks such as arith- metic induction, symbolic manipulation, and commonsense reasoning with increasing size of models (Wei et al., 2022; Chowdhery et al., 2022). However, it is still unclear what the underlying capabilities of these LMs are. Sur- prisingly, we find that these models have limi- tations on certain basic symbolic manipulation tasks such as copy, reverse, and addition. When the total number of symbols or repeating sym- bols 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 re- sults 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 re- peating symbols, shedding new insights on the boundary of large LMs in induction. 1 Introduction Transformer-based large pretrained Language Mod- els, such as GPT3 and T5 (Vaswani et al., 2017; Brown et al., 2020; Raffel et al., 2020), have been widely used as few-shot learners in many NLP tasks. Recent work even finds these models can achieve state-of-the-art performance in arithmetic and symbolic reasoning (Nye et al., 2021; Wei et al., 2022). Although these models exhibit surprisingly impressive capabilities in complex arithmetic rea- soning tasks, such as MultiArith (Roy and Roth, 2015) and GSM8k (Cobbe et al., 2021), it has also ∗ The first two authors (Jing and Hong) contributed equally to this work. Figure 1: Examples of addition: the baseline setting (top) and Scratchpad (Nye et al., 2021) with intermedi- ate steps (bottom). A similar method with more detailed demonstration is introduced in (Recchia, 2021). been pointed out that they tend to make certain calculation errors and perform significantly worse when the number of math operations increases in equations (Wei et al., 2022). Brown et al. (2020) find that GPT3 displays strong proficiency in 2- digit arithmetic addition, but struggles in arithmetic addition on numbers with more than three digits. Nogueira et al. (2021) also observe that the fine- tuned T5 model can not correctly add or subtract arbitrarily long numbers. Larger models might perform better on the testing data, but worse on numbers that are longer than the training data (out- of-distribution, OOD) (Nogueira et al., 2021). Figure 1 shows two possible addition exemplars for LMs on addition problem. The scratchpad …

Content truncated to 500 words