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Small Language Models are Equation Reasoners

Bumjun Kim, Kunha Lee, Juyeon Kim, Sangam Lee

TL;DR

This paper investigates why sLM perform poorly on arithmetic reasoning tasks and hypothesizes that natural language format variability introduces high ambiguity for these smaller models, and conducts experiments with equation-only format, which is a reasoning format that unifies arithmetic reasoning previously expressed in natural language formats into mathematical equations.

Abstract

Chain-of-Thought (CoT) reasoning has enabled Large Language Model (LLM) to achieve remarkable performance in various NLP tasks, including arithmetic problem-solving. However, this success does not generalize to small language model (sLM) like T5, due to their limited capacity and absence of emergent abilities associated with larger models. Recent works to enhance sLM through knowledge distillation have yielded some improvements but still face significant limitations, particularly high ambiguity from the variability in natural language expressions and substantial computational costs. In this paper, we investigate why sLM perform poorly on arithmetic reasoning tasks and hypothesize that natural language format variability introduces high ambiguity for these smaller models. Based on this hypothesis, we conduct experiments with equation-only format, which is a reasoning format that unifies arithmetic reasoning previously expressed in natural language formats into mathematical equations. Experiment results demonstrate that equation-only format effectively boosts the arithmetic reasoning abilities of sLM, especially in very small models like T5-Tiny.

Small Language Models are Equation Reasoners

TL;DR

This paper investigates why sLM perform poorly on arithmetic reasoning tasks and hypothesizes that natural language format variability introduces high ambiguity for these smaller models, and conducts experiments with equation-only format, which is a reasoning format that unifies arithmetic reasoning previously expressed in natural language formats into mathematical equations.

Abstract

Chain-of-Thought (CoT) reasoning has enabled Large Language Model (LLM) to achieve remarkable performance in various NLP tasks, including arithmetic problem-solving. However, this success does not generalize to small language model (sLM) like T5, due to their limited capacity and absence of emergent abilities associated with larger models. Recent works to enhance sLM through knowledge distillation have yielded some improvements but still face significant limitations, particularly high ambiguity from the variability in natural language expressions and substantial computational costs. In this paper, we investigate why sLM perform poorly on arithmetic reasoning tasks and hypothesize that natural language format variability introduces high ambiguity for these smaller models. Based on this hypothesis, we conduct experiments with equation-only format, which is a reasoning format that unifies arithmetic reasoning previously expressed in natural language formats into mathematical equations. Experiment results demonstrate that equation-only format effectively boosts the arithmetic reasoning abilities of sLM, especially in very small models like T5-Tiny.
Paper Structure (8 sections, 2 figures, 1 table)

This paper contains 8 sections, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Works
  3. Large Language Model(LLM)
  4. Arithmetic Reasoning
  5. Experiments
  6. Experimental Setting
  7. Result
  8. Conclusion

Figures (2)

  • Figure 1: Overview of our experiment. We conduct experiment with two format: natural language format and equation-only format. Equation-only format corresponds to each specific mathematical problem with only a single reasoning format, eliminating variability in format and preventing sLM from experiencing ambiguity.
  • Figure 2: Cross-attention score map of T5 model