Chain-of-thoughts (CoT) requires large language models (LLMs) to generate
intermediate steps before reaching the final answer, and has been proven
effective to help LLMs solve complex reasoning tasks. However, the inner
mechanism of CoT still remains largely unclear. In this paper, we empirically
study the role of CoT tokens in LLMs on two compositional tasks: multi-digit
multiplication and dynamic programming. While CoT is essential for solving
these problems, we find that preserving only tokens that store intermediate
results would achieve comparable performance. Furthermore, we observe that
storing intermediate results in an alternative latent form will not affect
model performance. We also randomly intervene some values in CoT, and notice
that subsequent CoT tokens and the final answer would change correspondingly.
These findings suggest that CoT tokens may function like variables in computer
programs but with potential drawbacks like unintended shortcuts and
computational complexity limits between tokens. The code and data are available
at https://github.com/solitaryzero/CoTs_are_Variables.
