Exploring the Compositional Deficiency of Large Language Models in Mathematical Reasoning
CoRR(2024)
Abstract
Human cognition exhibits systematic compositionality, the algebraic ability
to generate infinite novel combinations from finite learned components, which
is the key to understanding and reasoning about complex logic. In this work, we
investigate the compositionality of large language models (LLMs) in
mathematical reasoning. Specifically, we construct a new dataset
MathTrap[3] by introducing carefully designed logical
traps into the problem descriptions of MATH and GSM8k. Since problems with
logical flaws are quite rare in the real world, these represent “unseen”
cases to LLMs. Solving these requires the models to systematically compose (1)
the mathematical knowledge involved in the original problems with (2) knowledge
related to the introduced traps. Our experiments show that while LLMs possess
both components of requisite knowledge, they do not spontaneously
combine them to handle these novel cases. We explore several methods to
mitigate this deficiency, such as natural language prompts, few-shot
demonstrations, and fine-tuning. We find that LLMs' performance can be
passively improved through the above external intervention. Overall,
systematic compositionality remains an open challenge for large language
models.
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