PuzzleBench: Can LLMs Solve Challenging First-Order Combinatorial Reasoning Problems?

Krishna Kartik, Chinmay Mittal, Mausam ., Parag Singla

Abstract:

Recent works show that the largest of the large
language models (LLMs) can solve many simple reasoning tasks expressed in natural language, without any/much supervision. But, can
they also solve challenging first-order combinatorial reasoning problems, such as graph coloring, knapsack and cryptarithmetic? To answer this question, we present PuzzleBench, a
dataset of 31 such challenging problems along
with a few solved instances for each problem.
These problems are all first order, i.e., they
can be instantiated with problem instances of
varying sizes, and most of them are NP-hard,
requiring several reasoning steps to reach the
solution. We first observe that LLMs, even
when aided by symbolic solvers, perform rather
poorly on our dataset. In response, we propose
a new approach, Puzzle-LM, which combines
LLMs with both symbolic solvers and program
interpreters, along with feedback from solved
examples, to achieve huge performance gains.
Our extensive experimentation and analyses offer new insights into the reasoning abilities and
limitations of present-day LLMs.