Premise Order Matters in Reasoning with Large Language Models

TL;DR

Premise order can drastically alter LLM reasoning performance even when the underlying task remains the same. The authors introduce benchmarks for logical and mathematical reasoning to quantify this effect, including forward, backward, and intermediate premise orders (tau). Across multiple state-of-the-art models under zero-shot, greedy decoding, forward order consistently yields the best accuracy, with notable drops for other orderings, especially as problem length and distractors increase. The results reveal pervasive premise-order brittleness across domains and motivate future work on training and prompting strategies to mitigate this bias.

Abstract

Large language models (LLMs) have accomplished remarkable reasoning performance in various domains. However, in the domain of reasoning tasks, we discover a frailty: LLMs are surprisingly brittle to the ordering of the premises, despite the fact that such ordering does not alter the underlying task. In particular, we observe that LLMs achieve the best performance when the premise order aligns with the context required in intermediate reasoning steps. For example, in deductive reasoning tasks, presenting the premises in the same order as the ground truth proof in the prompt (as opposed to random ordering) drastically increases the model's accuracy. We first examine the effect of premise ordering on deductive reasoning on a variety of LLMs, and our evaluation shows that permuting the premise order can cause a performance drop of over 30%. In addition, we release the benchmark R-GSM, based on GSM8K, to examine the ordering effect for mathematical problem-solving, and we again observe a significant drop in accuracy, relative to the original GSM8K benchmark.

Figures (15)

• Figure 1: Premise order affects the reasoning performance: a failure case for logical reasoning. Left: rules are sorted in the same order as the ground truth proof (forward order with $\tau=1$ as defined in Section \ref{['sec:benchmark-logic']}). Right: the wrong prediction with GPT-4-turbo after shuffling the rule set ($\tau=0$). Distracting rules are in bold and light blue.
• Figure 2: R-GSM example where the original problem can be correctly solved by all LLMs in our evaluation, but all of them failed on the reordered one. Different calculation steps and their corresponding problem statements are annotated in light blue. Specifically, the reasoning steps of the original problem follows the ordering of problem statements, while the reordered problem does not.
• Figure 3: Logical reasoning without distracting rules. See Table \ref{['tab:logic-num-rules']} in Appendix \ref{['app:exp-logic']} for accuracy numbers.
• Figure 4: Logical reasoning with distracting rules. See Tables \ref{['tab:logic-distractors-5']} and \ref{['tab:logic-distractors-10']} for accuracy numbers.
• Figure 5: Results on different $\tau$ without distracting rules. See Table \ref{['tab:logic-order-0-distractors']} for accuracy numbers.