Can Large Language Models Always Solve Easy Problems if They Can Solve Harder Ones? (2024)

Abstract: Large language models (LLMs) have demonstrated impressive capabilities, but still suffer from inconsistency issues (e.g. LLMs can react differently to disturbances like rephrasing or inconsequential order change). In addition to these inconsistencies, we also observe that LLMs, while capable of solving hard problems, can paradoxically fail at easier ones. To evaluate this hard-to-easy inconsistency, we develop the ConsisEval benchmark, where each entry comprises a pair of questions with a strict order of difficulty. Furthermore, we introduce the concept of consistency score to quantitatively measure this inconsistency and analyze the potential for improvement in consistency by relative consistency score. Based on comprehensive experiments across a variety of existing models, we find: (1) GPT-4 achieves the highest consistency score of 92.2% but is still inconsistent to specific questions due to distraction by redundant information, misinterpretation of questions, etc.; (2) models with stronger capabilities typically exhibit higher consistency, but exceptions also exist; (3) hard data enhances consistency for both fine-tuning and in-context learning. Our data and code will be publicly available on GitHub.

## introduction with the increases in pre-training corpora and the number of parameters @xcite @xcite , large language models (llms) have shown remarkable performance across various natural language processing (nlp) tasks, even generating expert-level responses to user queries. the extraordinary capabilities of llms hold potential for further real-world applications @xcite @xcite , which necessitate higher requirements for model trustworthiness @xcite ; li 1 https://github.com/qwenlm/consiseval a counter-intuitive phenomenon occurs when an llm, which can solve a harder problem, surprisingly goes wrong on an easier problem. @xcite and consistency @xcite . however, llms still suffer from inconsistency issues: semantically equivalent queries @xcite and insignificant order changes of inputted contents @xcite can lead to divergent outcomes; llms can also behave differently in the generation versus validation of the same content @xcite ; moreover, logical transformations like negation and symmetry can also induce inconsistent behaviors @xcite . in addition to previous work, we also find llms able to solve hard problems surprisingly fail to solve easier ones (as shown in figure 1 ), suffering from the hard-to-easy inconsistency. unlike llms, humans are naturally consistent reasoners, and it is undisputed that an individual proficient in calculus can easily address simpler arithmetic problems. however, why this difference exists is still unknown and relevant research to explore hardto-easy consistency of llms is still lacking. to systematically evaluate this consistency of llms, we develop consiseval, a hard-to-easy consistency evaluation benchmark, through automatic generation and human annotation. consi-seval encompasses data from three domains: instruction following, code, and mathematics, each entry consisting of a pair of questions with a strict order of difficulty. considering the absence of an off-the-shelf metric, we propose a new metric consistency score, which is defined as the conditional probability of a model correctly answering easy questions provided that it has correctly answered harder ones, for quantitative assessment of consistency from a probabilistic stance. further, to analyze the potential for improvement in consistency if model capability remains unchanged, we introduce the concept of relative consistency score. the calculation of our metrics relies on the probability of a model answering each question correctly through a single sampling, for which we design two probability estimation methods. based on our benchmark and metrics, we conduct extensive experiments on various llms. among evaluated models, gpt-4 @xcite achieves the highest cs of 92.2%, demonstrating notable hard-to-easy consistency. nonetheless, gpt-4 also exhibits inconsistent behaviors to specific prompts due to distraction by redundant information, misinterpretation of questions, etc. further, we find models with stronger capabilities typically exhibit higher consistency, but exceptions where powerful models demonstrate poor consistency also exist. additionally, we discover that models show higher consistency when trained under hard data than easy data, and that holds the same under few-shot setting (in-context learning with harder demonstration examples shows better consistency). we summarize our contributions as follows: ## consiseval benchmark to systematically evaluate the hard-to-easy consistency of llms, we develop consiseval with data from code, mathematics, and instruction-following domains, which are widely considered to be difficult but of significant importance for llms @xcite @xcite . different from traditional benchmarks in which data are usually individual, there are only pairwise data in consiseval: one datum is comprised of two questions (an easy question and a harder one) with a strict order of difficulty, and we present some example data from consiseval in ## evaluation metrics firstly, we formulate the evaluation problem and introduce mathematical notations in §3.1. considering that there is no off-the-shelf metric to utilize, then we propose a new metric named consistency score ( §3.2) to measure the hard-to-easy consistency quantitatively. further, we introduce the concept of relative consistency score ( §3.3) to analyze the potential for improvement in consistency. we model sampling an answer from an llm for a given question as a stochastic process, wherein the answer is correct with a fixed probability p. the computation of our metrics requires access to p, and §3.4 discusses how to estimate p by maximum likelihood estimation. ## conclusion we observe an anomalous phenomenon where llms able to solve hard problems paradoxically fail at easier ones. to evaluate this hard-to-easy inconsistency, we construct consiseval by automatic generation and human annotation. furthermore, we propose consistency score to measure this inconsistency quantitatively and relative consistency score to analyze the potential for improvement in consistency. based on our dataset and metrics, we conduct comprehensive experiments on numerous existing models, finding that there are exceptions where some powerful models demonstrate poor consistency, though models with stronger capabilities usually exhibit higher consistency. case study shows though state-of-the-art gpt-4 achieves the highest cs of 92.2%, still suffers from inconsistency due to distraction by redundant information, misinterpretation of questions, etc. besides, we also find hard data benefits consistency for both fine-tuning and icl. our benchmark and metrics can facilitate research in consistency of llms, ultimately paving the way for building more trustworthy and reliable ai in the future.