Decoding Stumpers: Large Language Models vs. Human Problem-Solvers (2023)

Abstract: This paper investigates the problem-solving capabilities of Large Language Models (LLMs) by evaluating their performance on stumpers, unique single-step intuition problems that pose challenges for human solvers but are easily verifiable. We compare the performance of four state-of-the-art LLMs (Davinci-2, Davinci-3, GPT-3.5-Turbo, GPT-4) to human participants. Our findings reveal that the new-generation LLMs excel in solving stumpers and surpass human performance. However, humans exhibit superior skills in verifying solutions to the same problems. This research enhances our understanding of LLMs’ cognitive abilities and provides insights for enhancing their problem-solving potential across various domains.

## introduction since their inception, large language models (llms) have astonished the scientific community with their ability to tackle complex tasks @xcite @xcite . these emerging capabilities, along with shared principles with human cognition and the brain, have motivated significant efforts to utilize deep language models and, recently, llms for explaining neural activity @xcite @xcite , predicting human behavior @xcite , and even providing a theoretical framework for the human mind @xcite . recent advancements, particularly the ability of llms to perform tasks requiring different skills such as mathematical calculations, analytical reasoning and use of world knowledge, have led several papers to declare that llms possess what is termed in the cognitive literature system 2 capabilities @xcite . the dual-system model of the mind has arguably been the most prevalent model of thought and behavior in psychology, economics and social science in general @xcite @xcite , especially in addressing systematic limitations of cognitive and artificial systems. in simple terms, system 1 is associated with effortless, associative processes and is often thought of as compatible with neural nets implementation, while system 2 is related to effortful, serial, and often symbolic processes @xcite . a famous example where system 1's heuristic hinders a solution is described in box 1. box 1: the bat and the ball "a bat and a ball cost 1.10 dollars in total. the bat costs 1 dollar more than the ball. how much does the ball cost?" the immediate but incorrect response is to assume that the ball costs 10 cents. however, a symbolic-serial approach formulation of the problem "x + (x + 1) = 1.10" yields the correct solution of 0.05 dollars. while this type of questions (cognitive reflective test; crt) are considered hard to solve, as they tend to elicit wrong responses @xcite , people can be primed to solve them correctly by insisting on a formalist approach (i.e., applying system 2 instead of system 1; @xcite ). in contrast, problems that require insight (i.e., have neither an intuitive/associative solution nor a symbolic one) are hard for humans and often elicit no response (i.e., humans are "stuck"; @xcite ). consider, for example, the riddle in box 2: box 2: blood relatives "alex is bobbie's blood relative, and bobbie is charlie's blood relative, but alex is not a blood relative of charlie. how come?". answer: alex and charlie can be related to bobbie from different sides of the family, e.g., they could be his parents, uncles, etc. this riddle typically challenges human intuition (system 1) because humans tend to consider alex, bobbie, and charlie as blood relatives. however, a symbolic solution (system 2) is typically also not available to humans who try to solve it, as there is no clear algorithm to follow to reach a solution. facing this question, humans seem to be anchored (or stuck) in the framing according to which the three men are blood relatives and cannot escape it to generate an alternative framing of the problem that would yield effective explanations of the situation @xcite . the above-mentioned question is an example of a stumper. a stumper is a one-step intuition riddle, the solution to which is typically so elusive that it does not come to mind, at least initially -leaving the responder stumped. stumpers do not fall within the system 1 or system 2 frameworks but are related to creative thinking @xcite . importantly, once presented with a solution, people can easily classify it as right or wrong -a simple system-2 task. in this paper, we demonstrate that recent llms (e.g., gpt-3.5 and gpt-4) outperform humans in solving stumpers but lag behind humans in classifying solutions as right or wrong. the dataset used for our analysis consists of all 76 stumpers curated in @xcite . each stumper is a textual description of a narrative or scenario that requires a unique solution. to enhance the number of stumpers beyond this exhaustive list, we generated two similar riddles for each stumper, by asking gpt-3.5-turbo to change the names and wording of the original data-set. after the generation, we manually approved or edited each stumper to reduce confusion and alternative solutions as much as we could. this process resulted in a set of additional 152 stumpers. as the set of new stumpers was not validated with human participants and may differ from the original set, we present the results for the original set in the body of this paper and the detailed results in the appendix. the data also includes correct and incorrect solutions, which allowed a comparative analysis of the accuracy and reasoning strategies of the responses given by models and human participants. a dataset sample can be found in appendix a. ## models and experiments the study involved four language models: davinci-2, davinci-3, gpt-3.5-turbo, and gpt-4. additionally, 81 human participants (@xmath0; ages 20-54, @xmath1.52, @xmath2.73) were recruited via an online survey participation platform (prolific). when solving each stumper, both humans and models were presented with a prompt. to normalize the answers across conditions, models, and participants, all prompts started with a standardized definition of a correct answer to a riddle: an answer to a riddle is correct only if it is consistent with all the riddle's clues, sensical, specific, logical, and fitting with the context of the riddle. see prompts examples in appendix c. ## results and observations we replaced participants who reported knowing their riddle or finding the answer online. two authors evaluated the responses unanimously, with only one response being disagreed upon, leading to its exclusion. llms proficiency at solving stumpers our results are provided in figure 1 . solving a stumper by chance has virtually zero probability, given the infinitesimal likelihood of randomly arriving at the correct solution among countless potential answers. human participants in our sample have accurately solved 38.15% of the stumpers, replicating the 35% accuracy found in @xcite . improved performance of the advanced models a two-way anova was conducted to examine the effects of the models and the prompting: the chat models (gpt-3.5-turbo and gpt-4; @xmath3.8% for the original stumper, 43.4% for the enhanced dataset) have performed significantly better than the gpt-3 model (davinci-2 and davinci-3; @xmath4.6% for the original stumper, 22.5% for the enhanced data-set) [f(1,4)=686, @xmath5.00001]. the main effect of prompt was not significant [f(1, 4) = 0.023, @xmath6.887], but the interaction was [f(1, 4) = 30.82, @xmath7.005], indicating that the prompt has a positive impact on the performance of the gpt-3 models and a negative impact on the performance of the chat models. see results for the original data-set in figure 1 . see results for the enhanced set in appendix b. answer verification the answer verification task was tested once with the ground-truth answers (figure 2 ) and once with the model's responses vs. ground truth (figure 3 ). different scores are reported for correct and incorrect responses. while humans performed perfectly at verification when knowing to generate the answer (100%) and above chance even when they failed to generate (63.8%), most models performed below the chance level (@xmath8. a two-way anova was conducted to compare the models' ability to choose the answer generation d a v i n c i -2 d a v i n c i -3 g p t -3 . 5 -t u r b o g p t -4 0.2 0.3 0.4 0.5 0.6 0.28 0.26 0.55 0.58 0.32 0.33 0.51 0.51 percent correct naïve p rompt humans figure 1: performance of the different models. human performance is presented in the dashed line. correct answer from the ground-truth. the models did not show different performances [f(3,3)=2.43, @xmath9.24], nor did the models' previous success in solving the stumper [f(1, 3) = 5.25, @xmath10.106]. for the model's responses (figure 3 ), a threeway anova was conducted, with model type, the correctness of the response, and the prompt type. here, too, no effects were found for the model type [f(3,10)=1.28 @xmath11.33] or the prompt [f(1,10)=0.13, @xmath12 ## discussion and conclusions this study compared the stumper-solving abilities of llms and humans. we found that while the the results showed that llms, specifically the llms used in this study, demonstrated proficiency in solving stumpers that are obstructed by misleading representations. the models correctly solved 26%-58% of the stumpers, outperforming human participants and surpassing the chance level (figure 1 ). this suggests that llms possess the skills required for solving these types of questions. the study revealed an improvement in performance for more advanced models. the chat models, gpt-3.5-turbo and gpt-4, which are finetuned with human feedback during training, outperformed the gpt-3 models (davinci-2 and davinci-3). this indicates that advancements in model training contribute to enhanced problem-solving abilities. prompting the models with additional pairs of riddles and their ground-truth answers had a positive impact on the performance of the gpt-3 models, further emphasizing the importance of context and prior knowledge in solving stumpers. despite their ability to generate correct answers, the models fell short in the task of answer verification compared to human participants (figure 2 ). to further stress this problem, we have asked the models to compare their correct responses against a false response (figure 3 , full bars), demonstrating their inconsistency and inability to verify an-swers. humans, however, demonstrated a higher proficiency in recognizing the correct answer, even when they were unable to solve the problem initially (figure 2 ). this suggests that humans possess a verification capability, considered a system 2 process, which has not yet fully emerged in llms. interestingly, the davinci-3 model showed good performance in recognizing correct answers curated by the authors (70%; figure 2 ) and by itself (85%; figure 3 ). the overall pattern of results suggests that gpt-3 aligns better with human capabilities, as its answer-verification capabilities are better than its solving capabilities. this pattern stands in contrast to gpt-3.5 and gpt-4, which solve stumpers better than they verify their solutions. this finding indicates that for disciplines interested in using llms to model human behavior or cognition, davinci-3 is likely a more suitable model to employ. this is in line with @xcite , which shows how gpt-3 (but not gpt-4 and gpt-3.5) exhibits similar biases and errors as demonstrated by humans. another reason to consider davinci-3 over gpt-4 and gpt-3.5 in modeling human behavior is the fact that the results acquired here, as well as the psychological literature, suggest that it is easier for humans to classify a correct response than generates it @xcite , a pattern of result similar to davinci-3 and not congruent with gpt-4 and gpt-3.5 performance. this is closely related to the literature showing that recognition is considered easier than recall, as the former requires only identifying the presence of familiar information, whereas the latter demands retrieving specific information from memory without external cues @xcite . the challenge of answer verification is closely related to the problem of text classification, which has been found to be challenging for llms @xcite . there is a significant discrepancy between the abilities to generate a correct answer and to classify a correct response. this has important implications for estimating llm capabilities, as many nlp benchmarks are designed based on the model's ability to classify correct answers @xcite @xcite @xcite . one possible implication is the necessity of including interaction-based measures @xcite , based on continuous human-llm interaction, when evaluating llms. like in oral ex-ams, the opportunity to react to the models' output in tailored follow-up questions allows the evaluator a deeper probing into the models' capabilities @xcite . furthermore, the findings from this study can inform the development of benchmark tasks for evaluating the intelligence and human-like behavior of llms. stumpers provide a challenging domain that tests problem-solving, associative capacities, and verification skills. by designing more comprehensive benchmarks and evaluating llms' performance on these tasks, we can gain a better understanding of their cognitive capabilities and identify areas for improvement. in conclusion, this study investigated the ability of large language models (llms) to solve stumpers, challenging riddles characterized by elusive solutions. our findings demonstrate that llms, especially the advanced models gpt-3.5-turbo and gpt-4, exhibit a remarkable proficiency in solving stumpers, surpassing human performance in some cases. these results highlight the potential of llms as powerful problem-solving tools and provide insights into the cognitive processes involved in solving complex puzzles. our analysis also uncovered that the human ability to verify solutions has not been fully developed yet in llms. future research can build upon these findings to explore the role of context, expand the variety of stumpers, and investigate the generalizability of llms in different domains, contributing to developing more robust and human-like artificial intelligence.