Large Language Model Recall Uncertainty is Modulated by the Fan Effect (2024)

Abstract: This paper evaluates whether large language models (LLMs) exhibit cognitive fan effects, similar to those discovered by Anderson in humans, after being pre-trained on human textual data. We conduct two sets of in-context recall experiments designed to elicit fan effects. Consistent with human results, we find that LLM recall uncertainty, measured via token probability, is influenced by the fan effect. Our results show that removing uncertainty disrupts the observed effect. The experiments suggest the fan effect is consistent whether the fan value is induced in-context or in the pre-training data. Finally, these findings provide in-silico evidence that fan effects and typicality are expressions of the same phenomena.

## introduction some subfields of ai are explicitly interested in understanding and mimicking the nature of human cognition (cognitive modeling, computational psychology, affective computing) but even more implicitly rely on models of human cognition (humancomputer interaction, embodied robotics, collaborative robotics, ai assistive technology, computational game theory). a model that, through training, learned to implicitly exhibit human-like cognitive behaviors could be of tremendous value both to the explicit study of human cognition as an ethical test subject, and as a more faithful model of human behavior to those fields that seek to develop systems to work along side human counterparts. we believe that some large language models (llm) may be excellent candidates for such a role. llms process information in a manner that is fundamentally different from humans. the matrix multiplications, maximum inner product search, and perceptron networks may have, at some level, been inspired by the biological neuronal system. https://github.com/jessetnroberts/large-languagemodel-recall-uncertainty-is-modulated-by-the-fan-effect but beyond the superficial, the systems bear no similarities. in spite of algorithmic and mechanistic dissimilarity, a growing body of work suggests that by merely training on human-language data, large language models learn to exhibit human-like cognitive behaviors as shown in in this paper, we survey the work applying cognitive science inspired evaluations to llms to analyze, understand, and catalog their relation to human cognition. we extend the existing work by providing the first investigation of human-like fan effects à la @xcite in llms. this effect is specifically interesting because it has a relation to the previously studied typicality effect, and it is understood to be an expression of human categorization uncertainty that has been precisely measured through response time delay. our results show that (1) some llms exhibit human-like fan effects based on the typicality of categorical items learned in pre-training; (2) some llms exhibit human-like fan effects based on the relative frequency of items in the model context; and (3) with uncertainty mitigated, the observed fan effect is disrupted. of the models tested, mistral @xcite and solar @xcite exhibit noteworthy human-like fan effects, including nuanced differential fan effects previously observed in humans @xcite . the results have two practical implications: llms learn to exhibit human-like uncertainty and that uncertainty may interfere with recall tasks. our results additionally provide in-silico evidence that the fan effect is a special case of typicality as is true in cobweb models @xcite . understanding the cognitive behaviors acquired from language is essential to the successful application of llms in human-adjacent scenarios. generally speaking, human-like cognitive effects may serve to smooth interactions between machine and human. alternatively, a minority of discrepancies may serve to undermine the interactions. phenomena study by measure(s) statistic significance systematic perturbation theory of mind bubeck et al. (2023) qualitative ---kosinski (2023) frequency ---sap et al. (2022) frequency ---ullman (2023) frequency ---trott et al. (2023) token probs χ 2 + β reported -ma et al. (2023) frequency ---li et al. (2023) frequqncy ---logical reasoning binz and schulz (2023) token probs χ 2 + t + β reported -mccoy et al. (2019) frequency ---lamprinidis (2023) frequency ---yax et al. (2024) token probs χ 2 reported -lampinen et al. (2023) frequency χ 2 + t reported -framing & anchoring binz and schulz (2023) token probs χ 2 + t + β reported -jones and steinhardt (2022) frequency ---suri et al. (2023) frequency -reported -decision-making binz and schulz (2023) token probs χ 2 + t + β reported -jones and steinhardt (2022) frequency ---coda-forno et al. (2024) frequency β reported -hagendorff et al. (2023) frequency χ 2 reported -typicality misra et al. (2021) token probs r + ρ reported -roberts et al. (2024b) token probs r reported model priming sinclair et al. (2022) token probs --data roberts et al. (2024b) token probs w reported data + model michaelov et al. (2023) token probs --data emotion induction coda-forno et al. (2023) frequency r + t + probit β reported - ## background the fan effect is a psychological effect in human categorization behavior, first identified in @xcite , where subjects take longer to recognize and accept or reject concepts that have overlapping features with concepts previously presented in a learning set. this has most commonly been studied using concepts made up of person-place pairs. more formally, given some training concept set @xmath3, y 1 >, ..., < x n , y @xmath4, where x and y are features of the concepts, response time when performing recognition tasks for an arbitrarily chosen query @xmath5, y @xmath6. the effect is apparent regardless of whether or @xmath7, y @xmath8. fan effects have subsequently been found to present with varying strength across different contexts. this tendency is dubbed the differential fan effect. differential fan effects have been investigated across object type and concept presentation modality. it was first identified by @xcite , in which the fan effect was found to occur in instances where presented concepts have the same object associated with multiple places (that is to say, the object feature had a high fan value) but not when multiple persons were associated with a single place (i.e. the place feature had a high fan value). @xcite later extended this to different object types, specifically small locations and inanimate objects. @xcite found that fan effects do not seem to present when concepts are presented via images rather than text, suggesting that differential fan effect context is affected by modality in addition to content. there remains some debate on the mechanism of the fan effect in human subjects, particularly in regard to explaining differential fan effects. @xcite proposed a mechanism, based on the concept of mental models, by which subjects create and maintain models of the world based on learned facts and that some types of overlap in presented concepts necessitate the creation of more models than less overlapping concept sets of the same size. @xcite proposes a different mechanism, derived from a cognitive architecture in which fan effects are mediated by changing weights of edges in the concept network. this mechanism was further supported experimen-tally in @xcite but challenged for larger datasets in @xcite . fan effects are found by @xcite in probabilistic categories created by cobweb to be a special case of another phenomenon known as the typicality effect. this would seem to suggest that fan effects may arise as a consequence of categorization, with a potential explanation being that items closer to the categorical center are more likely to collide with other items, leading to recall uncertainty, while items further from the center are less likely to experience aliasing. typicality, first formalized and identified in humans by @xcite , refers to a tendency of humans to perform categorization tasks quicker when prompted with a more typical member of a category than with a less typical member of a category, with level of typicality determined by how common the features of an instance of a category are among all members of the same category and among contrasting categories. that is, both an item's intracategory similarity and its inter-category similarity affect typicality assessments. for example, given pictures of two birds, a robin and a penguin, human subject response time will be higher when answering whether the penguin is a bird than whether the robin is a bird. ## in-pretraining (typicality) fan effect anderson originally observed the fan effect in the response times of humans when correctly responding to questions. however, in @xcite , the authors observed human-like fan effects in a cobweb model and found they were consistent with a special case of typicality. based on this observation and extant work regarding the presence of typicality effects in llms, we hypothesize that llms may exhibit a fan effect induced by the relative typicality of categorical items acquired from pretraining. specifically we formulate rq3.1. ## in-context fan effect we investigate the presence of fan effects as originally defined in @xcite in the context of concepts composed of categorical features. this addresses the question of whether fan effects show up in concepts defined and fan values induced exclusively in-context. we formulate this as rq4.1. we augment our analysis to investigate the presence of differential fan effect as described in radvansky and zacks (1991), providing rq4.2. research question 4.1. given a list of simple concepts defined by their composite features that is presented to an llm, are absence/presence prediction probabilities modulated by feature fan values such that probabilities conditioned on high fan features tend to be lower than probabilities conditioned on low fan features? research question 4.2. given a list of simple concepts defined by their composite features that is presented to an llm, is correlation of absence/presence prediction probability with fan value modulated by the fan values of one feature more strongly than another feature? ## conclusions our experiments are the first to evaluate llms for the presence of human-like fan effects. we have shown that mistral and solar have learned to exhibit fan effects from training on human language data. this paper is not the first to identify so-lar and mistral as important human-like llms. @xcite found solar and mistral to be significantly more human-like than a large body of other open-source models when evaluated in a game theoretic context. given mistral was built from llama-2 and solar was built from mistral, the authors propose the more human-like behavior may be the result of an improved representation acquired through additional training of mistral with sliding window attention. our results show that fan effects are present both when the fan value is induced in-pretraining in the form of intra-category typicality and when the fan value is induced in-context in the form of repeated items within a list. the presence of typicality-based fan effects in language models lends further credence to the findings of @xcite suggesting that fan effects are a special case of typicality effects. additionally, we find that when uncertainty is mitigated, the fan effect is disrupted with divergent disruption patterns across llms. the divergent patterns across mistral and solar beg further investigation. however, we are unaware of any cognitive science literature that addresses fan effects in a disruptive scenario with mitigated uncertainty. therefore, it is unclear how a human may behave in a similar context. we therefore call for human experiments. similarly, when the fan value is derived from place instead of person in the anderson experiment, both mistral and solar exhibit a disruption of the fan effect in agreement with nuanced work regarding differential fan effects @xcite . again, each of these models diverges in the nature of the disruption but shows a consistent pattern of fan effects in the case of true absence when the fan value is calculated on the person feature. finally, we hope this paper will prove synergistic with the wider cognitive science and computational linguistic communities. by adapting experiments to evaluate the presence of known human cognitive effects in llms, we may gain new insight into cognitive effects. these insights not only help to explain the factors which influence the behavior of complex language models but also provide new potential hypotheses regarding the cognitive behavior of humans.