Perceptions of Linguistic Uncertainty by Language Models and Humans (2024)

Abstract: *Uncertainty expressions* such as ‘probably’ or ‘highly unlikely’ are pervasive in human language. While prior work has established that there is population-level agreement in terms of how humans quantitatively interpret these expressions, there has been little inquiry into the abilities of language models in the same context. In this paper, we investigate how language models map linguistic expressions of uncertainty to numerical responses. Our approach assesses whether language models can employ theory of mind in this setting: understanding the uncertainty of another agent about a particular statement, independently of the model’s own certainty about that statement. We find that 7 out of 10 models are able to map uncertainty expressions to probabilistic responses in a human-like manner. However, we observe systematically different behavior depending on whether a statement is actually true or false. This sensitivity indicates that language models are substantially more susceptible to bias based on their prior knowledge (as compared to humans). These findings raise important questions and have broad implications for human-AI and AI-AI communication.

## introduction the expression of uncertainty is ubiquitous in human communication -in relaying predictions ("it is likely to rain tomorrow"), conveying imperfect knowledge ("i think i have a copy in my desk"), and describing unknown information ("the artifact could be more than 500 years old"). expressing uncertainty is particularly critical in fields such as medicine, law, and politics, where statements including uncertainty expressions (e.g., "likely," "doubtful") are frequently used to support medical, judicial, and political decisions @xcite . domain experts use these expressions to communicate uncertainty across a variety of situations, such as the likelihood of sideeffects of a medical treatment @xcite , the chances of a not-guilty verdict in legal cases @xcite , the probability of environmental events resulting from climate change @xcite , or the likelihood of emergence of military conflicts @xcite . prior work has found that, in general, humans are well-attuned to the use of such uncertainty expressions, exhibiting population-level agreement in mapping these expressions to corresponding probabilities @xcite @xcite . however, the topic of how large language models (llms) interpret linguistic uncertainty has received relatively little attention. in particular, given text where a speaker expresses uncertainty about a particular statement, this paper investigates whether llms can interpret the uncertainty not as a function of the model's internal beliefs, but by objectively assessing the speaker's uncertainty about the statement. consider the motivating example in figure 1 : when writing a headline for a statement qualified by the word "probable," chatgpt expresses substantially different uncertainty depending on its prior belief about the statement. 1 in this example, chatgpt is conflating the speaker's uncertainty with its own uncertainty about the statement-in effect, a failure of "theory of mind." in this work, we investigate the abilities of llms to provide quantitative interpretations of uncertainty expressions, focusing in particular on how the prior knowledge of an llm affects this ability. to this end, we propose to evaluate models' figure 1 : two interactions with chatgpt (june 2024) concerning the generation of a headline for a short passage. both passages are structured identically and qualified with the word "probable," but the first is about climate change and the second about the link between vaccines and autism. for the first passage, chatgpt generates a confident-sounding headline, using the words "conclude" and "comprehensive." the second headline is weaker, with words like "suggests" and "possible." the models' sensitivity to their prior knowledge has concerning implications for the use of llms in tasks in which they must process and generate text containing uncertainty expressions, e.g., summarizing scientific reports or writing news arti-cles @xcite . when an llm's ability to quantify uncertainty can be "poisoned" by its beliefs, its downstream performance is dependent on its parametric or pretraining knowledge (which can be obsolete or wrong @xcite ), rather than on critical contextual information @xcite . further, this means that the biases of a model (including the many well-documented potentially harmful biases of llms, e.g., @xcite ; @xcite ; @xcite ; @xcite ; @xcite ) can subtly manifest in how it interprets and generates uncertainty language and, as a consequence, have broader implications for human-ai and ai-ai interactions. interested in the efficacy of how humans communicate uncertainty linguistically, researchers have examined how individuals map uncertainty expressions into numerical values across different fields and expertise levels @xcite ; @xcite ; @xcite ; fore (2019); inter alia). although there can be considerable variation in responses at the individual level, these studies have revealed consistent and systematic patterns relating uncertainty expressions and numerical responses at the population level @xcite @xcite . uncertainty quantification in llms. the need for more reliable llms has prompted researchers to investigate new methods for communicating the internal uncertainty of llms. proposed methods can be differentiated in terms of the information used to estimate the model's uncertainty: from token-level information @xcite @xcite , to dissimilarities across multiple samples @xcite @xcite @xcite , to training external classifiers using the inputs and/or llms' representations @xcite @xcite , or even directly eliciting confidence estimates from llms as output tokens @xcite . furthermore, several works have analyzed the impact of llm-articulated uncertainty in human-ai interaction, finding that participants adjust their perception of llms' correctness when shown llm outputs that include uncertainty expressions @xcite @xcite . with the goal of calibrating human-ai interaction, chaudhry et al. @xcite propose fine-tuning llms to convey uncertainty expressions that faithfully reflect their intrinsic uncertainty. while these works investigate how we can gauge llms' intrinsic uncertainty and how humans react to various uncertainty expressions in text, there has been far less work on the questions we focus on in this paper, i.e., how llms interpret linguistic uncertainty and how closely these interpretations match those of humans. ## baseline human study as a baseline for how people map uncertainty expressions to numerical probabilities, we first conducted an experiment in which 94 humans were shown uncertainty expressions and asked to provide corresponding numerical responses. we focused on a set of 14 uncertainty expressions (e.g., "almost certain," "unlikely"-the full list is provided in appendix c and is also shown on the y-axis in figure 3 ), drawn from @xcite and @xcite . in this initial experiment, our goal is to assess how people perceive these uncertainty expressions "in the wild," putting them in the context of plausible real-world statements. in addition, we use types of statements that attempt to minimize the potential for people to conflate their own beliefs about these statements with their assessment of the confidence of the person making the statement. to this end, we constructed a set of statements (u, s, e) which include uncertainty expressions @xmath0. by presenting statements as being made by a specific speaker s, 3 we are asking participants to use theory of mind to estimate how likely it is that the speaker believes that the statement is true. we then query participants about the speaker's degree of certainty, clearly distinguishing this notion from the participant's own beliefs. for instance, given the statement "sonia believes it is unlikely it will rain today," we can ask participants to quantify with a numerical response how likely sonia thinks it is that it will rain today, distinct from the participants' own beliefs about how likely it is to rain. we use the term numerical response throughout the paper to refer to the participant's numerical assessment of the likelihood that speaker s believes statement e to be true when using uncertainty expression u. we instruct participants that responses should be numbers between 0 and 100, where 0 implies that speaker s believes there is a 0% chance that statement e is true while 100 implies the speaker believes there is a 100% chance that the statement is true. in our baseline experiment, we use nonverifiable statements to separate the meaning of the uncertainty expressions from uncertainty about the statements themselves. non-verifiable statements are statements that are not sufficiently grounded with specific contextual information to allow an external observer to be confident in either the truth or falsity of the statement. for example, in the context of a prompt such as "maria believes it is likely that [statement]," we consider statements such as her boss has two pets or her flight will land around 6pm non-verifiable-as there is not enough context for an observer to be able to assess the likelihood that the statement is true. in contrast, verifiable statements (which we discuss further in section 4.1) can be verified as correct or incorrect in a context-free sense (e.g., the capital city of peru is lima); humans and llms will often have strong prior beliefs about the likelihood that such statements are true. we manually constructed a set of 60 nonverifiable statements and systematically combined these with 14 uncertainty expressions. we randomly selected speaker names, generating sentences describing the belief of a hypothetical speaker in the form: "[speaker] believes it is [uncertainty expression] that @xcite ." for each sentence, participants were asked to quantify the speaker's belief about the statement. in particular, they were asked what the probability is from the speaker's perspective that the statement is correct. participants then provided their response quantized to numerical bins 0, 5, 10, . . . , 95, 100 (see example in figure 2 ). each of the 94 participants provided annotations for 28 randomly chosen statements (and speaker names). as a result, every uncertainty expression was annotated twice by each participant. the outcome of this experiment 4 is an empirical distribution over the 2 × 94 numerical responses 0 10 20 30 40 50 60 70 80 90 100 numerical response almost certain highly likely very likely probable somewhat likely possible uncertain somewhat unlikely unlikely not likely doubtful very unlikely highly unlikely 0.0 0.2 0.4 0.6 0.8 1.0 empirical frequency that participants associated with each uncertainty expression. for example, figure 9 reflects the histogram of responses assigned to the phrases "very likely" and "very unlikely"; results for all 14 uncertainty expressions can be summarized in a heatmap as shown in figure 3 . we note that our results are in agreement with prior work on human perceptions of uncertainty expressions @xcite @xcite , including consistent ordering in aggregate population patterns, in terms of the mode of the empirical distributions. ## methodology our full set of experiments includes experiments with both humans and llms as participants and with both non-verifiable (nv) and verifiable (v) statements. the baseline experiment, as described in section 3, consists of human participants and non-verifiable statements (denoted human+nv). in this section, we describe extensions to include verifiable statements and llm participants, resulting in three additional sets of experiments: human+v, llm+v, llm+nv. to help us draw comparisons be-tween the three additional settings and the baseline experiment, we conclude this section with the description of two metrics. ## results this section examines the ability of several wellknown llms to interpret uncertainty expressions. we begin by assessing models' abilities to produce numerical responses that resemble human-like trends (e.g., higher numerical responses assigned to higher-certainty expressions and vice-versa). we then study the effect of prior knowledge in the perception of uncertainty of both humans and models. we conclude with an assessment of the generalizability of our findings. ## conclusions we evaluate the abilities of llms to interpret uncertainty in language and evaluate numerous models in this context. our results show that many llms can competently map uncertainty expressions to numerical responses in a way that aligns with population-level human perceptions, although the responses they choose can be much less diverse than those by humans. additionally, we find that llms are more susceptible to conflating their own uncertainty about a statement with the statement speaker's uncertainty, resulting in output that is biased by the llm's belief about the statement. by highlighting systematic inconsistencies related to the perceptions of linguistic uncertainty in the presence of knowledge, we shed light into overlooked model behaviors that are critical for understanding human-ai communication and downstream llm performance.