The human brain is constantly predicting its environment by forming expectations based on the meaningful environmental statistics we encounter in life (e.g. bananas are yellow, sometimes green, but never blue or red; Aslin, 2017; Turk-Browne et al., 2005; Siegelman et al., 2019). Furthermore, perception is largely driven by these expectations (de Lange et al., 2018; Gau and Noppeney, 2016). In the predictive processing framework, the brain constructs and updates internal models of the world that aim to accurately predict incoming sensory data by minimizing prediction errors (Sprevak and Smith, 2023). Prediction errors are abstractly defined as the difference between an expected and obtained outcome and are crucial concepts in models of learning (den Ouden et al., 2012; Montague et al., 2004; Schultz, 2006). Pupil dilation may be a reliable biomarker of neural prediction error signals. Such a biomarker would be advantageous for investigating the neural computations involved in learning and decision-making due to the relative ease of measuring pupil size with a standard eye-tracking device. To achieve this aim, we must investigate the computational signatures reflected in pupil dilation to determine whether they genuinely represent prediction error signals during learning.
While reaction times (RT) scale with uncertainty, confidence, and reward expectation during perceptual decision-making (Colizoli et al., 2018; de Gee et al., 2021; Ratcliff et al., 2016; Urai et al., 2017), there is no overt behavioral marker that reflects the brain’s processing of a prediction error following feedback on a decision outcome when the brain supposedly updates its internal model(s) of the world (Sprevak and Smith, 2023). Pupil dilation under constant luminance is a peripheral marker of the brain’s central arousal system (de Gee et al., 2017; Lloyd et al., 2023; McGinley et al., 2015; Murphy et al., 2014a; Reimer et al., 2016). Evidence suggests that the brain leverages its arousal system to relay computational variables to circuits that execute inference and action selection (Montague et al., 2004; de Gee et al., 2017; Aston-Jones and Cohen, 2005; Glimcher, 2011; Lak et al., 2017; Sara, 2009; Schultz, 2002; Yu and Dayan, 2005). A growing body of literature suggests that pupil dilation may be a reliable physiological marker reflecting a prediction error signal in the post-feedback pupil response (Colizoli et al., 2018; de Gee et al., 2021; Browning et al., 2015; Kayhan et al., 2019; Koenig et al., 2018; Nassar et al., 2012; O’Reilly et al., 2013; Preuschoff et al., 2011; Satterthwaite et al., 2007; Van Slooten et al., 2018; Rutar et al., 2023). Whether a prediction error signal is detectable in pupil dilation will depend on the specific definition of ‘prediction error’, how it is operationalized, as well as the temporal nature of the signal itself. For instance, an unsigned prediction error is defined as the difference between expected and unexpected events but is agnostic to whether the events are better or worse than expected. In contrast, a signed prediction error indicates whether an outcome was better or worse than expected. Relatedly, reward prediction errors are a type of signed prediction error indicating whether an obtained reward was better or worse than expected (den Ouden et al., 2012).
In recent years, pupil dilation has received increased attention in psychology and human neuroscience research for its ability to reflect cognitive and computational variables involved in memory, attention, perception, and decision-making. For instance, pupil dilation has been shown to reflect stimulus expectancy and surprise (de Gee et al., 2021; O’Reilly et al., 2013; Preuschoff et al., 2011; Alamia et al., 2019; Bianco et al., 2020; Friedman et al., 1973; Kamp and Donchin, 2015; Kloosterman et al., 2015; Knapen et al., 2016; Kuchinke et al., 2007; Lavín et al., 2013; Liao et al., 2016; Qiyuan et al., 1985; Raisig et al., 2010; Silvestrin et al., 2021; Wetzel et al., 2016; Zhao et al., 2019; Ghilardi et al., 2024), decision uncertainty (Colizoli et al., 2018; Urai et al., 2017; Nassar et al., 2012; O’Reilly et al., 2013; Van Slooten et al., 2018; Friedman et al., 1973; de Berker et al., 2016; Findling et al., 2019; Geng et al., 2015; Fan et al., 2023; Krishnamurthy et al., 2017; Lempert et al., 2015; Murphy et al., 2014b; Richer and Beatty, 1987; Vincent et al., 2019), and the updating of belief states in internal models including (reward) prediction errors (Colizoli et al., 2018; de Gee et al., 2021; Browning et al., 2015; Kayhan et al., 2019; Koenig et al., 2018; Nassar et al., 2012; O’Reilly et al., 2013; Preuschoff et al., 2011; Satterthwaite et al., 2007; Van Slooten et al., 2018; Lavín et al., 2013; Filipowicz et al., 2020; Harris et al., 2022; Pajkossy et al., 2023; Cheadle et al., 2014; He et al., 2024). Zénon, 2019 proposed that the plethora of cognitive phenomena reflected in pupil dilation can be unified under an information-theoretic framework. Under Zénon’s hypothesis, the common factor driving all cognitive processes reflected in pupil dilation can be quantified in terms of information gain, defined as the divergence between posterior and prior beliefs. A unified framework that relates pupil dilation to cognition through information theory would be beneficial for several reasons. First, a unified framework would enable us to more accurately quantify cognitive processes by allowing us to connect physiological responses like arousal with cognitive functions. Second, such an approach could reveal how effectively an individual integrates new information and adjusts their predictions. Finally, a unified framework would allow researchers to apply consistent metrics across different contexts and tasks, facilitating comparisons between studies and enhancing our overall understanding of cognitive processes linked to pupil dilation.
We reasoned that the link between prediction error signals and information gain in pupil dilation is through precision weighting. Precision refers to the amount of uncertainty (inverse variance) of both the prior belief and sensory input in the prediction error signals (Sprevak and Smith, 2023; Clark, 2017; Kwisthout et al., 2017; Iglesias et al., 2013; Yon and Frith, 2021). More precise prediction errors receive more weighting and therefore have greater influence on model updating processes. The precision weighting of prediction error signals may provide a mechanism for distinguishing between known and unknown sources of uncertainty, related to the inherent stochastic nature of a signal versus insufficient information on the part of the observer, respectively (Kwisthout et al., 2017; Yon and Frith, 2021; Press et al., 2020). In Bayesian frameworks, information gain is fundamentally linked to prediction error, modulated by precision (Kwisthout et al., 2017; Iglesias et al., 2013; Mathys et al., 2011; Yanagisawa et al., 2019; Kwisthout, 2017; Dijkstra et al., 2025; Smith et al., 2022; van Lieshout et al., 2025; Buckley et al., 2017). In non-hierarchical Bayesian models, information gain can be derived as a function of prediction errors and the precision of the prior and likelihood distributions, a relationship that can be approximately linear (Yanagisawa et al., 2019). In hierarchical Bayesian inference, the update in beliefs (posterior mean changes) at each level is proportional to the precision-weighted prediction error; this update encodes the information gained from new observations (Kwisthout et al., 2017; Iglesias et al., 2013; Mathys et al., 2011; Kwisthout, 2017; Dijkstra et al., 2025). Neuromodulatory arousal systems are well-situated to act as precision weighting mechanisms in line with predictive processing frameworks (Friston, 2008; Moran et al., 2013). Empirical evidence suggests that neuromodulatory systems broadcast precision-weighted prediction errors to cortical regions (de Gee et al., 2021; Harris et al., 2022; Iglesias et al., 2013; Haarsma et al., 2021). Therefore, the hypothesis that feedback-locked pupil dilation reflects a prediction error signal is similarly in line with Zenon’s main claim that pupil dilation generally reflects information gain, through precision weighting of the prediction error. We expected a prediction error signal in pupil dilation to be proportional to the information gain.
Information gain can be operationalized within information theory as the Kullback-Leibler (KL) divergence between the posterior and prior belief distributions of a Bayesian observer, representing a formalized quantity that is used to update internal models (O’Reilly et al., 2013; Modirshanechi et al., 2023; Poli et al., 2024). Itti and Baldi, 2005 termed the KL divergence between posterior and prior belief distributions as ‘Bayesian surprise’ and showed a link to the allocation of attention. The KL divergence between posterior and prior belief distributions has been previously considered to be a proxy of (precision-weighted) prediction errors (Press et al., 2020; Dijkstra et al., 2025). According to Zénon’s hypothesis, if pupil dilation reflects information gain during the observation of an outcome event, such as feedback on decision accuracy, then pupil size will be expected to increase in proportion to how much novel sensory evidence is used to update current beliefs (O’Reilly et al., 2013; Zénon, 2019). To our knowledge, there is a paucity of research on whether the pupil response is correlated with information gain, specifically focused on the interval following decision outcome/feedback presentation (O’Reilly et al., 2013; Fleischmann et al., 2025). Using a saccadic planning task, O’Reilly et al., 2013 found that pupil dilation scaled negatively with information gain following target onset. While a significant correlation between post-target pupil dilation and information gain was obtained, the direction of this result seems at odds with the hypothesis that an increase in information gain would lead to greater pupil dilation, an issue we will return to in the Discussion. In contrast, Fleischmann et al., 2025 reported a positive relationship between pupil dilation and information gain, which remained consistent across two auditory tasks requiring participants to predict either the temporal or spatial distributions of auditory sequences. Two other recent studies investigated a relationship between pupil dilation and information gain; however, the pupil dilation interval investigated occurred prior to information about decision outcome (Zénon et al., 2024; Shirama et al., 2024). Zénon et al., 2024 similarly found that larger pupil responses were associated with more information gain with respect to the first operand during an arithmetic sum of two numbers. Finally, Shirama et al., 2024 reported that the covariance between pupil and information gain depended on performance accuracy while participants predicted numbers in a changing environment. Specifically, in the low-performance group, pupil dilation positively tracked information gain. However, in the high-performance group, the direction was reversed. Taken together, there is evidence for both a positive and negative scaling between pupil dilation and information gain, depending on the task context and decision interval investigated.
The temporal dynamics of the relationship between the pupil response and information gain or prediction errors have not been consistently investigated. The temporal dynamics of prediction error signals in pupil dilation are likely informative because the brain’s process of updating internal models may contain an inherent temporal dimension (Nienborg and Roelfsema, 2015). Different temporal components of the pupil signal may correspond to different stages of predictive processing, for instance, as proposed by the hybrid predictive coding model (Tscshantz et al., 2023). These temporal dynamics can shed light on the mechanisms of predictive processing by clarifying the timing of learning updates in relation to feedback presentation (Sales et al., 2019). The temporal dynamics of prediction error signals may also help differentiate between types of learning, indicate how attention and cognitive load are allocated during tasks, and implicate specific brain regions or neural processes involved in learning (Colantonio et al., 2023; Stemerding et al., 2022). Previous studies have shown different temporal response dynamics of prediction error signals in pupil dilation following feedback on decision outcome: While some studies suggest that the prediction error signals arise around the peak (~1 s) of the canonical impulse response function of the pupil (de Gee et al., 2021; Preuschoff et al., 2011; Lavín et al., 2013; Cheadle et al., 2014; He et al., 2024; Burlingham et al., 2022), other studies have shown evidence that prediction error signals (also) arise considerably later with respect to feedback on choice outcome (Colizoli et al., 2018; Browning et al., 2015; Van Slooten et al., 2018; Lavín et al., 2013; He et al., 2024). A relatively slower prediction error signal following feedback presentation may suggest deeper cognitive processing, increased cognitive load from sustained attention or ongoing uncertainty, or that the brain is integrating multiple sources of information before updating its internal model. Taken together, the literature on prediction error signals in pupil dilation following feedback on decision outcome does not converge to produce a consistent temporal signature. The specific time window analyzed across different tasks can affect whether a prediction error signal is detected at all. The emergence of consistent results is important for validating the pupil as a biomarker of prediction error, by facilitating comparative research, informing predictive models, uncovering neural mechanisms, as well as improving practical applications. Many factors could potentially explain these discrepant results, such as different task contexts (e.g. stimulus modality, reward-based learning, probabilistic learning vs. perceptual discrimination), different approaches to the pupil analyses such as using simple contrasts or model-based regression, and different interpretations of what constitutes a ‘prediction error’. Given these discrepancies, it is crucial to investigate the specific conditions under which pupil dilation reflects a (precision-weighted) prediction error.
Aims of the current study
The current study was motivated by Zénon’s hypothesis (Zénon, 2019) concerning the relationship between pupil dilation and information gain, particularly in light of the varying sources of signal and noise introduced by task context and pupil dynamics. By demonstrating how task context can influence which signals are reflected in pupil dilation, and highlighting the importance of considering their temporal dynamics, we aim to promote a more nuanced and model-driven approach to cognitive research using pupillometry. The literature summarized above prompted us to investigate whether the pupil’s response to decision outcomes during learning aligns with a prediction error signal defined within an information-theoretic framework. While Zénon theoretically proposed a direct link between pupil dilation and information gain, this hypothesis has not been thoroughly tested in empirical studies. We sought to fill this gap in the literature and shed light on the relationship between information gain and uncertainty during learning as reflected in pupil dilation.
In the current study, we investigated whether the pupil’s response to decision outcome (i.e. feedback) in the context of associative learning reflects a prediction error as defined operationally as an interaction between stimulus-pair frequency and accuracy, while also exploring the time course of this prediction error signal. Thereafter, we tested whether these prediction error signals correlated with information gain, defined formally as the KL divergence between posterior and prior belief distributions of the ideal observer. We reasoned that information gain should be proportional to the (precision-weighted) prediction error signals potentially arising from neuromodulatory arousal networks. To do so, we adapted a simple model of trial-by-trial learning of stimulus probabilities based on information theory from previous literature (O’Reilly et al., 2013; Mars et al., 2008; Poli et al., 2020). For completeness, Shannon surprise and entropy were also computed and related to the post-feedback pupil response. We analyzed two independent datasets featuring distinct associative learning paradigms, one characterized by increasing entropy and the other by decreasing entropy as the tasks progressed. By examining these different tasks, we aimed to identify commonalities (if any) in the results across varying contexts. Additionally, the contrasting directions of entropy in the two tasks enabled us to disentangle the correlation between stimulus-pair frequency and information gain in the post-feedback pupil response.
In the first data set, participants were instructed to predict the upcoming orientation (left vs. right) of a visual target based on the probability of visual and auditory cues. In the second data set, participants were first exposed to letter-color pairs of stimuli in different frequency conditions during an odd-ball detection task. The letter-color pair contingencies were irrelevant to the odd-ball task performance. The participants subsequently completed a decision-making task in which they had to decide which letter was presented together most often with which color during the previous odd-ball detection task (match vs. no match). Pupil dilation was recorded during the decision-making tasks in both data sets, and the post-feedback pupil response was the event of interest. We did not formally compare the results across the two data sets given substantial differences between these two task contexts. We expected the post-feedback pupil dilation to scale with information gain in both tasks in a relatively early time window, following the results of O’Reilly et al. We explored whether later prediction error components in the post-feedback pupil dilation might reflect other information-theoretic variables, such as Shannon surprise or entropy.
To preview, the results show for the first time that whether the pupil dilates or constricts along with information gain was context dependent. Our findings are overall in line with Zénon’s hypothesis that pupil dilation reflects information-theoretic processing and furthermore suggest that these signatures in pupil dilation are complex and multifaceted. This study provides empirical evidence that the pupil’s response can shed light on model updating during learning, demonstrating the potential of this easily measured physiological indicator for exploring internal belief states.