Theory-Based Bayesian Models of Elementary School Children’s Pupillary Surprise

• In Event: Learning From Surprise in Childhood: Empirical, Methodological, and Theoretical Advances

Abstract

Human beings are excellent learners, known for creating rich “intuitive theories” (Gopnik & Wellman, 2012; Carey, 2004; Keil, 2003). But, while humanity’s remarkable cognition inspires the innovative design of intelligent machines (e.g., “XDATA” and “ASKE” (DARPA, 2012; 2018), the influence of our emotions is often overlooked. This is critical to address, as affective components, like surprise, may be vital for finding errors and revising theories (Brod, Hasselhorn & Bunge, 2018). Here, we describe work that quantifies the affective state surprise as it affects learning.

First, we describe different computational representations of possible prior beliefs. This step is critical for future stages as it allows us to classify children’s prior theories formally. We focus on children’s beliefs of water displacement (Brod & Theobold, in prep), as these beliefs develop during early schooling and provide a domain to measure initial belief and learning. We looked at whether pretest predictions were best described by different generative models; one that judges using object sizes, one that judges using object material, one that judges using mass, or one based on random guessing. We found good fits for the winning model for each child, and the distribution of best-fitting models was approximately equal across models.

Second, we importantly describe an initial quantitative account of “real-time” surprise responses. We generated log-likelihoods of surprise based on prior beliefs and observed evidence, correlated to a physiological measurement suggested to capture surprise: pupil dilation. Here, children were given test trials and either made predictions or post hoc evaluations. We hypothesized that the correlation between model predictions and pupil dilation will be stronger when children are predicting, as engaging their prior beliefs may increase surprise, compared to children who are not.

The model predicted surprise was computed from the likelihood of observing a trial, given the best fitting model for each child. We tested our models against only the first four trials, as children received feedback during this phase and may have started revising their beliefs. The correlations between the model and dilation results were high at both the individual (r(165)=.14, p<0.05) and average level (r(9)=.55, p<0.05), but only in the Prediction condition. In the postdiction condition, dilation was not correlated to the surprise model (r(169)=-.11, p>0.05; r(9)=-.50, p>0.05), and was significantly different from the prediction condition (z=2.34, p<0.01). Performance of our generative models correlates with the pupil dilation measure, fitting well with past research, finding that the process of making a prediction may prompt a stronger surprise-pupillary response compared to others who did not recall prior theories.

We also investigated summation models, taking the sum of each generative model’s trial-by-trial predictions, weighted by their log-likelihood fit. The correlation trends remained, but were nonsignificant (r(165)=.09, p>0.05; r(169)=-.09, p>0.05; z=1.72, p<0.05), suggesting that perhaps children’s initial responses are influenced by prior theories. Future work entails designing Bayesian models that incorporate surprise into the likelihoods, providing a learning bias within the observed data’s weight given prior beliefs, with comparison to the full trial-by-trial data for estimating fits to children’s actual learning.

Authors

• Joseph Colantonio, Rutgers University - Newark
  Presenting Author

• Igor Bascandziev, Rutgers University - Newark
  Non-Presenting Author

• Maria Theobald, Leibniz Institute for Research and Information in Education
  Non-Presenting Author

• Garvin Brod, DIPF & Goethe University Frankfurt
  Non-Presenting Author

• Elizabeth Bonawitz, Rutgers University - Newark
  Non-Presenting Author