The ability to represent possibilities: implications for Bayesian models of learning in development

The ability to represent possibilities: implications for Bayesian models of learning in development

Luisa Andreuccioli -
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One of the broad research questions that I am interested in pursuing is when children become able to represent alternative possibilities. Evidence suggests that children consistently fail tasks that require them to represent mutually exclusive possibilities until around their fourth year of age (Leahy et al. 2022; Leahy, 2023), despite there being large (though mostly indirect) evidence that even preverbal infants can compute probabilities over different possible outcomes (e.g., Cesana-Arlotti, 2018; Téglás et al., 2007; Xu & Garcia, 2008).  

In an attempt to reconcile these apparently contrasting findings, Leahy & Carey (2020) have proposed that young children are unable to represent multiple possibilities, and can only represent possibilities minimally. In particular, when faced with multiple possibilities, minimal representers make a simulation about which outcome may be true and treat such simulation as knowledge (Leahy & Carey, 2020; Leahy, 2023).

If this were true, it would imply that, across infancy, hypothesis testing may only occur through sequential simulation (i.e., simulating and considering one hypothesis at a time).This, however, seems to contrast the view of the “child as scientist” (Gopnik et al. 1999) – the view that the way children learn and build theories about the world is comparable to a scientists’ expertise with conducting scientific investigation. Most theories of cognitive development (1) resort to Bayesian models of learning to explain how children are capable of accruing so much information over such a short period of time (e.g., “theory theory”, Gopnik & Wellman, 2012; “rational constructivism”, Xu & Kushnir, 2013) and that (2), these Bayesian models require that the learner is able to generate and consider a (potentially infinite) space of hypotheses (or possibilities) (Perfors et al. 2011). 

As argued by Leahy & Carey (2020) however, the process of generating one single hypothesis – or simulation – at a time, is still, in principle, consistent with Bayesian models of learning. Although it is not implausible to assume that learning in young children may happen this way, and although most of the existing evidence of infants’ abilities could be explained this way, it seems extremely costly and inefficient for young learners to generate, approve or discard one single hypothesis at a time. It is perhaps for this reason that most theories of cognitive development assume that young children can generate and hold more than one hypotheses in mind.

References: 

Cesana-Arlotti, N., Martín, A., Téglás, E., Vorobyova, L., Cetnarski, R., & Bonatti, L. L. (2018). Precursors of logical reasoning in preverbal human infants. Science, 359(6381), 1263-1266.

Gopnik, A., Meltzoff, A. N., & Kuhl, P. K. 1. (1999). The scientist in the crib: minds, brains, and how children learn. New York, William Morrow & Co.

Gopnik, A., & Wellman, H. M. (2012). Reconstructing constructivism: causal models,  Bayesian learning mechanisms, and the theory theory. Psychological Bulletin, 138(6), 1085.

Leahy, B. P., & Carey, S. E. (2020). The acquisition of modal concepts. Trends in Cognitive Sciences, 24(1),65-78. 

Leahy, B., Huemer, M., Steele, M., Alderete, S., & Carey, S. (2022). Minimal representations of possibility at age 3. Proceedings of the National Academy of Sciences, 119(52), e2207499119.

Leahy, B. (2023). Don't you see the possibilities? Young preschoolers may lack possibility concepts. Developmental Science, e13400.

Perfors, A., Tenenbaum, J. B., Griffiths, T., Xu, F. (2011). A tutorial introduction to Bayesian models of cognitive development. Cognition, 120(3), 302–321.

Téglás, E., Girotto, V., Gonzalez, M., & Bonatti, L. L. (2007). Intuitions of probabilities shape expectations about the future at 12 months and beyond. Proceedings of the National Academy of Sciences, 104(48).

Xu, F., & Garcia, V. (2008). Intuitive statistics by 8-month-old infants. Proceedings of the National Academy of Sciences, 105(13), 5012-5015.

Xu, F., & Kushnir, T. (2013). Infants are rational constructivist learners. Current Directions in Psychological Science, 22(1), 28-32.