Alison Gopnik, Thomas L. Griffiths, and Christopher G. Lucas
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From flexibility to efficiency
Another factor may be that as children grow older, there are changes in the way they learn that make them intrinsically less flexible and less able to attend to unusual possibilities. There are complementary computational, neuroscientific, and evolutionary reasons for thinking this might be true.
A Bayesian learner, whether that learner is a child or a computer, must have some technique for searching through the vast space of possible hypotheses and trying to find the most likely option. Recent studies have explored the search methods children might use (e.g., Bonawitz, Denison, Griffiths, & Gopnik, 2014; Denison, Bonawitz, Gopnik, & Griffiths, 2013).
Using an analogy to physics, computer scientists talk about different search “temperatures.” In “high-temperature” searches, the learner searches broadly but is less likely to “settle” on any one answer for long—the learner bounces widely around in the space of hypotheses like a molecule bouncing around in a hot liquid.
From a Bayesian perspective, raising the temperature of a search will have an effect equivalent to “flattening” the prior—initial differences among hypotheses will make less of a difference. In addition, however, it will have the effect of weakening the likelihoods.
High-temperature searches are wide ranging but very variable, and the learner can move away from good hypotheses as well as bad ones. Low-temperature searches are more likely to quickly lead to “good enough” hypotheses. However, the learner risks getting stuck in a “local minimum”—passing up potentially better but more unusual hypotheses that are further away from his or her initial guess.
One way to compromise between the advantages and drawbacks of high and low temperature is to start with a high-temperature search and gradually “cool off.” This is called simulated annealing in computer science, by analogy to the heating and cooling that leads to robustness in metallurgy (Kirkpatrick, Gelatt, & Vecchi, 1983). By beginning with a high-temperature search, a learner can explore the possibilities more widely before focusing more narrowly on the likely candidates.
If children initially perform high-temperature searches and gradually “cool off” to perform low-temperature ones as they grow older, this might explain why younger learners sometimes infer unusual hypotheses better than older learners. How could we discriminate between this simulated-annealing idea and the related flat-prior idea? In Lucas et al. (2014), we included a “baseline” condition. Participants in this condition saw only the ambiguous events—they never saw the unambiguous new data that pointed to each principle. If adults initially thought that the “individual” hypothesis was more likely than the “combination” hypothesis, and children did not, that should have been reflected in this baseline condition. But, in fact, both children and adults preferred the “individual” hypothesis initially. The difference seemed to be that children were more willing to switch to the alternative hypothesis. A Bayesian model consistent with the annealing possibility matched children’s judgments. However, more studies of the dynamics of learning are necessary to distinguish these possibilities.
Findings in neuroscience also mesh well with the annealing idea (e.g., Thompson-Schill, Ramscar, & Chrysikou, 2009). An early period of neural flexibility and plasticity is succeeded by a more narrow and inflexible, though more efficient, set of procedures. In particular, as children get older, frontal areas of the brain exert more control over other areas. This frontal control is associated with focused attention and better planning and executive control. However, this control has costs. Empirically, disruptions to frontal control, resulting in a more “child-like” brain, can actually lead to better performance in cognitive tasks that involve exploring a wide range of possibilities (e.g., Chrysikou et al., 2013). There may be an intrinsic trade-off between exploitation and exploration—between swift, focused, efficient adult action and wide-ranging, exploratory child-like learning.
A pattern of early cognitive exploration also makes sense from an evolutionary perspective. Across many species, flexibility, brain size, and intelligence are associated with a long, protected period of immaturity—a long childhood. Human beings have the largest brains, the most flexible intelligence, and the longest childhood of any species. One explanation for this distinctive life history is that an early protected period allows young organisms to explore possibilities in an unconstrained way. This early exploratory learning, in turn, allows learners to act more effectively when they grow older (Buchsbaum, Bridgers, Weisberg, & Gopnik, 2012). Childhood may be evolution’s way of performing simulated annealing.
Adults may sometimes be better at the tried and true, while children are more likely to discover the weird and wonderful. This may be because as we get older, we both know more and explore less.
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""""
From flexibility to efficiency
Another factor may be that as children grow older, there are changes in the way they learn that make them intrinsically less flexible and less able to attend to unusual possibilities. There are complementary computational, neuroscientific, and evolutionary reasons for thinking this might be true.
A Bayesian learner, whether that learner is a child or a computer, must have some technique for searching through the vast space of possible hypotheses and trying to find the most likely option. Recent studies have explored the search methods children might use (e.g., Bonawitz, Denison, Griffiths, & Gopnik, 2014; Denison, Bonawitz, Gopnik, & Griffiths, 2013).
Using an analogy to physics, computer scientists talk about different search “temperatures.” In “high-temperature” searches, the learner searches broadly but is less likely to “settle” on any one answer for long—the learner bounces widely around in the space of hypotheses like a molecule bouncing around in a hot liquid.
From a Bayesian perspective, raising the temperature of a search will have an effect equivalent to “flattening” the prior—initial differences among hypotheses will make less of a difference. In addition, however, it will have the effect of weakening the likelihoods.
High-temperature searches are wide ranging but very variable, and the learner can move away from good hypotheses as well as bad ones. Low-temperature searches are more likely to quickly lead to “good enough” hypotheses. However, the learner risks getting stuck in a “local minimum”—passing up potentially better but more unusual hypotheses that are further away from his or her initial guess.
One way to compromise between the advantages and drawbacks of high and low temperature is to start with a high-temperature search and gradually “cool off.” This is called simulated annealing in computer science, by analogy to the heating and cooling that leads to robustness in metallurgy (Kirkpatrick, Gelatt, & Vecchi, 1983). By beginning with a high-temperature search, a learner can explore the possibilities more widely before focusing more narrowly on the likely candidates.
If children initially perform high-temperature searches and gradually “cool off” to perform low-temperature ones as they grow older, this might explain why younger learners sometimes infer unusual hypotheses better than older learners. How could we discriminate between this simulated-annealing idea and the related flat-prior idea? In Lucas et al. (2014), we included a “baseline” condition. Participants in this condition saw only the ambiguous events—they never saw the unambiguous new data that pointed to each principle. If adults initially thought that the “individual” hypothesis was more likely than the “combination” hypothesis, and children did not, that should have been reflected in this baseline condition. But, in fact, both children and adults preferred the “individual” hypothesis initially. The difference seemed to be that children were more willing to switch to the alternative hypothesis. A Bayesian model consistent with the annealing possibility matched children’s judgments. However, more studies of the dynamics of learning are necessary to distinguish these possibilities.
Findings in neuroscience also mesh well with the annealing idea (e.g., Thompson-Schill, Ramscar, & Chrysikou, 2009). An early period of neural flexibility and plasticity is succeeded by a more narrow and inflexible, though more efficient, set of procedures. In particular, as children get older, frontal areas of the brain exert more control over other areas. This frontal control is associated with focused attention and better planning and executive control. However, this control has costs. Empirically, disruptions to frontal control, resulting in a more “child-like” brain, can actually lead to better performance in cognitive tasks that involve exploring a wide range of possibilities (e.g., Chrysikou et al., 2013). There may be an intrinsic trade-off between exploitation and exploration—between swift, focused, efficient adult action and wide-ranging, exploratory child-like learning.
A pattern of early cognitive exploration also makes sense from an evolutionary perspective. Across many species, flexibility, brain size, and intelligence are associated with a long, protected period of immaturity—a long childhood. Human beings have the largest brains, the most flexible intelligence, and the longest childhood of any species. One explanation for this distinctive life history is that an early protected period allows young organisms to explore possibilities in an unconstrained way. This early exploratory learning, in turn, allows learners to act more effectively when they grow older (Buchsbaum, Bridgers, Weisberg, & Gopnik, 2012). Childhood may be evolution’s way of performing simulated annealing.
Adults may sometimes be better at the tried and true, while children are more likely to discover the weird and wonderful. This may be because as we get older, we both know more and explore less.
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