Learning & development
One of the major unsolved problems in cognitive development concerns the nature of transition mechanisms. How does the child progress from one stage of reasoning to the next? We have shown that cognitive transitions can be modeled with neural networks that grow as well as learn. We applied Fahlman's cascade-correlation algorithm, which recruits new hidden units when network error cannot be further reduced by quantitative adjustment of connection weights, to modeling phenomena such as reasoning about balance scale, seriation, and conservation tasks, shift learning, infant habituation, acquisition of personal pronouns, and integration of velocity, time, and distance information. This modeling work has shed light on a variety of other issues in cognitive development. How is knowledge represented at various stages? What accounts for the particular orders of stages? Why does development take a particular shape? Why do children develop non-normative rules?
As a single example, a cascade-correlation model of Piaget’s transitive inference task captured the distance effect – faster inferences about pairs of sticks that are farther apart in length than for pairs close together in length. This figure shows that the greater the split (or distance) between two sticks the quicker the judgment about which is longer, which is also true of children of various ages. Age differences were implemented by varying the score-threshold parameter, which controls depth of learning, also simulating the finding that older children are quicker to respond than younger children (because greater learning depth is achieved with a smaller score threshold). In contrast, Piaget’s analysis led to the opposite prediction that response time would increase with split, because each increment of split requires an extra transitive inference. The child (and a network) was trained on the relative lengths of adjacent pairs of sticks and tested on pairs of sticks at various distances apart. The length comparison output of a cascade-correlation network was passed as input to a constraint-satisfaction network that answered questions about which stick was longer or shorter than the other.
As a single example, a cascade-correlation model of Piaget’s transitive inference task captured the distance effect – faster inferences about pairs of sticks that are farther apart in length than for pairs close together in length. This figure shows that the greater the split (or distance) between two sticks the quicker the judgment about which is longer, which is also true of children of various ages. Age differences were implemented by varying the score-threshold parameter, which controls depth of learning, also simulating the finding that older children are quicker to respond than younger children (because greater learning depth is achieved with a smaller score threshold). In contrast, Piaget’s analysis led to the opposite prediction that response time would increase with split, because each increment of split requires an extra transitive inference. The child (and a network) was trained on the relative lengths of adjacent pairs of sticks and tested on pairs of sticks at various distances apart. The length comparison output of a cascade-correlation network was passed as input to a constraint-satisfaction network that answered questions about which stick was longer or shorter than the other.
