Models of A-not-B

About

This page provides some additional information relevant to the discussion about Smith, Thelen, Titzer, & McLin (1999) and Munakata, McClelland, Johnson, & Siegler (1997).

Thelen, Schöner, Scheier, & Smith (2001)

Thelen, Smith and colleagues followed up on their empirical work in Smith et al. (1999) with a dynamic field model described in Thelen et al. (2001).

The modeling effort begins with a task analysis as described in Figure 1.

Thelen et al. (2001) Figure 1

The model begins by describing a movement field.

Thelen et al. (2001) Figure 6

The movement field receives task input and specific input from a separate input field shown below and a memory field (not shown).

Thelen et al. (2001) Figure 8

Figures 10 and 11 show illustrations of how the input and memory fields evolve with repeated trials at the A location.

Thelen et al. (2001) Figures 10 and 11

Munakata et al. (1997)

This figure shows the basic architecture of the network.

Munakata et al. (1997) Figure 7.

This figure shows how the model’s input maps to the sequence of events that occur in the behavioral task.

Munakata et al. (1997) Figure 8.

This figure shows how the difference in activation evolves with each epoch of training.

Munakata et al. (1997) Figure 9.

This is illustrated in Figure 9, where we graph the magnitude of a network’s sensitivity to an occluded object reappearing from behind a barrier as a function of training experience and length of occlusion period. The sensitivity depends on the extent to which the network distinguishes between events with and without balls and is defined as the network’s predicted activation for the ball unit at the time step when the ball should reappear (when there is in fact a ball behind the occluder), minus the network’s predicted activation for the ball unit at the same time step, when a ball should not reappear (when in fact no ball was present before the occluder moved in).

– Munakata et al. (1997) p. 699

The following two figures show the activation of the internal units in different phases of the simulation.

Munakata et al. (1997) Figure 11.

Munakata et al. (1997) Figure 12.

Models as maps

\[y_i=A+B+A*B+\epsilon_i\]

References

Munakata, Y., McClelland, J. L., Johnson, M. H., & Siegler, R. S. (1997). Rethinking infant knowledge: Toward an adaptive process account of successes and failures in object permanence tasks. Psychological Review, 104, 686–713. https://doi.org/10.1037/0033-295x.104.4.686

Smith, L. B., Thelen, E., Titzer, R., & McLin, D. (1999). Knowing in the context of acting: The task dynamics of the a-not-B error. Psychological Review, 106, 235–260. https://doi.org/10.1037/0033-295X.106.2.235

Thelen, E., Schöner, G., Scheier, C., & Smith, L. B. (2001). The dynamics of embodiment: A field theory of infant perseverative reaching. The Behavioral and Brain Sciences, 24, 1-34; discussion 34-86. Retrieved from https://www.ncbi.nlm.nih.gov/pubmed/11515285