Generalizing the dynamic field theory of spatial cognition across real and developmental time scales

Abstract

Within cognitive neuroscience, computational models are designed to provide insights into the organization of behavior while adhering to neural principles. These models should provide sufficient specificity to generate novel predictions while maintaining the generality needed to capture behavior across tasks and/or time scales. This paper presents one such model, the dynamic field theory (DFT) of spatial cognition, showing new simulations that provide a demonstration proof that the theory generalizes across developmental changes in performance in four tasks-the Piagetian A-not-B task, a sandbox version of the A-not-B task, a canonical spatial recall task, and a position discrimination task. Model simulations demonstrate that the DFT can accomplish both specificity-generating novel, testable predictions-and generality-spanning multiple tasks across development with a relatively simple developmental hypothesis. Critically, the DFT achieves generality across tasks and time scales with no modification to its basic structure and with a strong commitment to neural principles. The only change necessary to capture development in the model was an increase in the precision of the tuning of receptive fields as well as an increase in the precision of local excitatory interactions among neurons in the model. These small quantitative changes were sufficient to move the model through a set of quantitative and qualitative behavioral changes that span the age range from 8 months to 6 years and into adulthood. We conclude by considering how the DFT is positioned in the literature, the challenges on the horizon for our framework, and how a dynamic field approach can yield new insights into development from a computational cognitive neuroscience perspective.

Fig. 1

A simulation of the dynamic field theory performing one spatial recall trial. In each panel, location is across the x-axis, activation on the y-axis, and time on the z-axis. (A) Inputs to the model are presented directly to the model already in an object-centered reference frame (see text for details of the calibration process that transforms spatial information from an egocentric frame of reference in the full model). After this shift, activation is passed to the model consisting of 5 layers: (B) a perceptual field; (C) a long-term memory field associated with this perceptual field; (D) a shared layer of (inhibitory) interneurons; (E) a spatial working memory field; (F) a long-term memory field associated with the spatial working memory field. Solid arrows show excitatory connections between layers, and dashed arrows show inhibitory connections between layers.

Fig. 2

The local excitation (+) / lateral inhibition (-) function used for child (A) and adult (B) simulations. Dashed line indicates the zero threshold.

Fig. 3

Simulations of the infant A-not-B task. Both simulations began with four trials to the A location (not shown), then used identical input (A) on the first B trial. Note that these simulations include only the relevant layers of the model, SWM (B, D) and LTM_SWM (C, E). Local excitatory interactions were lowest for the “young” infant simulations (B-C), which showed an A-not-B error (see peak circled in B). Local excitation was increased for the “older” infant simulation (D-E), which correctly responded at B (see peak circled in D). Axes are as in Fig. 1.

Fig. 4

Simulations of the sandbox A-not-B task. Both simulations began with four trials to the A location with identical inputs (not shown). On the first B trial, the target was presented either near (A-C) or far (D-F) from A. When B was near A (see A), the peak in SWM (B) drifted toward the activation from LTM_SWM (C). When B was far from A (see D), on the other hand, the peak in SWM remained stable and did not drift (E). Axes are as in Fig. 1.

Fig. 5

Simulations of spatial recall trials with child (A-D) and adult (E-H) parameter settings. To approximate developmental changes in reference frame calibration, the inputs are broader and weaker in the child model (A) relative to the adult model (E). In the child model, midline does not provide enough focused input to form a peak in PF (B), and the target peak in SWM (D) is attracted toward the sub-thresholds activation from midline. In the adult model, on the other hand, midline forms a peak in PF (F), which contributes inhibition via Inhib (G) to SWM (H), resulting in the peak being repelled from midline. Axes are as in Fig. 1.

Fig. 6

The DFT performing same (A-C) and different (D-F) responses in position discrimination. In both simulations, S1 was presented at −40°, with S2 presented at −40° for same and −30° for different. Note that, for simplicity, we did not include reference input in these simulations. Axes are as in Fig. 1.