Theo Rhodes

Scaling laws in cognitive sciences

Scaling laws are ubiquitous in nature, and they pervade neural, behavioral and linguistic activities. A scaling law suggests the existence of processes or patterns that are repeated across scales of analysis. Although the variables that express a scaling law can vary from one type of activity to the next, the recurrence of scaling laws across so many different systems has prompted a search for unifying principles. In biological systems, scaling laws can reflect adaptive processes of various types and are often linked to complex systems poised near critical points. The same is true for perception, memory, language and other cognitive phenomena. Findings of scaling laws in cognitive science are indicative of scaling invariance in cognitive mechanisms and multiplicative interactions among interdependent components of cognition.

Intrinsic and extrinsic contributions to heavy tails in visual foraging

Eyes move over visual scenes to gather visual information. Studies have found heavy-tailed distributions in measures of eye movements during visual search, which raises questions about whether these distributions are pervasive to eye movements, and whether they arise from intrinsic or extrinsic factors. Three different measures of eye movement trajectories were examined during visual foraging of complex images, and all three were found to exhibit heavy tails: Spatial clustering of eye movements followed a power law distribution, saccade length distributions were lognormally distributed, and the speeds of slow, small amplitude movements occurring during fixations followed a 1/f spectral power law relation. Images were varied to test whether the spatial clustering of visual scene information is responsible for heavy tails in eye movements. Spatial clustering of eye movements and saccade length distributions were found to vary with image type and task demands, but no such effects were found for eye movement speeds during fixations. Results showed that heavy-tailed distributions are general and intrinsic to visual foraging, but some of them become aligned with visual stimuli when required by task demands. The potentially adaptive value of heavy-tailed distributions in visual foraging is discussed.

Drawing from Memory: Hand-Eye Coordination at Multiple Scales

Eyes move to gather visual information for the purpose of guiding behavior. This guidance takes the form of perceptual-motor interactions on short timescales for behaviors like locomotion and hand-eye coordination. More complex behaviors require perceptual-motor interactions on longer timescales mediated by memory, such as navigation, or designing and building artifacts. In the present study, the task of sketching images of natural scenes from memory was used to examine and compare perceptual-motor interactions on shorter and longer timescales. Eye and pen trajectories were found to be coordinated in time on shorter timescales during drawing, and also on longer timescales spanning study and drawing periods. The latter type of coordination was found by developing a purely spatial analysis that yielded measures of similarity between images, eye trajectories, and pen trajectories. These results challenge the notion that coordination only unfolds on short timescales. Rather, the task of drawing from memory evokes perceptual-motor encodings of visual images that preserve coarse-grained spatial information over relatively long timescales as well.

Patterns of interaction-dominant dynamics in individual versus collaborative memory foraging.

The extent to which a cognitive system’s behavioral dynamics fit a power law distribution is considered indicative of the extent to which that system’s behavior is driven by multiplicative, interdependent interactions between its components. Here, we investigate the dynamics of memory processes in individual and collaborating participants. Collaborative dyads showed the characteristic collaborative inhibition effect when compared to nominal groups in terms of the number of items retrieved in a categorical recall task, but they also generate qualitatively different patterns of search behavior. To categorize search behavior, we used multi-model inference to compare the degree to which five candidate models (normal, exponential, gamma, lognormal, and Pareto) described the temporal distribution of each individual and dyad’s recall processes. All individual and dyad recall processes were best fit by interaction-dominant distributions (lognormal and Pareto), but a clear difference emerged in that individual behavior is more power law, and collaborative behavior was more lognormal. We discuss these results in terms of the cocktail model (Holden et al. in Psychol Rev 116(2):318–342, 2009), which suggests that as a task becomes more constrained (such as through the necessity of collaborating), behavior can shift from power law to lognormal. This shift may reflect a decrease in the dyad’s ability to flexibly shift between perseverative and explorative search patterns. Finally, our results suggest that a fruitful avenue for future research would be to investigate the constraints modulating the shift from power law to lognormal behavior in collaborative memory search.