Network Symmetry and Binocular Rivalry Experiments

Abstract

Hugh Wilson has proposed a class of models that treat higher-level decision making as a competition between patterns coded as levels of a set of attributes in an appropriately defined network (Cortical Mechanisms of Vision, pp. 399–417, 2009; The Constitution of Visual Consciousness: Lessons from Binocular Rivalry, pp. 281–304, 2013). In this paper, we propose that symmetry-breaking Hopf bifurcation from fusion states in suitably modified Wilson networks, which we call rivalry networks, can be used in an algorithmic way to explain the surprising percepts that have been observed in a number of binocular rivalry experiments. These rivalry networks modify and extend Wilson networks by permitting different kinds of attributes and different types of coupling. We apply this algorithm to psychophysics experiments discussed by Kovács et al. (Proc. Natl. Acad. Sci. USA 93:15508–15511, 1996), Shevell and Hong (Vis. Neurosci. 23:561–566, 2006; Vis. Neurosci. 25:355–360, 2008), and Suzuki and Grabowecky (Neuron 36:143–157, 2002). We also analyze an experiment with four colored dots (a simplified version of a 24-dot experiment performed by Kovács), and a three-dot analog of the four-dot experiment. Our algorithm predicts surprising differences between the three- and four-dot experiments.

Symmetries Constrain Dynamics in a Family of Balanced Neural Networks

“…However, the literature we are aware of identifies symmetry-breaking in a structured network dominated by deterministic behavior. For example, symmetry breaking has been hypothesized to underlie the dynamics of visual hallucinations [15] and ambiguous visual percepts [14]; central pattern generators which govern rhythmic behaviors of breathing, eating and swimming [9,32,36]; and periodic head/limb motions [21,8,20]. Most recently, Kriener et al [26] investigate a Dale's Law-conforming orientation model, and find that the dynamics are affected by a translation symmetry imposed by the regularity of the cell grid.…”

Computational models in the age of large datasets

“…Conceptual models examine the consequences of broad assumptions. These kinds of models are useful for conducting rigorous thought experiments: one might ask how noise impacts latency in a forced choice between multiple alternatives [1], or how network topology determines the fusion and rivalry of visual percepts [2]. While conceptual models must be constrained by data in the sense that they cannot violate known facts about the world, they do not strive to assimilate or reproduce detailed experimental measurements.…”

Symmetry types and phase-shift synchrony in networks

“…Many biological phenomena, such as respiration [1,2], locomotion [4,6,12,13,25], or rivalry [5] are characterized by robust rhythmic patterns that exhibit particular phase relationships or phaseshifts. The neuronal networks responsible for these behaviors can be represented as coupled systems of differential equations that exhibit periodic behavior corresponding to these phase-shift patterns.…”