Ambiguous visual images can generate dynamic and stochastic switches in perceptual interpretation known as perceptual rivalry. Such dynamics have primarily been studied in the context of rivalry between two percepts, but there is growing interest in the neural mechanisms that drive rivalry between more than two percepts. In recent experiments, we showed that split images presented to each eye lead to subjects perceiving four stochastically alternating percepts (Jacot-Guillarmod et al. Vision research, 133, 37–46, 2017): two single eye images and two interocularly grouped images. Here we propose a hierarchical neural network model that exhibits dynamics consistent with our experimental observations. The model consists of two levels, with the first representing monocular activity, and the second representing activity in higher visual areas. The model produces stochastically switching solutions, whose dependence on task parameters is consistent with four generalized Levelt Propositions, and with experiments. Moreover, dynamics restricted to invariant subspaces of the model demonstrate simpler forms of bistable rivalry. Thus, our hierarchical model generalizes past, validated models of binocular rivalry. This neuromechanistic model also allows us to probe the roles of interactions between populations at the network level. Generalized Levelt’s Propositions hold as long as feedback from the higher to lower visual areas is weak, and the adaptation and mutual inhibition at the higher level is not too strong. Our results suggest constraints on the architecture of the visual system and show that complex visual stimuli can be used in perceptual rivalry experiments to develop more detailed mechanistic models of perceptual processing.
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We thank Martin Golubitsky for helpful suggestions. Funding was provided by DHS-2014-ST-062-000057, NSF HRD-1800406 and NSF CNS-1831980 (YW); NSF DMS-1615737, NSF DMS-1853630 (ZPK); NIH-1R01MH115557 (KJ and ZPK); DBI-1707400 (KJ).
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Z.P. Kilpatrick, K Josić contributed equally to this work.
Appendix A: Choice of parameter values
We had to set a number of parameters in our model to capture the perceptual alternations observed experimentally. To do so we first let α = β, and chose a set of parameter values so that the corresponding deterministic model had a periodic solution with E1(t) = E2(t) and E3(t) = E4(t). i.e. the periodic solution associated with the alternation of single-eye percepts. We then used XPPAUT to obtain the bifurcation diagram shown in Fig. 10, where the green curve in (A) is a branch of stable periodic solutions and the green curve in (B) is the corresponding periods of the periodic solutions in (A). We choose the values of input strength Ii all to be equal and in the interval (0.8, 1.25) so that the model displayed decreases in dominance duration with increasing input strength I .
Changing the values of α and β changes the bifurcation diagram. However, by continuity, as long as parameter values are not far from those we used to obtain the bifurcation diagram, the dynamics of the system remains similar. In many of our simulations, we fixed the input values I to 1.2, and other values at α = 0.3, w = 1,g = 0.5,ci = 1,ν = γ = 0.45,κ = 0.5. τ = 10ms, τh = τa = 1000ms, δ = 0.03. The parameter values of w, g,ν,γ and κ roughly follow the values used in the literature (Seely and Chow 2011; Wilson 2003). We then numerically found the same qualitative results hold for I ∈ [1, 1.25].
Appendix B: Simulation procedure
To obtain the results shown in the figure, for each given parameter set we ran 100 realizations of the model for 300 seconds each and computed the dominance durations, predominance, and visit ratio for each percept. We pooled all dominance durations of one class of percepts (e.g., single-eye percepts or grouped percepts) and computed its average and standard deviation across occurrences and realizations.
Appendix C: Simulation results with feedback from higher to lower level
Our hierarchical model with sufficiently weak feedback from the higher level to the lower level can also capture the three main observations reported by Jacot-Guillarmod et al. (2017) with the minor difference that the average dominance duration increases (Fig. 9). Increasing the adaptation rate κ in the top level had little or no effect on the dominance duration of percepts (Fig. 11a shows single-eye percepts, but results for grouped percepts were similar) over a large interval (0, 0.8). The main effect of top down excitatory feedback from a percept we observed was to increase that percept’s dominance duration (Fig. 11b).
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Wang, Y., Kilpatrick, Z.P. & Josić, K. A hierarchical model of perceptual multistability involving interocular grouping. J Comput Neurosci 48, 177–192 (2020). https://doi.org/10.1007/s10827-020-00743-8