Derived patterns in binocular rivalry networks

Abstract

Binocular rivalry is the alternation in visual perception that can occur when the two eyes are presented with different images. Wilson proposed a class of neuronal network models that generalize rivalry to multiple competing patterns. The networks are assumed to have learned several patterns, and rivalry is identified with time periodic states that have periods of dominance of different patterns. Here, we show that these networks can also support patterns that were not learned, which we call derived. This is important because there is evidence for perception of derived patterns in the binocular rivalry experiments of Kovács, Papathomas, Yang, and Fehér. We construct modified Wilson networks for these experiments and use symmetry breaking to make predictions regarding states that a subject might perceive. Specifically, we modify the networks to include lateral coupling, which is inspired by the known structure of the primary visual cortex. The modified network models make expected the surprising outcomes observed in these experiments.

Fig. 1

a Necker cube illusion [7] and b rivalry [6]

Fig. 2

Two-node architecture modeling two units

Fig. 3

From Kovács et al. [2] ©(1996) National Academy of Sciences, USA. a Learned images in monkey-text rivalry experiment. b Learned images in scrambled monkey-text experiment

Fig. 4

From Kovács et al. [2] ©(1996) National Academy of Sciences, USA. a Learned images in conventional colored dot experiment. b Learned images in scrambled colored dot experiment

Fig. 5

Architecture for a Wilson network. a Inhibitory connections between nodes in an attribute column. b Excitatory connections in a learned pattern. c Excitatory lateral connections

Fig. 6

a Distinct areas in scrambled monkey-text experiment. b Schematic two-attribute two-pattern Wilson network for scrambled monkey-text experiment with reciprocal inhibition in attribute columns and reciprocal excitation in learned patterns. c Wilson network with reciprocal lateral excitation

Fig. 7

Simulations of network in Fig. 6(c) showing stable rivalry for equations in (11), where $\mathcal{G}(z)=\frac{0.8}{1+e^{-7.2(z-0.9)}}$, $I=2$, $w=0.25$, $\beta =1.5$, $g=1$, $\epsilon =0.6667$. In a, $\delta =0$ and in b$\delta =0.5$, where δ is the strength of the lateral coupling

Fig. 8

a Images in simplification of the conventional colored dot experiment in <abbrgrp></abbrgrp>. b Network with two learned patterns corresponding to the simplified experiment; symmetry group is $\Gamma ={\mathbf{S}}_4\times {\mathbf{Z}}_2(\rho )$. $\mathit{UL}=\text{upper left}$, $\mathit{LL}=\text{lower left}$, $\mathit{LR}=\text{lower right}$, $\mathit{UR}=\text{upper right}$

Fig. 9

a Images in simplification of the scrambled colored dot experiment in <abbrgrp></abbrgrp>. b Network with two learned patterns and lateral coupling corresponding to the simplified experiment; symmetry group is $\Gamma ={\mathbf{D}}_4\times {\mathbf{Z}}_2(\rho )$

Fig. 10

Predicted percept alternations for proposed conventional colored dot experiment. Rivalry between two red and two green dot patterns: a diagonal; b adjacent top and bottom; c adjacent sides

Fig. 11

Predicted percept alternations for proposed conventional colored dot experiment. Rivalry in a rotating wave

Fig. 12

Predicted percept alternations for proposed conventional colored dot experiment. Rivalry between three dots of one color

Fig. 13

aRegions A–F in image rectangle of scrambled monkey-text experiment. b Network with six attribute columns corresponding to monkey or text image in each region. All inhibitory couplings are shown, but only “nearest neighbor” learned and lateral couplings are shown