Competition with and without priority control: linking rivalry to attention through winner-take-all networks with memory

Abstract

Competition is ubiquitous in perception. For example, items in the visual field compete for processing resources, and attention controls their priority (biased competition). The inevitable ambiguity in the interpretation of sensory signals yields another form of competition: distinct perceptual interpretations compete for access to awareness. Rivalry, where two equally likely percepts compete for dominance, explicates the latter form of competition. Building upon the similarity between attention and rivalry, we propose to model rivalry by a generic competitive circuit that is widely used in the attention literature-a winner-take-all (WTA) network. Specifically, we show that a network of two coupled WTA circuits replicates three common hallmarks of rivalry: the distribution of dominance durations, their dependence on input strength ("Levelt's propositions"), and the effects of stimulus removal (blanking). This model introduces a form of memory by forming discrete states and explains experimental data better than competitive models of rivalry without memory. This result supports the crucial role of memory in rivalry specifically and in competitive processes in general. Our approach unifies the seemingly distinct phenomena of rivalry, memory, and attention in a single model with competition as the common underlying principle.

Keywords: attention; binocular rivalry; modeling; psychophysics; vision; winner-take-all network.

Figure 1

Network models: the three models tested in this study. (A) Model 1: a single WTA circuit; each excitatory unit is recurrently coupled to itself with weight α and to the inhibitory unit with weight β2. In turn, the inhibitory unit is coupled to both excitatory units with weight β1, but not to itself. Input is applied to both excitatory units, and the perceptual states are recorded directly from these units. (B) Model 2: identical to model 1, except that both excitatory units are adapting (see Methods in the Supporting Information for details). (C) Model 3: two WTA circuits, as used in model 1, are coupled by connecting their excitatory units across circuits; all connections between the circuits have the same weight ϕ, but feedback connections cross between the two sets of neurons representing different states. Input is applied to map I, and percepts are recorded from map P.

Figure 2

Raw activity. Activity traces for the three models when noisy input (strength 6.5 for models 1 and 2 and strength 5.5 for model 3) is applied to both eyes (see Methods in the Supporting Information for units). All models show bistable behavior, with the excitatory units (blue, red) alternating in dominance. The currently dominant percept, according to the definition used throughout, is indicated by the red and blue bars on top of each plot for models 1 and 2, and for the percept units of model 3. Green trace represents the activity of the inhibitory unit.

Figure 3

Dominance distributions. Example distributions of dominance durations for the three models and experiment 1 for a medium input strength. Modeling data are based on a single simulation run and experimental data on a single individual. Dominance durations are pooled over both percepts. Insets depict finer resolution for the left-most bin (model 1) or two left-most bins (model 2), corresponding to five time units to ease comparison with model 3.

Figure 4

Levelt's propositions. (A) Levelt's first proposition tested for the three models and data of experiment 1; relative dominance is color coded individually per panel. In the panel for model 1, some simulations are stuck within the same state throughout, and—as for all analysis the last period is excluded—no data is available, indicated in gray. (B) Levelt's second proposition: log dominance duration for one eye (ipsilateral eye) while input strength to this eye and to the other eye (contralateral eye) are varied independently. Data are collapsed over both eyes (left/right) or units (i1/i2, p1/p2). Log scale is used for illustration, and correlations are computed on the original data. (C) Levelt's third and fourth propositions: dependence of switch rate on input strength to either eye.

Figure 5

Blanking, model output. (A) Time course of an experimental blanking trial. Blank intervals are not to scale. (B) Input function for modeling blanking in the models; typical example with added noise. At onset there is a steep rise with exponential decay to the sustained activity; at offset a smooth relaxation to baseline. (C) Example traces of model 3 for three different blanking durations. Blue and red curves correspond to neurons p1 and p2, respectively. (D) Experimental data for blanking in a single subject. Percept changes more frequently in the absence of blanks (<90 s, >270 s), and stabilization depends on blank duration.

Figure 6

Blanking, model results. (A) Survival probability, (B) switch probability, and (C) their sum for the three models and the data of experiment 2. Different line colors indicate different input strengths (consistent within each column as given in the top-row panels).