Bistable perception, precision and neuromodulation

Abstract

Bistable perception follows from observing a static, ambiguous, (visual) stimulus with two possible interpretations. Here, we present an active (Bayesian) inference account of bistable perception and posit that perceptual transitions between different interpretations (i.e. inferences) of the same stimulus ensue from specific eye movements that shift the focus to a different visual feature. Formally, these inferences are a consequence of precision control that determines how confident beliefs are and change the frequency with which one can perceive-and alternate between-two distinct percepts. We hypothesized that there are multiple, but distinct, ways in which precision modulation can interact to give rise to a similar frequency of bistable perception. We validated this using numerical simulations of the Necker cube paradigm and demonstrate the multiple routes that underwrite the frequency of perceptual alternation. Our results provide an (enactive) computational account of the intricate precision balance underwriting bistable perception. Importantly, these precision parameters can be considered the computational homologs of particular neurotransmitters-i.e. acetylcholine, noradrenaline, dopamine-that have been previously implicated in controlling bistable perception, providing a computational link between the neurochemistry and perception.

Keywords: active inference; bistable perception; neuromodulators; precision.

Fig. 1

A graphical representation of the Necker cube model. the figure provides a graphical illustration of the generative model with two hidden state factors and two outcome modalities. The first hidden state, the fixation point, has three levels: bottom-left, top-right, and initial fixation (IF). The second hidden state, orientation, has two levels, right and left orientation. The outcome modality features has three levels: “Corner 1” (C1), “Corner 2” (C2), and Null. Here, C1 and C2 denote the two opposite corners and their surrounding areas, and the Null outcome is only plausible under the initial fixation point at the first time-step. There is an identity mapping from fixation point hidden factor to where outcomes. The likelihood function of the generative model, i.e. the probability of an outcome given a hidden state, is encoded such that (i) the bottom-left fixation point is more informative about the right orientation as the agent perceives the related C1 corner, (ii) the top-right fixation point is more informative about left orientation as the agent perceives the related C2 corner there, and (iii) the IF mapped onto a null outcome (i.e. neither C1 nor C2). The fixation point transitions (i.e. representing the state transitions across time) are completely precise. This encodes the eye movements between different fixation locations. Conversely, orientation transitions for the generative process are noncontrollable and transition to the same orientation over time. Here, is a small number that prevents numerical overflow.

Fig. 2

A graphical illustration of how different precision values change the likelihood and priors of the generative model. (A) A modulation of the likelihood matrix via the sensory precision (). Each row is for a different fixation point with bottom-left on the first and top-right on the second, where the x-axis represents the orientation states and the y-axis the feature outcomes. (B) This panel shows how the state transition precision () perturbations influence the categorical probability distribution of the orientation transition. The x-axis represents the orientation states at the current time point () and the y-axis the orientation states at the next time point (). Here, low values lead to a flat distribution which limits the capacity to project current beliefs about orientation states to past and future epochs whereas with high the state transition matrix becomes more precise and the capacity to pass messages between epochs increases. (C) An intuition of how the γ parameter modulates the expected free energy G, which is assumed to be [0, 0, 1]' for simplicity. For all plots, the scale goes from white (low probability) to black (high probability), and gray indicates gradations in-between. The key difference to note is how the probability distribution shifts from imprecise to precise mappings as we move from low precision values (e.g. ) to high precision values (e.g. ). Note, and values above 0.5 look visually similar and have been deliberately excluded. Furthermore, the different values have been scaled up to 10 for a visual clarity.

Fig. 3

An example trial with 32 time-steps. The first row represents the posterior probability for the hidden state orientation. The second row shows which actions, i.e. eye movements, have been selected (cyan dots) and the posterior probability of each policy. This has only 31 time-steps as actions are modeled for the next step. The last row depicts the sampled outcomes over time with cyan dots and the preferences over outcomes with different shades in the background. Here, the light and dark shades illustrate that the agent has a strong aversion for the Null outcome (−20 nats) observed only at the IF point but has a relatively higher preference for the C1 and C2 outcomes observed at the bottom-left and top-right locations, respectively. A perceptual switch is highlighted using the red dashed boxes, where the red arrow in the second row shows that the switch is (mostly) accompanied with an action toward the preferred fixation point. The red box in the last row shows that observing the outcome C1 facilitated the perceptual switch from the left to the right orientation in this instance, as shown in the first row. The example simulation is for the following precision combination: .

Fig. 4

The average number of switches for different precision combinations. We plot the average number of switches across 32 trials—each comprising of 32 time-steps. Each heatmap is associated with distinct values. The x-axis is associated with and y-axis plots the different value. The average switch count ranges from 0 (dark blue) to 15 (yellow).

Fig. 5

Dissociating individual precision terms. For (A) and (B), each data point represents the average switch posterior probability (A; y-axis) and the number of switches (B; y-axis) across different precision values (x-axis). The curves represent the fitted polynomials for each precision value: ζ (blue diamond), ω (green square), and γ (cyan triangle). (C) The joint-plot of the association between number of switches and posterior switch probability. The x-axis presents the posterior switch probability, y-axis the number of switches. Here, each plot presents a different precision term.