Active efficient coding explains the development of binocular vision and its failure in amblyopia

Abstract

The development of vision during the first months of life is an active process that comprises the learning of appropriate neural representations and the learning of accurate eye movements. While it has long been suspected that the two learning processes are coupled, there is still no widely accepted theoretical framework describing this joint development. Here, we propose a computational model of the development of active binocular vision to fill this gap. The model is based on a formulation of the active efficient coding theory, which proposes that eye movements as well as stimulus encoding are jointly adapted to maximize the overall coding efficiency. Under healthy conditions, the model self-calibrates to perform accurate vergence and accommodation eye movements. It exploits disparity cues to deduce the direction of defocus, which leads to coordinated vergence and accommodation responses. In a simulated anisometropic case, where the refraction power of the two eyes differs, an amblyopia-like state develops in which the foveal region of one eye is suppressed due to inputs from the other eye. After correcting for refractive errors, the model can only reach healthy performance levels if receptive fields are still plastic, in line with findings on a critical period for binocular vision development. Overall, our model offers a unifying conceptual framework for understanding the development of binocular vision.

Keywords: accommodation; active perception; amblyopia; efficient coding; vergence.

Fig. 1.

The action–perception loop in active efficient coding. The sensory input is obtained by sampling input signals from the environment (e.g., via eye movements). A percept is formed by neural encoding, which drives the selection of actions and thereby, shapes the sampling process. Therefore, perception depends on both neural encoding and active input sampling. Classic efficient coding theories do not consider the active sampling component (orange).

Fig. 2.

Model architecture, with solid arrows representing the flow of sensory information and dashed arrows representing the flow of control commands. Sampled input images with given defocus blur and disparity are whitened at the retinal stage $R$ and contrast adjusted through an interocular suppression mechanism based on the recent history of cortical activity (Left). Thereafter, they are encoded by a set of binocular neurons that represents the cortical encoding $C$ (Center). The cortical population activity serves as input to two reinforcement learning modules (Right) that control vergence and accommodation commands. Details are in Materials and Methods.

Fig. 3.

Input sampling from the environment. (A) Object (obj.) position, vergence (verg.) distance, and left (l.) and right (r.) accommodation (acc.) distance are represented as different plane positions. (B) Abstraction of A. The gray horizontal bar indicates the range where objects are presented during the simulation and also, indicates the fixation range (i.e., possible vergence plane positions). Horizontal axes indicate reachable accommodation plane positions for the left (light blue) and right (green) eyes. Note that, when the stimulus is placed at, for example, position 0, it cannot be focused by the right eye in this example. Accommodation and vergence errors are measured as the distance between the respective planes and the object position in a.u. (C) Position range of accommodation and vergence planes under different conditions. Same scheme as in B. (D) Examples of retinal input images for different plane position configurations. For better visibility, disparity shifts and defocus blur are increased compared to actual values.

Fig. 4.

The feedback loop of active efficient coding and reward dependencies. (A) Positive feedback loop of active efficient coding. An efficiently encoded stimulus is preferred over other stimuli (acting). Therefore, the sensory system is more frequently exposed to the stimulus, and neural circuits adapt to reflect this overrepresentation (statistical learning), which further increases encoding efficiency (neural coding). (B) Normalized (norm.) vergence (verg.) reward for different disparity distributions and neural populations (averaged over 300 textures). The receptive fields of 300 neurons adapted to different distributions of input disparities with color-coded SDs. Gray indicates unbiased/uniform, pink and purple indicate Laplacian distributed, and dark blue indicates model trained under healthy conditions. In each case, stimuli seen at zero absolute (abs.) disparity produce the highest average (avg.) vergence reward (i.e., the most efficient encoding). This advantage is even more pronounced when small disparities have been encountered more frequently (i.e., for smaller $\sigma$). (C) Normalized accommodation (acc.) reward for different whitening filters. Zero-blur input yields the highest accommodation reward independent of the size of the whitening filter. However, smaller whitening filters induce a stronger preference for focused input. The smallest filter (dark blue) was used for the simulation (Materials and Methods has details).

Fig. 5.

Interocular suppression model. (A) When mostly right (left) monocular neurons $c_j$ are activated to encode an input image patch, the right (left) contrast unit $y_r$ ($y_l$) is excited, and the left (right) retinal image is suppressed in subsequent iterations. Color hue indicates response selectivity for left eye (blue) or right eye (green). Dashed (solid) lines indicate inhibitory (excitatory) interactions. Connection strength is represented by line thickness. We model interocular suppression as being scale specific (i.e., when the high-resolution foveal region of the left eye is suppressed, the low-resolution periphery of the left eye may still provide unattenuated input) (Materials and Methods). (B) Feedback cycle of the suppression model. Disparate inputs to both eyes lead to preferential recruitment of monocular neurons, which results in interocular suppression inducing competition between the eyes. This impedes precise vergence eye movements and exacerbates disparate input (purple; left cycle). On a slower timescale, receptive fields (RFs) adapt to suppression by becoming more monocular, which makes future suppression more likely (red; right cycle). Dashed lines indicate feedback that affects future input processing.

Fig. 6.

Model performance. (A) Average (avg.) absolute (abs.) vergence (verg.) and accommodation (acc.) errors of the left (l.) and right (r.) eye after training under healthy and anisometropic conditions. The dashed line indicates the expected average vergence error when accommodation planes are moved randomly under healthy conditions. (B) Vergence performance of the formerly anisometropic model after correction of all refractive errors at iteration $5\times 10^6$ (vertical gray line). The (dotted) solid line indicates the model with (non-)plastic receptive fields (RFs). The initial increase in the vergence error is due to the recalibration of the reinforcement learning module. (C) Histogram of foveal RFs binocularity as measured by the right monocular (monoc.) dominance $d_{\left(\cdot ,r\right)}$ before and after refractive error correction (Materials and Methods has details).