Scene statistics and noise determine the relative arrangement of receptive field mosaics

Many sensory systems utilize parallel ON and OFF pathways that signal stimulus increments and decrements, respectively. These pathways consist of ensembles or grids of ON and OFF detectors spanning sensory space. Yet, encoding by opponent pathways raises a question: How should grids of ON and OFF detectors be arranged to optimally encode natural stimuli? We investigated this question using a model of the retina guided by efficient coding theory. Specifically, we optimized spatial receptive fields and contrast response functions to encode natural images given noise and constrained firing rates. We find that the optimal arrangement of ON and OFF receptive fields exhibits a transition between aligned and antialigned grids. The preferred phase depends on detector noise and the statistical structure of the natural stimuli. These results reveal that noise and stimulus statistics produce qualitative shifts in neural coding strategies and provide theoretical predictions for the configuration of opponent pathways in the nervous system.

Across many sensory systems, neurons encode information about either increments or decrements of stimuli in the environment, so-called ON and OFF signals. This division between ON and OFF signaling has been observed in visual (1, 2), thermosensory (3), auditory (4), olfactory (5), and electrosensory (6) systems. This organization has the advantage that neurons can be tasked with signaling increments or decrements in steady-state stimulus levels with fewer spikes, thereby resulting in more efficient neural codes (7, 8). Moreover, when the number of potential stimuli is large, neurons often specialize; for example, they only respond to a small region of visual space or a narrow auditory frequency band. The combination of these coding strategies raises two questions. First, how should a particular set of detectors, either the ON or OFF cells, arrange themselves most efficiently to cover stimulus space? Second, what is the optimal relative arrangement of ON and OFF detector grids? For one system, the retina, the answer to the first question is clear from previous work: Detectors of a particular type tile stimulus space and exhibit overlap near the 1-sigma boundary of a Gaussian receptive field (9–13). The answer to the second question, what might be called the “sensor alignment problem,” has received comparatively little attention and is the focus of this study.Conceptually, there are three general possibilities for how the sensor alignment problem could be solved. One possibility is that the grids of sensors are statistically independent, meaning the locations of receptive fields in one grid provide no information about the receptive field locations in the other grid. A second possibility is that the two grids are aligned, meaning the receptive field centers in one grid are closer than expected by chance. The third possibility is that the two grids are antialigned, meaning the receptive field centers in the two grids are further apart than expected by chance. On general information theory grounds, the optimal solution is likely to depend on noise in the encoding process and the statistics of the encoded stimuli (14, 15).While most anatomical studies of retinal mosaics indicate they are statistically independent (16–18, but see ref. 19), we have recently shown that grids of ON and OFF receptive field (henceforth called “mosaics”) formed by retinal ganglion cells (RGCs) are antialigned when those cells encode similar visual features (20). Here, we show how these results can be explained through the lens of efficient coding theory (7). This theory argues that sensory systems should aim to reduce the redundancy present in sensory input while minimizing metabolic costs, thereby reliably encoding natural stimuli with fewer spikes. Efficient coding theory has been successful at explaining many aspects of sensory processing and retinal physiology, including center-surround receptive fields, the formation of mosaics, and a greater proportion of OFF than ON cells (7, 11, 15, 21, 22). Thus, we asked whether efficient coding theory might predict the optimal spatial arrangement of ON and OFF receptive field mosaics within the retina. Our approach to this question involved optimizing a model that approximates the processing performed by many RGCs (21). By maximizing the mutual information between an (input) library of natural images and (output) spike rates, we examined the effects of image statistics and encoding noise on the optimal arrangement of ON and OFF mosaics.In this model, we found that the optimal spatial arrangement was a pair of approximately hexagonal mosaics of ON and OFF receptive fields. However, surprisingly, the relative alignment of these mosaics depended on the input noise, output noise, and the statistics of the natural image set. When output noise was low, the mosaics were aligned, with ON and OFF receptive fields centered at nearby locations more often than expected by chance. When output noise was relatively high, antialignment became the favored arrangement. Surprisingly, the content of the image set also strongly influenced the transition between aligned and antialigned mosaics. In particular, when image sets contained more “outlier” images with particularly large luminance or contrast values, antialignment became the favored state for fixed input and output noise. We demonstrate analytically and confirm computationally that as noise parameters or stimulus statistics vary, mutual information changes smoothly, while the optimal mosaic arrangements undergo a sudden, qualitative shift. Finally, we confirm these predictions by showing that systematic manipulations of the training dataset change the phase boundary in a manner predicted by an analytical model. These findings underscore the crucial role played by both noise and the statistics of natural stimuli for understanding specialization and coordination in sensory processing.