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Title: Transformation of Stimulus Correlations by the Retina}
Article:
Abstract:
Redundancies and correlations in the responses of sensory neurons may seem to waste neural resources, but they can also carry cues about structured stimuli and may help the brain to correct for response errors. To investigate the effect of stimulus structure on redundancy in retina, we measured simultaneous responses from populations of retinal ganglion cells presented with natural and artificial stimuli that varied greatly in correlation structure; these stimuli and recordings are publicly available online. Responding to spatio-temporally structured stimuli such as natural movies, pairs of ganglion cells were modestly more correlated than in response to white noise checkerboards, but they were much less correlated than predicted by a non-adapting functional model of retinal response. Meanwhile, responding to stimuli with purely spatial correlations, pairs of ganglion cells showed increased correlations consistent with a static, non-adapting receptive field and nonlinearity. We found that in response to spatio-temporally correlated stimuli, ganglion cells had faster temporal kernels and tended to have stronger surrounds. These properties of individual cells, along with gain changes that opposed changes in effective contrast at the ganglion cell input, largely explained the pattern of pairwise correlations across stimuli where receptive field measurements were possible.
Introduction:
An influential theory of early sensory processing argues that sensory circuits should conserve scarce resources in their outputs by reducing correlations present in their inputs[1]–[3]. At the same time, recent work has clarified that some redundancy in the retinal output is useful for hedging against noise[4],[5]. Moreover, sensory outputs with varying amounts of correlation can engage cortical circuits differently and thus result in a different sensory “code”[6]. Thus, some degree of redundancy appears to be useful to the brain when dealing with response variability and making decisions based on probabilistic input[7]. Indeed, correlations between neurons in visual cortex are largely unchanged between unstructured and naturalistic visual stimuli[8]. In the absence of neural mechanisms supporting adaptation to the structure of sensory inputs, increased stimulus correlation would induce a corresponding change in neural correlation. Alternatively, the retina may dynamically adjust its coding strategy to represent the new stimulus class efficiently. To explore this possibility, we characterized the impact of stimulus structure on retinal output correlation. Previous studies have examined pairwise correlations amongst retinal ganglion cell spike trains in specific stimulus conditions[9]–[14] but did not report the changes in correlation for the same pairs across stimuli. Are there mechanisms that might allow the retina to adjust its functional properties when stimulus correlations change? Traditionally, retinal ganglion cells( RGCs) have been described by a fixed linear receptive field followed by a static nonlinearity[15], where surround inhibition acts linearly to suppress pairwise correlations in natural visual input[2],[3]. In this view, the receptive field and nonlinearities might vary dynamically with stimulus correlations, possibly by changing the strength of lateral inhibition to maintain a fixed amount of output correlation. Indeed, correlation-induced changes in receptive fields have been observed in the LGN and visual cortex[16],[17]. To test these ideas, we performed a series of experiments in which we presented the retina with several stimuli with varying degrees of spatial and temporal correlations. The retina never fully decorrelated its input; even for the least correlated white noise checkerboard stimuli, some correlations were present between pairs of retinal ganglion cell spike trains. Responding to natural movies, however, output correlations were only moderately increased compared to correlations in responses to white noise checkerboards, despite the dramatic difference in input-induced correlations. Specifically, the differences in output correlations were much less than those predicted by a non-adapting linear-nonlinear functional model responding to these stimuli. We found a similar result for spatio-temporal exponentially correlated stimuli, with an even smaller change in output correlations. In this way, pairwise output correlations change by a relatively small amount as compared to the expected input-induced change in response to stimuli that span a broad range of spatio-temporal correlations. Stimuli with only spatial correlations, on the other hand, produced increases in output correlations similar to the input-induced changes predicted by a static, non-adapting functional model. In the extreme case, for temporally uncorrelated full-field flicker, the output correlation increased substantially. These results suggest a key role for temporal processing in maintaining the level of output correlations. Indeed, we observed a robustly faster response timecourse and a modest skew towards stronger inhibitory surrounds in response to spatio-temporally correlated stimuli. These changes were sufficient to largely explain the observed relative suppression of pairwise correlations in the retinal output for those experimental conditions where receptive field measurements could be made.
Discussion:
Our principal finding is that the mammalian retina maintains a moderate level of output correlation across a wide range of spatio-temporally correlated stimuli ranging from white noise checkerboards( with limited correlations) to natural movies( with wide spatial and temporal correlations). While the amount of output correlation varies between stimuli, the changes are much less than predicted by a non-adapting linear-nonlinear functional model. Our data also suggest a differential effect of spatial versus temporal correlations on the functional properties of the retinal output. We focused here on spatial variations in our stimuli, but it would be interesting to design future studies to explore the space-time differences more systematically. In response to spatio-temporal exponential noise, where the receptive fields could be estimated, we showed that the relative invariance of output correlations is largely accounted for by the observed changes in the linear receptive field( faster temporal kernels and slightly stronger surround inhibition for more correlated stimuli) and by changes in the nonlinear gain( anti-correlated to changes in effective contrast). The latter findings give an interpretation of the results in terms of a conventional functional model( here a linear-nonlinear cascade), but the measurement of output correlations is model-independent. Classifying cells into classes revealed a slight dependence of excess correlation on cell class: most robustly, opposite polarity ON-OFF pairs showed the greatest increase in correlation magnitude when stimulus correlation increased. Indeed, if the retinal output is split across parallel functional channels, redundancy is likely to be highest within a channel due to shared circuit inputs. It may thus be advantageous, from an information encoding perspective, for decorrelation to act within a channel, with residual correlations across classes signaling to downstream areas relevant relationships between the information in different channels. Pitkow and Meister[14] showed that salamander retina partly decorrelates naturalistic inputs but that the response to white noise is more correlated than the input, in part due to receptive field overlap between ganglion cells. Here we demonstrated a similar phenomenon in mammalian retina: consistent with their results, we found that changes in output correlations were often smaller than changes in input correlations. We also extended their findings by showing explicitly that this partial decorrelation occurs in individual pairs of neurons. In[14], it was also suggested that the linear receptive field measured from white noise was insufficient to explain the amount of decorrelation seen for naturalistic stimuli, and the bulk of the decorrelation was attributed to changes in the threshold of a functional model of ganglion cells. However, the authors did not directly measure the( possibly different) receptive fields of ganglion cells responding to correlated stimuli, nor did they follow particular cell pairs across different stimuli. Our measurements suggest that the nonlinear processing proposed in[14] can be described in terms of adaptation of the linear receptive field and nonlinear gain with the net effect that output correlations are reduced relative to the expected input-induced correlations, as was observed in visual cortex by[8]. Our results also recall those of[16],[23],[17], and[24], who showed that receptive fields in LGN and primary visual cortex differ in structure when probed with natural movies versus random stimuli. We also found that the gain of retinal ganglion cells responding to correlated stimuli changes with “effective contrast” and, i. e. with the standard deviation of the input to the nonlinearity in a linear-nonlinear model of ganglion cells. In classical contrast gain control, firing rates and response kinetics adapt to temporal contrast and to the spatial scale of stimuli[21],[22]. As increased stimulus correlation may produce a qualitatively similar input to the inner plexiform layer as increased contrast, some of the cellular mechanisms underlying contrast adaptation might also contribute to the phenomena we have uncovered. This provides an avenue for future study of the functional mechanisms underlying adaptation to correlations. We have focused in the present work on the failure of a non-adapting linear-nonlinear model to capture the relatively small scale of observed excess correlations and have seen that adaptation in the linear filter might remedy this discrepancy. Alternatively, shared circuitry in the population of neurons may be engaged by correlated inputs and require explicit inclusion in any functional model of retinal responses to different classes of correlated stimuli[9],[25]. Such shared circuitry leads to noise in one neuron being passed to multiple nearby neurons and is thus measured by “noise correlations. ” While addition of fixed, stimulus-independent noise correlation would not greatly change our results, a change in noise correlation with stimulus would provide a different candidate mechanism to account for our data[26]. This is another avenue for future work. We have focused here on the effects of spatial correlations in an experimental design where we could compare receptive fields computed from responses to two different stimuli. Thus, we used relatively weak exponential correlations to ensure that we were not measuring artifacts of the stimulus correlations themselves. Recovering receptive fields from strongly correlated stimuli can require long recording times. Because our experimental design involved comparisons between several different stimuli, we were only able to recover receptive fields for moderately correlated stimuli. Future work could simply present each stimulus for a longer duration to assess receptive field changes at a population level rather than analyzing multiple stimuli in one experiment. In such experiments with more data from each cell, alternative methods of receptive field estimation such as Maximally Informative Dimensions[17] could potentially be applied. Further work could also include parallel studies with stimuli including temporal correlations only to complement our findings on responses to spatial correlations. Finally, it would be interesting to determine the timecourse of the adaptations observed here. Knowing whether a change in stimulus correlations induces changes in receptive fields and output correlations within seconds, tens of seconds, or longer would help to clarify the relationship between processing of correlations and adaptation to other stimulus features such as contrast. Again, the design of our experiments precluded making these measurements – we focused on long segments to measure steady-state processing of correlations, whereas assessing the timecourse of changes requires finer and more systematic sampling of transitions between stimuli. Why would the retina need to adapt, in the behaving animal, to variations in spatial correlations? While natural scenes are scale-invariant on average, the specific correlations do vary depending on the scene and the viewing distance( see Fig. 1A). Barlow originally suggested that sensory systems should decorrelate their inputs to make efficient use of limited neural bandwidth[1]. Consistent with this idea, we found that retina removes redundancies in spatio-temporally correlated stimuli but also that the retinal output is not completely decorrelated. Rather, the output correlations are reduced to a lower level, roughly similar to correlations in responses to white noise checkerboards when considered relative to the much larger input-induced correlations predicted by a non-adapting functional model of neural response. What drives this tradeoff? Recall that redundancy can be useful to protect against noise, to facilitate downstream computations, or to enable separate modulation of information being routed to distinct cortical targets. Thus, it may be that a certain degree of output correlation between retinal ganglion cells represents a good balance between the benefits of decorrelation and the benefits of redundancy[5]. Sensory outputs with varying amounts of correlation may also be decoded differently by cortex[6], in which case maintaining a fixed visual code might require that retinal output correlations are within the range expected by downstream visual areas. In these interpretations, it makes sense that the retina adapts to maintain correlation within a relatively narrow range across stimulus conditions, as we have found.
An influential theory of early sensory processing argues that sensory circuits should conserve scarce resources in their outputs by reducing correlations present in their inputs . Measuring simultaneous responses from large numbers of retinal ganglion cells responding to widely different classes of visual stimuli , we find that output correlations increase when we present stimuli with spatial , but not temporal , correlations . On the other hand , we find evidence that retina adjusts to spatio-temporal structure so that retinal output correlations change less than input correlations would predict . Changes in the receptive field properties of individual cells , along with gain changes , largely explain this relative constancy of correlations over the population .