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We have created encoding manifolds to reveal the overall responses of a brain area to a variety of stimuli. Encoding manifolds organize response properties globally: each point on an encoding manifold is a neuron, and nearby neurons respond similarly to the stimulus ensemble in time. We previously found, using a large stimulus ensemble including optic flows, that encoding manifolds for the retina were highly clustered, with each cluster corresponding to a different ganglion cell type. In contrast, the topology of the V1 manifold was continuous. Now, using responses of individual neurons from the Allen Institute Visual Coding-Neuropixels dataset in the mouse, we infer encoding manifolds for V1 and for five higher cortical visual areas (VISam, VISal, VISpm, VISlm, and VISrl). We show here that the encoding manifold topology computed only from responses to various grating stimuli is also continuous, not only for V1 but also for the higher visual areas, with smooth coordinates spanning it that include, among others, orientation selectivity and firing-rate magnitude. Surprisingly, the encoding manifold for gratings also provides information about natural scene responses. To investigate whether neurons respond more strongly to gratings or natural scenes, we plot the log ratio of natural scene responses to grating responses (mean firing rates) on the encoding manifold. This reveals a global coordinate axis organizing neurons' preferences between these two stimuli. This coordinate is orthogonal (i.e., uncorrelated) to that organizing firing rate magnitudes in VISp. Analyzing layer responses, a preference for gratings is concentrated in layer 6, whereas preference for natural scenes tends to be higher in layers 2/3 and 4. We also find that preference for natural scenes dominates the responses of neurons that prefer low (0.02 cpd) and high (0.32 cpd) spatial frequencies, rather than intermediate ones (0.04 to 0.16 cpd). Conclusion: while gratings seem limited and natural scenes unconstrained, machine learning algorithms can reveal subtle relationships between them beyond linear techniques. 

The retina and primary visual cortex (V1) both exhibit diverse neural populations sensitive to diverse visual features. Yet it remains unclear how neural populations in each area partition stimulus space to span these features. One possibility is that neural populations are organized into discrete groups of neurons, with each group signaling a particular constellation of features. Alternatively, neurons could be continuously distributed across feature-encoding space. To distinguish these possibilities, we presented a battery of visual stimuli to the mouse retina and V1 while measuring neural responses with multi-electrode arrays. Using machine learning approaches, we developed a manifold embedding technique that captures how neural populations partition feature space and how visual responses correlate with physiological and anatomical properties of individual neurons. We show that retinal populations discretely encode features, while V1 populations provide a more continuous representation. Applying the same analysis approach to convolutional neural networks that model visual processing, we demonstrate that they partition features much more similarly to the retina, indicating they are more like big retinas than little brains. 

Abstract Invoking the manifold assumption in machine learning requires knowledge of the manifold's geometry and dimension, and theory dictates how many samples are required. However, in most applications, the data are limited, sampling may not be uniform, and the manifold's properties are unknown; this implies that neighborhoods must adapt to the local structure. We introduce an algorithm for inferring adaptive neighborhoods for data given by a similarity kernel. Starting with a locally conservative neighborhood (Gabriel) graph, we sparsify it iteratively according to a weighted counterpart. In each step, a linear program yields minimal neighborhoods globally, and a volumetric statistic reveals neighbor outliers likely to violate manifold geometry. We apply our adaptive neighborhoods to nonlinear dimensionality reduction, geodesic computation, and dimension estimation. A comparison against standard algorithms using, for example, k-nearest neighbors, demonstrates the usefulness of our approach. 

Assessments of the mouse visual system based on spatial-frequency analysis imply that its visual capacity is low, with few neurons responding to spatial frequencies greater than 0.5 cycles per degree. However, visually mediated behaviors, such as prey capture, suggest that the mouse visual system is more precise. We introduce a stimulus class—visual flow patterns—that is more like what the mouse would encounter in the natural world than are sine-wave gratings but is more tractable for analysis than are natural images. We used 128-site silicon microelectrodes to measure the simultaneous responses of single neurons in the primary visual cortex (V1) of alert mice. While holding temporal-frequency content fixed, we explored a class of drifting patterns of black or white dots that have energy only at higher spatial frequencies. These flow stimuli evoke strong visually mediated responses well beyond those predicted by spatial-frequency analysis. Flow responses predominate in higher spatial-frequency ranges (0.15–1.6 cycles per degree), many are orientation or direction selective, and flow responses of many neurons depend strongly on sign of contrast. Many cells exhibit distributed responses across our stimulus ensemble. Together, these results challenge conventional linear approaches to visual processing and expand our understanding of the mouse’s visual capacity to behaviorally relevant ranges.