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Understanding circuit properties from physiological data presents two challenges: (i) recordings do not reveal connectivity, and (ii) stimuli only exercise circuits to a limited extent. We address these challenges for the mouse visual system with a novel neural manifold obtained using unsupervised algorithms. Each point in our manifold is a neuron; nearby neurons respond similarly in time to similar parts of a stimulus ensemble. This ensemble includes drifting gratings and flows, i.e., patterns resembling what a mouse would “see” running through fields. Regarding (i), our manifold differs from the standard practice in computational neuroscience: embedding trials in neural coordinates. Topology matters: we infer that, if the circuit consists of separate components, the manifold is discontinuous (illustrated with retinal data). If there is significant overlap between circuits, the manifold is nearly-continuous (cortical data). Regarding (ii), most of the cortical manifold is not activated with conventional gratings, despite their prominence in laboratory settings. Our manifold suggests organizing cortical circuitry by a few specialized circuits for specific members of the stimulus ensemble, together with circuits involving ‘multi-stimuli’-responding neurons. To approach real circuits, local neighborhoods in the manifold are identified with actual circuit components. For retinal data, we show these components correspond to distinct ganglion cell types by their mosaic-like receptive field organization, while for cortical data, neighborhoods organize neurons by type (excitatory/inhibitory) and anatomical layer. In summary: the topology of neural organization reflects well the underlying anatomy and physiology of the retina and the visual cortex. 

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. 

Two interleaved stimulus sets were identical except for the background. In one, the flow stimuli background was the mid-gray of the interstimulus interval (equal background, eqbg), leading to a change of 9-10% in the space-average luminance. In the other, the space-average luminance of the entire stimulus field was adjusted to a constant (equal luminance, eqlum) within 0.5%; i.e., the background was slightly lightened when the dots in the flow were dark, and darkened when the dots were bright. Most cortical cells appeared to respond similarly to the two stimulus sets, as if stimulus structure mattered but not the background change, while the responses of most retinal ganglion cells appeared to differ between the two conditions. Machine learning algorithms confirmed this quantitatively. A manifold embedding of neurons to the two stimulus sets was constructed using diffusion maps. In this manifold, the responses of the same cell to eqlum and eqbg stimuli were significantly closer to one another for V1 rather than for the retina. Geometrically, the median ratio of the distance between the responses of each cell to the two stimulus sets as compared to the distance to the closest cell on the manifold was 3.5 for V1 compared to 12.7 for retina. Topologically, the fraction of cells for which the responses of the same cell to the two stimulus sets were connected in the diffusion map datagraph was 53% for V1 but only 9% for retina; when retina and cortex were co-embedded in the manifold, these fractions were 44% and 6%. While retina and cortex differ on average, it will be intriguing to determine whether particular classes of retinal cells behave more like V1 neurons, and vice versa. 

Deep neural network modeling of biological visual processing is widespread: brains are archetypal pattern analyzers and deep CNNs are currently the best object classifiers. Implicit is the assumption that cortex can be well approximated by CNNs, from which it follows that CNNs are an appropriate foundation for AI. We examine whether this approximation holds using a novel neural manifold obtained with machine learning techniques. 

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.