Stimuli are represented in the brain by the collective population responses of sensory neurons, and an object presented under varying conditions gives rise to a collection of neural population responses called an 'object manifold'. Changes in the object representation along a hierarchical sensory system are associated with changes in the geometry of those manifolds, and recent theoretical progress connects this geometry with 'classification capacity', a quantitative measure of the ability to support object classification. Deep neural networks trained on object classification tasks are a natural testbed for the applicability of this relation. We show how classification capacity improves along the hierarchies of deep neural networks with different architectures. We demonstrate that changes in the geometry of the associated object manifolds underlie this improved capacity, and shed light on the functional roles different levels in the hierarchy play to achieve it, through orchestrated reduction of manifolds' radius, dimensionality and inter-manifold correlations.

Despite variations in appearance we robustly recognize objects. Neuronal populations responding to objects presented under varying conditions form object manifolds and hierarchically organized visual areas are thought to untangle pixel intensities into linearly decodable object representations. However, the associated changes in the geometry of object manifolds along the cortex remain unknown. Using home cage training we showed that mice are capable of invariant object recognition. We simultaneously recorded the responses of thousands of neurons to measure the information about object identity available across the visual cortex and found that lateral visual areas LM, LI and AL carry more linearly decodable object identity information compared to other visual areas. We applied the theory of linear separability of manifolds, and found that the increase in classification capacity is associated with a decrease in the dimension and radius of the object manifold, identifying features of the population code that enable invariant object coding.

Stimuli are represented in the brain by the collective population responses of sensory neurons, and an object presented under varying conditions gives rise to a collection of neural population responses called an "object manifold." Changes in the object representation along a hierarchical sensory system are associated with changes in the geometry of those manifolds, and recent theoretical progress connects this geometry with "classification capacity," a quantitative measure of the ability to support object classification. Deep neural networks trained on object classification tasks are a natural testbed for the applicability of this relation. We show how classification capacity improves along the hierarchies of deep neural networks with different architectures. We demonstrate that changes in the geometry of the associated object manifolds underlie this improved capacity, and shed light on the functional roles different levels in the hierarchy play to achieve it, through orchestrated reduction of manifolds' radius, dimensionality and inter-manifold correlations.

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We consider the problem of classifying data manifolds where each manifold represents invariances that are parameterized by continuous degrees of freedom. Conventional data augmentation methods rely on sampling large numbers of training examples from these manifolds. Instead, we propose an iterative algorithm, [Formula: see text], based on a cutting plane approach that efficiently solves a quadratic semi-infinite programming problem to find the maximum margin solution. We provide a proof of convergence as well as a polynomial bound on the number of iterations required for a desired tolerance in the objective function. The efficiency and performance of [Formula: see text] are demonstrated in high-dimensional simulations and on image manifolds generated from the ImageNet data set. Our results indicate that [Formula: see text] is able to rapidly learn good classifiers and shows superior generalization performance compared with conventional maximum margin methods using data augmentation methods.

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The NEURON simulation environment is a commonly used tool to perform electrical simulation of neurons and neuronal networks. The NEURON User Interface, based on the now discontinued InterViews library, provides some limited facilities to explore models and to plot their simulation results. Other limitations include the inability to generate a three-dimensional visualization, no standard mean to save the results of simulations, or to store the model geometry within the results. Neuronvisio () aims to address these deficiencies through a set of well designed python APIs and provides an improved UI, allowing users to explore and interact with the model. Neuronvisio also facilitates access to previously published models, allowing users to browse, download, and locally run NEURON models stored in ModelDB. Neuronvisio uses the matplotlib library to plot simulation results and uses the HDF standard format to store simulation results. Neuronvisio can be viewed as an extension of NEURON, facilitating typical user workflows such as model browsing, selection, download, compilation, and simulation. The 3D viewer simplifies the exploration of complex model structure, while matplotlib permits the plotting of high-quality graphs. The newly introduced ability of saving numerical results allows users to perform additional analysis on their previous simulations.

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