Soft-margin classification of object manifolds.

A neural population responding to multiple appearances of a single object defines a manifold in the neural response space. The ability to classify such manifolds is of interest, as object recognition and other computational tasks require a response that is insensitive to variability within a manifold. Linear classification of object manifolds was previously studied for max-margin classifiers.

Separability and geometry of object manifolds in deep neural networks.

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.

Learning Data Manifolds with a Cutting Plane Method.

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.

Neuronvisio: A Graphical User Interface with 3D Capabilities for NEURON.

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.