Learning in Wilson-Cowan model for metapopulation

The Wilson-Cowan model for metapopulation, a Neural Mass Network Model, treats different subcortical regions of the brain as connected nodes, with connections representing various types of structural, functional, or effective neuronal connectivity between these regions. Each region comprises interacting populations of excitatory and inhibitory cells, consistent with the standard Wilson-Cowan model. By incorporating stable attractors into such a metapopulation model's dynamics, we transform it into a learning algorithm capable of achieving high image and text classification accuracy. We test it on MNIST and Fashion MNIST, in combination with convolutional neural networks, on CIFAR-10 and TF-FLOWERS, and, in combination with a transformer architecture (BERT), on IMDB, always showing high classification accuracy. These numerical evaluations illustrate that minimal modifications to the Wilson-Cowan model for metapopulation can reveal unique and previously unobserved dynamics.

Automatic Input Feature Relevance via Spectral Neural Networks

Working with high-dimensional data is a common practice, in the field of machine learning. Identifying relevant input features is thus crucial, so as to obtain compact dataset more prone for effective numerical handling. Further, by isolating pivotal elements that form the basis of decision making, one can contribute to elaborate on - ex post - models' interpretability, so far rather elusive. Here, we propose a novel method to estimate the relative importance of the input components for a Deep Neural Network. This is achieved by leveraging on a spectral re-parametrization of the optimization process. Eigenvalues associated to input nodes provide in fact a robust proxy to gauge the relevance of the supplied entry features. Unlike existing techniques, the spectral features ranking is carried out automatically, as a byproduct of the network training. The technique is successfully challenged against both synthetic and real data.