Deterministic versus stochastic dynamical classifiers: opposing random adversarial attacks with noise

The continuous-variable firing rate (CVFR) model, widely used in neuroscience to describe the complex dynamics of excitatory biological neurons, is here trained and tested as a dynamical classifier. To this end the model is supplied with a set of attractors which are a priori embedded in the inter-node coupling matrix, via its spectral decomposition. Learning amounts to tuning the residual parameters, in order to shape a non-equilibrium path which bridges the input (the data to be classified) and the output (the target memory slot). The imposed attractors are unaltered by the training, and this enables for ex post comparisons to be eventually drawn, e.g. as it concerns the size of their associated basins of attraction. A stochastic variant of the CVFR model is also studied and found to be robust to non-targeted adversarial attacks, which corrupt with a random perturbation the items to be eventually classified. Taken as a whole, here we show that a family of biologically plausible models written in terms of coupled ODEs can efficiently cope with a non-trivial classification task.