Dynamical learning in deep asymmetric recurrent neural networks

We investigate recurrent neural networks with asymmetric interactions and demonstrate that the inclusion of self-couplings or sparse excitatory inter-module connections leads to the emergence of a densely connected manifold of dynamically accessible stable configurations. This representation manifold is exponentially large in system size and is reachable through simple local dynamics, despite constituting a subdominant subset of the global configuration space. We further show that learning can be implemented directly on this structure via a fully local, gradient-free mechanism that selectively stabilizes a single task-relevant network configuration. Unlike error-driven or contrastive learning schemes, this approach does not require explicit comparisons between network states obtained with and without output supervision. Instead, transient supervisory signals bias the dynamics toward the representation manifold, after which local plasticity consolidates the attained configuration, effectively shaping the latent representation space. Numerical evaluations on standard image classification benchmarks indicate performance comparable to that of multilayer perceptrons trained using backpropagation. More generally, these results suggest that the dynamical accessibility of fixed points and the stabilization of internal network dynamics constitute viable alternative principles for learning in recurrent systems, with conceptual links to statistical physics and potential implications for biologically motivated and neuromorphic computing architectures.