Inhibitory Hebbian Plasticity For Robust Stabilisation of Recurrent Neural Networks

Abstract

Cortical circuits are widely thought to operate in the so-called inhibition-stabilised network (ISN) regime, whereby recurrent excitation alone is unstable but the overall dynamics are stabilised through feedback inhibition. While such inhibitory feedback is commonly viewed as the circuit’s control mechanism, this dissertation investigates the role of inhibitory synaptic plasticity (ISP) as a form of meta-control — a plastic mechanism that autonomously tunes inhibitory connectivity to establish appropriate feedback loops for robust and adaptive stabilisation. However, how such meta-control is achieved in recurrent networks remains poorly understood. This thesis develops a theory of inhibitory synaptic plasticity and demonstrates that it approximates an optimal meta-control strategy for network stability. We prove analytically that a biologically plausible form of Hebbian ISP cannot destabilise network dynamics and, in fact, always increases system stability. This local learning rule shapes detailed inhibitory feedback loops that selectively suppress multiple unstable modes within the excitatory subcircuit. As a result, in networks with rich patterns of excitatory recurrence, ISP automatically places the circuit in a form of multi-dimensional ISN regime. We validate these theoretical predictions in networks with structured excitatory architectures, including spatially organised ring connectivity, heavy-tailed lognormal synaptic weight distributions, and embedded cell assemblies. In each case, Hebbian ISP adapts the inhibitory structure in a manner that not only curtails unstable dynamics, but also preserves the network’s capacity for diverse activity patterns and functional responses. These results support the hypothesis that cortical circuits may operate within a richer, multi-dimensional ISN regime than previously appreciated. Finally, this thesis introduces a diagnostic framework for experimental testing of the multi-dimensional ISN regime. We show that Hebbian ISP gives rise to a family of paradoxical effects: specifically, there exist multiple, detailed stimulation patterns to the inhibitory neurons that lead to paradoxical effects. These patterned paradoxical responses can be derived analytically and revealed empirically via a two-stage perturbation protocol, providing a concrete path toward experimental falsification of the proposed theory.