Structured stabilization in recurrent neural circuits through inhibitory synaptic plasticity

Inhibitory interneurons play a dual role in recurrently connected biological circuits: they regulate global neural activity to prevent runaway excitation, and contribute to complex neural computations. While the first role can be achieved through unstructured connections tuned for homeostatic rate stabilization, computational tasks often require structured excitatory-inhibitory (E/I) connectivity. Here, we consider a broad class of pairwise inhibitory spike-timing dependent plasticity (iSTDP) rules, demonstrating how inhibitory synapses can self-organize to both stabilize excitation and generate functionally relevant connectivity structures — a process we call “structured stabilization”. We show that in both E/I circuit motifs and large spiking recurrent neural networks the choice of iSTDP rule can lead to either mutually connected E/I pairs, or to lateral inhibition, where an inhibitory neuron connects to an excitatory neuron that does not directly connect back to it. In a one-dimensional ring network, if two inhibitory populations follow these distinct forms of iSTDP, the effective connectivity within the excitatory population self-organizes into a Mexican-hat-like profile with excitatory influence in the center and inhibitory influence away from the center. This leads to emergent dynamical properties such as surround suppression and modular spontaneous activity. Our theoretical work introduces a family of rules that retains the broad applicability and simplicity of spike-timing-based plasticity, while promoting structured, self-organized stabilization. These findings highlight the rich interplay between iSTDP rules, circuit structure, and neuronal dynamics, offering a framework for understanding how inhibitory plasticity shapes network function.