Stability and Wandering of Bumps in Neural Fields with Interneuron Subtypes

Abstract: The maintenance of continuous variable information in working memory is thought to rely on persistent patterns of cortical activity. In delayed-estimation tasks, neural activity can form localized activity peaks, or ``bumps,'' whose positions track the remembered variable. Such activity is well described by continuous-attractor neural field models, but most existing models collapse cortical inhibition into a single homogeneous population. Here, we introduce a stochastic neural field model with distinct excitatory, parvalbumin-expressing (PV), and somatostatin-expressing (SST) populations to examine how inhibitory subtype structure shapes persistent activity. Using a Heaviside firing-rate approximation, we derive stationary bump solutions and reduce their linear stability to separate shifting and scaling modes. We show that population thresholds and inhibitory timescales determine both bump stability and the mechanism by which stability is lost, while inhibitory connection strengths and spatial scales substantially reshape the stable parameter region. In particular, broader SST connectivity promotes stable bump states. Finally, we derive an effective diffusion coefficient for noise-driven bump wandering and show that increasing the SST spatial footprint reduces the rate of memory diffusion. Together, these results demonstrate how inhibitory subtype structure can shape both the deterministic stability and stochastic precision of continuous-attractor memories.