Dynamic attractors

Networks of interconnected neurons display diverse patterns of collective spiking activity. Relating this collective activity to the network's connectivity structure is a key goal of computational neuroscience. We approach this question for clustered networks, which can form via biologically realistic learning rules and allow for the re-activation of previously evoked patterns. Previous studies of clustered networks have focused on metastabilty between fixed points corresponding to individual clusters, leaving open the question of whether clustered spiking networks can display more rich dyna

…revealed a mechanism governed by dynamic attractors, pivotal in sustaining neuronal activity. This mechanism, shaped by time-varying inputs reflecting temporal predictions, is instrumenta

…mostly been implemented through static attractors. Thus, it remains unclear if and how RNNs can encode memories in the relative phase of oscillations. Here we show that such phase-dependent coding can arise through the training of RNNs on memory tasks. We characterize how the emerg

Threshold-linear networks (TLNs) display a wide variety of nonlinear dynamics including multistability, limit cycles, quasiperiodic attractors, and chaos. Over the past few years, we have developed a detailed mathematical theory relating stable and unstable fixed points of TLNs to graph-theoretic properties of the underlying network. In particular, we have discovered that a special type of unstable fixed points, corresponding to "core motifs," are predictive of dynamic attractors. Recently, we have used these ideas to classify dynamic attractors in a two-parameter family of inhibition-dominate

…serves to shape and stabilize neural dynamics. The neurons in such networks exhibit intricate patterns of connectivity whose structure controls the allowed patterns of neural activity. In this work, we examine inhibitory threshold-linear networks whose dynamics are constrained by an underlying directed graph. We develop a set of parameter-independent graph rules that enable us to predict features of the dynamics, such as emergent sequences and dynamic attractors, from properties of the graph. These rules provide a di