Topic: limit cycles

Networks of interconnected neurons display diverse patterns of activity. Relating these patterns to the structure of the network is a central goal of theoretical neuroscience. Classic neural field and rate models have been powerful tools for this purpose due to their analytical tractability. Here, we show that the recently-developed combinatorial threshold-linear network (CTLN) model is a mean-field theory for excitatory-inhibitory Hawkes networks, with clustered connectivity, in an inhibition-stabilized regime. This mapping allows us to leverage powerful analytical results for CTLN networks

Experimental evidence suggests that the brain is able to encode memories in the phase of ongoing low-frequency oscillations. Recently, trainable recurrent neural networks (RNNs) have emerged as promising models of how neural circuits process information. However, short-term memory maintenance in these networks has 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