Mean-field approximations with adaptive coupling for networks with spike-timing-dependent plasticity [article]

Benoit Duchet, Christian Bick, Aine Byrne
2022 bioRxiv   pre-print
Understanding the effect of spike-timing-dependent plasticity (STDP) is key to elucidate how neural networks change over long timescales and to design interventions aimed at modulating such networks in neurological disorders. However, progress is restricted by the significant computational cost associated with simulating neural network models with STDP, and by the lack of low-dimensional description that could provide analytical insights. To approximate STDP in phase oscillator networks,
more » ... phase-difference-dependent plasticity (PDDP) rules have been developed, which prescribe synaptic changes based on phase differences of neuron pairs rather than differences in spike timing. Here we construct mean-field approximations for phase oscillator networks with STDP to describe the dynamics of large networks of adaptive oscillators. We first show that single-harmonic PDDP rules can approximate a simple form of symmetric STDP, while multi-harmonic rules are required to accurately approximate causal STDP. We then derive exact expressions for the evolution of the average PDDP coupling weight in terms of network synchrony. For adaptive networks of Kuramoto oscillators that form clusters, we formulate a low-dimensional description based on mean field dynamics and average coupling weight. Finally, we show that such a two-cluster mean-field model can be fitted to provide a low-dimensional approximation of a full adaptive network with symmetric STDP. Our framework represents a step towards a low-dimensional description of adaptive networks with STDP, and could for example inform the development of new therapies aimed at maximizing the long-lasting effects of brain stimulation.
doi:10.1101/2022.07.02.498537 fatcat:foivfo5sojc23ij2pauaqmlsgy