Poisson balanced spiking networks

Camille E. Rullán Buxó and Jonathan W. Pillow
PLOS Computational Biology 16, 1-27 (2020).

A central idea in neuroscience is that populations of neurons work together to efficiently perform computations, although just how they do that remains unclear. Boerlin et al (2013) proposed a powerful framework for embedding linear dynamical systems into populations of spiking neurons, which they called balanced spiking networks (BSNs). Their approach starts from the principle that neurons greedily fire spikes to reduce error in the network output. Here we focus on a key limitation of this framework, which is that the network may become unbalanced in the presence of physiologically plausible communication delays. To overcome this shortcoming, propose two different extensions of the BSN framework that rely on probabilistic spiking. In our first model, we replace deterministic spiking of the original BSN with a Poisson spiking rule. In the second, we re-formulate the BSN objective so that Poisson spiking emerges as a way to reduce the expected network error. Our work brings the BSN framework closer to biological realism by increasing the stability and, most importantly, allowing communication delays between neurons without sacrificing accuracy. Furthermore, both probabilistic approaches reproduce key experimentally observed spiking behaviors of neural populations.

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