Poisson balanced spiking networks

An important problem in computational neuroscience is to understand how networks of spiking neurons can carry out various computations underlying behavior. Balanced spiking networks (BSNs) provide a powerful framework for implementing arbitrary linear dynamical systems in networks of integrate-and-fire neurons. However, the classic BSN model requires near-instantaneous transmission of spikes between neurons, which is biologically implausible. Introducing realistic synaptic delays leads to an pathological regime known as “ping-ponging”, in which different populations spike maximally in alternating time bins, causing network output to overshoot the target solution. Here we document this phenomenon and provide a novel solution: we show that a network can have realistic synaptic delays while maintaining accuracy and stability if neurons are endowed with conditionally Poisson firing. Formally, we propose two alternate formulations of Poisson balanced spiking networks: (1) a “local” framework, which replaces the hard integrate-and-fire spiking rule within each neuron by a “soft” threshold function, such that firing probability grows as a smooth nonlinear function of membrane potential; and (2) a “population” framework, which reformulates the BSN objective function in terms of expected spike counts over the entire population. We show that both approaches offer improved robustness, allowing for accurate implementation of network dynamics with realistic synaptic delays between neurons. Both Poisson frameworks preserve the coding accuracy and robustness to neuron loss of the original model and, moreover, produce positive correlations between similarly tuned neurons, a feature of real neural populations that is not found in the deterministic BSN. This work unifies balanced spiking networks with Poisson generalized linear models and suggests several promising avenues for future research.Author summary: 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.