Chaos and reliability in balanced spiking networks with temporal drive

Abstract

Biological information processing is often carried out by complex networks of interconnected dynamical units. A basic question about such networks is that of reliability: if the same signal is presented many times with the network in different initial states, will the system entrain to the signal in a repeatable way? Reliability is of particular interest in neuroscience, where large, complex networks of excitatory and inhibitory cells are ubiquitous. These networks are known to autonomously produce strongly chaotic dynamics — an obvious threat to reliability. Here, we show that such chaos persists in the presence of weak and strong stimuli, but that even in the presence of chaos, intermittent periods of highly reliable spiking often coexist with unreliable activity. We elucidate the local dynamical mechanisms involved in this intermittent reliability, and investigate the relationship between this phenomenon and certain time-dependent attractors arising from the dynamics. A conclusion is that chaotic dynamics do not have to be an obstacle to precise spike responses, a fact with implications for signal coding in large networks.

Encoding in Balanced Networks: Revisiting Spike Patterns and Chaos in Stimulus-Driven Systems

“…We find that, despite chaos, the network’s spike patterns encode temporal features of stimuli with sufficient precision so that the responses to close-by stimuli can be accurately discriminated. We relate this coding precision to previous work grounded in the mathematical theory of dynamical systems, which shows that—at the level of multi-neuron spike patterns—chaotic networks do not produce as much variability as one might guess at first glance [14, 15]. This is because in such networks, the trial-to-trial variability of spike trains evoked by time-dependent stimuli leads to the formation of low-dimensional chaotic attractors.…”

“…We study a recurrent network of excitatory and inhibitory neurons with random, sparse coupling, as in [2, 3, 6, 14]. Every neuron i = 1, …, N in our network receives an external input signal I i ( t ), which we describe in more detail below.…”

“…neuron can either have all inhibitory or all excitatory outgoing synapses). We set N I = 0.2 N , N E = 0.8 N and couple the network according to the random and sparse, balanced state architecture [2, 3, 6, 14, 37] following a standard Erdös-Rényi scheme with mean in-degree K ≪ N . This means a synaptic connection from a neuron j to a neuron i is drawn randomly and independently with probability K / N E,I where E or I denotes the type of neuron j .…”

“…The dynamics of each neuron –representing an axis on the torus– is given by where F ( θ i ) = 1 + cos(2 πθ i ), Z ( θ i ) = 1 − cos(2 πθ i ) (the canonical phase response curve of a Type I neuron [39]), and g ( θ j ) is a sharp “bump” function, nonzero only near the spiking phase θ j = 1 ∼ 0. As in [14, 15], we set with b = 1/20 and d = 35/32. This phase coupling function is chosen to model the rapid rise and fall of post-synaptic currents, while being differentiable everywhere so that the vector field defined by Eq (2) remains smooth.…”

“…Indeed, chaos may represent a mechanism by which other sources of variability are amplified. Importantly, we find that chaos in driven networks produce a type of intermittent variability, with some spiking “events” predictably repeated across trials [14, 15] (cf. [30–32]).…”