A non-spiking neuron model with dynamic leak to avoid instability in recurrent networks

Abstract

Elements of recurrent excitatory synaptic loops are present within sensorimotor control loops in the brain. Such positive feedback loops can cause self-amplification, which is potentially dangerous for the brain (as in epilepsy) or which may cause disruptive effects on of the information passed within the neuronal circuitry. Here we introduce a simplified nonspiking neuron model, whose output accurately reflects summated synaptic inputs, with which we performed simulations of highly connected networks composed of excitatory and inhibitory neurons in equal proportions. The neuron model could be optionally equipped with a dynamic leak, i.e. dynamic short-circuit to the resting membrane potential, equivalent to a membrane time constant. Synaptic weights were randomly assigned across the network according to a range of different types and ranges of distribution. Networks were provided with random and semi-structured sensory inputs and we studied the spread of activity through the network. We find that in neurons without dynamic leak, recurrent networks produced high frequency noise components that were not present in the input signal, across all synaptic weight distributions. The addition of dynamic leak consistently removed such high frequency noise. Conduction delays between neurons, when explicitly included, tended to worsen the high frequency noise, which was rescued by dynamic leak also in this case. Our findings suggest that neuronal dynamic short circuit of voltage deviations towards the resting potential serve the beneficial function of protecting recurrent neuronal circuitry from inducing itself into spurious high frequency signal generation, thereby permitting the brain to utilize this architectural circuitry component.

A Model for Self-Organization of Sensorimotor Function: The Spinal Monosynaptic Loop

“…To evaluate our hypothesis of self-organization of sensorimotor function based on musculoskeletal mechanics and behavioral experience, we needed an artificial neuronal model suited for repeated simulations of arbitrary neural network (NN) connectivity among a variety of afferent and interneuron types. To this end, we used a linear summation neuron model with dynamic leak (Rongala et al, 2021) together with learning rules similar to previous simulations of cuneate neurons (Rongala et al, 2018), i.e. Hebbian-inspired calcium covariance learning rule.…”

“…The output of most CNS neurons is the action potential. However, in our previously published (Rongala et al, 2021) neuron model spiking is omitted, and each signal between neurons is instead a time-continuous voltage signal (A), which can be thought of as representing the combined activation of a population of asynchronously firing neurons of a given type. This simplification is valid because the spike output of the neuron can be considered a somewhat noisy probability density function of its membrane potential (Spanne et al, 2014a).…”

“…The neuronal model used in this article (Rongala et al, 2021) provides a simplified neuronal calcium dynamics model with a continuous output signal rather than spikes. Oja's learning rule (Oja, 1982) that we adapted for our model generates synaptic potentiation or depression according to the relative timing of calcium transients in the pre-and post-synaptic compartments of the synapse.…”

“…Indeed, skeletal linkages with higher number of degrees of freedom can become highly difficult to control, and an attempt to replicate them would risk consuming most of the energy on solving the high-dimensional control problem rather than the more fundamental issues we initially aimed to address. Our musculoskeletal plant is controlled by a spinal neuronal circuitry using a linear summation neuron model (LSM) (Rongala et al, 2021) which is a simplified version of a previously published implementation (Rongala et al, 2018) together with synaptic plasticity based on the Hebbian-inspired calcium co-variance learning rule (Sejnowski, 1977). In this paper, we describe how random twitching activation patterns, such as generated in the fetal spinal cord, could give rise to naturally occurring connectivity patterns of spindle Ia afferents to MNs, one of the first circuitry formation events during fetal development (Chen et al, 2003).…”

The BCM rule allows a spinal cord model to learn rhythmic movements

“…The neuron model was similar to a previous non-spiking model [21,22]. Each neuron had an output activity, which was a time continuous voltage, called firing rate, and was modeled as follows.…”