Recurrent biological neural networks: the weak and noisy limit

Emergence in the central nervous system

"Emergence" is an idea that has received much attention in consciousness literature, but it is difficult to find characterizations of that concept which are both specific and useful. I will precisely define and characterize a type of epistemic ("weak") emergence and show that it is a property of some neural circuits throughout the CNS, on micro-, meso- and macroscopic levels. I will argue that possession of this property can result in profoundly altered neural dynamics on multiple levels in cortex and other systems. I will first describe emergent neural entities (ENEs) abstractly. I will then show how ENEs function specifically and concretely, and demonstrate some implications of this type of emergence for the CNS.

Closed-Form Treatment of the Interactions between Neuronal Activity and Timing-Dependent Plasticity in Networks of Linear Neurons

Network activity and network connectivity mutually influence each other. Especially for fast processes, like spike-timing-dependent plasticity (STDP), which depends on the interaction of few (two) signals, the question arises how these interactions are continuously altering the behavior and structure of the network. To address this question a time-continuous treatment of plasticity is required. However, this is - even in simple recurrent network structures - currently not possible. Thus, here we develop for a linear differential Hebbian learning system a method by which we can analytically investigate the dynamics and stability of the connections in recurrent networks. We use noisy periodic external input signals, which through the recurrent connections lead to complex actual ongoing inputs and observe that large stable ranges emerge in these networks without boundaries or weight-normalization. Somewhat counter-intuitively, we find that about 40% of these cases are obtained with a long-term potentiation-dominated STDP curve. Noise can reduce stability in some cases, but generally this does not occur. Instead stable domains are often enlarged. This study is a first step toward a better understanding of the ongoing interactions between activity and plasticity in recurrent networks using STDP. The results suggest that stability of (sub-)networks should generically be present also in larger structures.

Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks IV: structuring synaptic pathways among recurrent connections

In neuronal networks, the changes of synaptic strength (or weight) performed by spike-timing-dependent plasticity (STDP) are hypothesized to give rise to functional network structure. This article investigates how this phenomenon occurs for the excitatory recurrent connections of a network with fixed input weights that is stimulated by external spike trains. We develop a theoretical framework based on the Poisson neuron model to analyze the interplay between the neuronal activity (firing rates and the spike-time correlations) and the learning dynamics, when the network is stimulated by correlated pools of homogeneous Poisson spike trains. STDP can lead to both a stabilization of all the neuron firing rates (homeostatic equilibrium) and a robust weight specialization. The pattern of specialization for the recurrent weights is determined by a relationship between the input firing-rate and correlation structures, the network topology, the STDP parameters and the synaptic response properties. We find conditions for feed-forward pathways or areas with strengthened self-feedback to emerge in an initially homogeneous recurrent network.

An implementation of reinforcement learning based on spike timing dependent plasticity

An explanatory model is developed to show how synaptic learning mechanisms modeled through spike-timing dependent plasticity (STDP) can result in long-term adaptations consistent with reinforcement learning models. In particular, the reinforcement learning model known as temporal difference (TD) learning has been used to model neuronal behavior in the orbitofrontal cortex (OFC) and ventral tegmental area (VTA) of macaque monkey during reinforcement learning. While some research has observed, empirically, a connection between STDP and TD, there has not been an explanatory model directly connecting TD to STDP. Through analysis of the learning dynamics that results from a general form of a STDP learning rule, the connection between STDP and TD is explained. We further demonstrate that a STDP learning rule drives the spike probability of a reward predicting neuronal population to a stable equilibrium. The equilibrium solution has an increasing slope where the steepness of the slope predicts the probability of the reward, similar to the results from electrophysiological recordings suggesting a different slope that predicts the value of the anticipated reward of Montague and Berns [Neuron 36(2):265-284, 2002]. This connection begins to shed light into more recent data gathered from VTA and OFC which are not well modeled by TD. We suggest that STDP provides the underlying mechanism for explaining reinforcement learning and other higher level perceptual and cognitive function.

Design principles of sensory processing in cerebellum-like structures. Early stage processing of electrosensory and auditory objects

Cerebellum-like structures are compared for two sensory systems: electrosensory and auditory. The electrosensory lateral line lobe of mormyrid electric fish is reviewed and the neural representation of electrosensory objects in this structure is modeled and discussed. The dorsal cochlear nucleus in the auditory brainstem of mammals is reviewed and new data are presented that characterize the responses of neurons in this structure in the mouse. Similarities between the electrosensory and auditory cerebellum-like structures are shown, in particular adaptive processes that may reduce responses to predictable stimuli. We suggest that the differences in the types of sensory objects may drive the differences in the anatomical and physiological characteristics of these two cerebellum-like structures.

Simple spontaneously active Hebbian learning model: homeostasis of activity and connectivity, and consequences for learning and epileptogenesis

A spontaneously active neural system that is capable of continual learning should also be capable of homeostasis of both firing rate and connectivity. Experimental evidence suggests that both types of homeostasis exist, and that connectivity is maintained at a state that is optimal for information transmission and storage. This state is referred to as the critical state. We present a simple stochastic computational Hebbian learning model that incorporates both firing rate and critical homeostasis, and we explore its stability and connectivity properties. We also examine the behavior of our model with a simulated seizure and with simulated acute deafferentation. We argue that a neural system that is more highly connected than the critical state (i.e., one that is "supercritical") is epileptogenic. Based on our simulations, we predict that the postseizural and postdeafferentation states should be supercritical and epileptogenic. Furthermore, interventions that boost spontaneous activity should be protective against epileptogenesis.

Stability of complex spike timing-dependent plasticity in cerebellar learning

Dynamics of spike-timing dependent synaptic plasticity are analyzed for excitatory and inhibitory synapses onto cerebellar Purkinje cells. The purpose of this study is to place theoretical constraints on candidate synaptic learning rules that determine the changes in synaptic efficacy due to pairing complex spikes with presynaptic spikes in parallel fibers and inhibitory interneurons. Constraints are derived for the timing between complex spikes and presynaptic spikes, constraints that result from the stability of the learning dynamics of the learning rule. Potential instabilities in the parallel fiber synaptic learning rule are found to be stabilized by synaptic plasticity at inhibitory synapses if the inhibitory learning rules are stable, and conditions for stability of inhibitory plasticity are given. Combining excitatory with inhibitory plasticity provides a mechanism for minimizing the overall synaptic input. Stable learning rules are shown to be able to sculpt simple-spike patterns by regulating the excitability of neurons in the inferior olive that give rise to climbing fibers.