Self Organisation and Hierarchical Concept Representation in Networks of Spiking Neurons

The aim of this work is to introduce modular processing mechanisms for cortical functions implemented in networks of spiking neurons. Neural maps are a feature of cortical processing found to be generic throughout sensory cortical areas, and self-organisation to the fundamental properties of input spike trains has been shown to be an important property of cortical organisation. Additionally, oscillatory behaviour, temporal coding of information, and learning through spike timing dependent plasticity are all frequently observed in the cortex. The traditional self-organising map (SOM) algorithm attempts to capture the computational properties of this cortical self-organisation in a neural network. As such, a cognitive module for a spiking SOM using oscillations, phasic coding and STDP has been implemented. This model is capable of mapping to distributions of input data in a manner consistent with the traditional SOM algorithm, and of categorising generic input data sets. Higher-level cortical processing areas appear to feature a hierarchical category structure that is founded on a feature-based object representation. The spiking SOM model is therefore extended to facilitate input patterns in the form of sets of binary feature-object relations, such as those seen in the field of formal concept analysis. It is demonstrated that this extended model is capable of learning to represent the hierarchical conceptual structure of an input data set using the existing learning scheme. Furthermore, manipulations of network parameters allow the level of hierarchy used for either learning or recall to be adjusted, and the network is capable of learning comparable representations when trained with incomplete input patterns. Together these two modules provide related approaches to the generation of both topographic mapping and hierarchical representation of input spaces that can be potentially combined and used as the basis for advanced spiking neuron models of the learning of complex representations

25th annual computational neuroscience meeting: CNS-2016

The same neuron may play different functional roles in the neural circuits to which it belongs. For example, neurons in the Tritonia pedal ganglia may participate in variable phases of the swim motor rhythms [1]. While such neuronal functional variability is likely to play a major role the delivery of the functionality of neural systems, it is difficult to study it in most nervous systems. We work on the pyloric rhythm network of the crustacean stomatogastric ganglion (STG) [2]. Typically network models of the STG treat neurons of the same functional type as a single model neuron (e.g. PD neurons), assuming the same conductance parameters for these neurons and implying their synchronous firing [3, 4]. However, simultaneous recording of PD neurons shows differences between the timings of spikes of these neurons. This may indicate functional variability of these neurons. Here we modelled separately the two PD neurons of the STG in a multi-neuron model of the pyloric network. Our neuron models comply with known correlations between conductance parameters of ionic currents. Our results reproduce the experimental finding of increasing spike time distance between spikes originating from the two model PD neurons during their synchronised burst phase. The PD neuron with the larger calcium conductance generates its spikes before the other PD neuron. Larger potassium conductance values in the follower neuron imply longer delays between spikes, see Fig. 17.Neuromodulators change the conductance parameters of neurons and maintain the ratios of these parameters [5]. Our results show that such changes may shift the individual contribution of two PD neurons to the PD-phase of the pyloric rhythm altering their functionality within this rhythm. Our work paves the way towards an accessible experimental and computational framework for the analysis of the mechanisms and impact of functional variability of neurons within the neural circuits to which they belong

Dimensions of control for subthreshold oscillations and spontaneous firing in dopamine neurons.

Dopaminergic neurons (DAs) of the rodent substantia nigra pars compacta (SNc) display varied electrophysiological properties in vitro. Despite this, projection patterns and functional inputs from DAs to other structures are conserved, so in vivo delivery of consistent, well-timed dopamine modulation to downstream circuits must be coordinated. Here we show robust coordination by linear parameter controllers, discovered through powerful mathematical analyses of data and models, and from which consistent control of DA subthreshold oscillations (STOs) and spontaneous firing emerges. These units of control represent coordinated intracellular variables, sufficient to regulate complex cellular properties with radical simplicity. Using an evolutionary algorithm and dimensionality reduction, we discovered metaparameters, which when regressed against STO features, revealed a 2-dimensional control plane for the neuron's 22-dimensional parameter space that fully maps the natural range of DA subthreshold electrophysiology. This plane provided a basis for spiking currents to reproduce a large range of the naturally occurring spontaneous firing characteristics of SNc DAs. From it we easily produced a unique population of models, derived using unbiased parameter search, that show good generalization to channel blockade and compensatory intracellular mechanisms. From this population of models, we then discovered low-dimensional controllers for regulating spontaneous firing properties, and gain insight into how currents active in different voltage regimes interact to produce the emergent activity of SNc DAs. Our methods therefore reveal simple regulators of neuronal function lurking in the complexity of combined ion channel dynamics

Novel and flexible parameter estimation methods for data-consistent inversion in mechanistic modelling

Predictions for physical systems often rely upon knowledge acquired from ensembles of entities, e.g. ensembles of cells in biological sciences. For qualitative and quantitative analysis, these ensembles are simulated with parametric families of mechanistic models (MMs). Two classes of methodologies, based on Bayesian inference and population of models, currently prevail in parameter estimation for physical systems. However, in Bayesian analysis, uninformative priors for MM parameters introduce undesirable bias. Here, we propose how to infer parameters within the framework of stochastic inverse problems (SIPs), also termed data-consistent inversion, wherein the prior targets only uncertainties that arise due to MM non-invertibility. To demonstrate, we introduce new methods to solve SIPs based on rejection sampling, Markov chain Monte Carlo, and generative adversarial networks (GANs). In addition, to overcome limitations of SIPs, we reformulate SIPs based on constrained optimization and present a novel GAN to solve the constrained optimization problem