Genetic algorithmic parameter optimisation of a recurrent spiking neural network model

Neural networks are complex algorithms that loosely model the behaviour of the human brain. They play a significant role in computational neuroscience and artificial intelligence. The next generation of neural network models is based on the spike timing activity of neurons: spiking neural networks (SNNs). However, model parameters in SNNs are difficult to search and optimise. Previous studies using genetic algorithm (GA) optimisation of SNNs were focused mainly on simple, feedforward, or oscillatory networks, but not much work has been done on optimising cortex-like recurrent SNNs. In this work, we investigated the use of GAs to search for optimal parameters in recurrent SNNs to reach targeted neuronal population firing rates, e.g. as in experimental observations. We considered a cortical column based SNN comprising 1000 Izhikevich spiking neurons for computational efficiency and biologically realism. The model parameters explored were the neuronal biased input currents. First, we found for this particular SNN, the optimal parameter values for targeted population averaged firing activities, and the convergence of algorithm by ~100 generations. We then showed that the GA optimal population size was within ~16-20 while the crossover rate that returned the best fitness value was ~0.95. Overall, we have successfully demonstrated the feasibility of implementing GA to optimise model parameters in a recurrent cortical based SNN.Comment: 6 pages, 6 figure

Synchronization of electrically coupled resonate-and-fire neurons

Electrical coupling between neurons is broadly present across brain areas and is typically assumed to synchronize network activity. However, intrinsic properties of the coupled cells can complicate this simple picture. Many cell types with strong electrical coupling have been shown to exhibit resonant properties, and the subthreshold fluctuations arising from resonance are transmitted through electrical synapses in addition to action potentials. Using the theory of weakly coupled oscillators, we explore the effect of both subthreshold and spike-mediated coupling on synchrony in small networks of electrically coupled resonate-and-fire neurons, a hybrid neuron model with linear subthreshold dynamics and discrete post-spike reset. We calculate the phase response curve using an extension of the adjoint method that accounts for the discontinuity in the dynamics. We find that both spikes and resonant subthreshold fluctuations can jointly promote synchronization. The subthreshold contribution is strongest when the voltage exhibits a significant post-spike elevation in voltage, or plateau. Additionally, we show that the geometry of trajectories approaching the spiking threshold causes a "reset-induced shear" effect that can oppose synchrony in the presence of network asymmetry, despite having no effect on the phase-locking of symmetrically coupled pairs

Wild oscillations in a nonlinear neuron model with resets: (II) Mixed-mode oscillations

This work continues the analysis of complex dynamics in a class of bidimensional nonlinear hybrid dynamical systems with resets modeling neuronal voltage dynamics with adaptation and spike emission. We show that these models can generically display a form of mixed-mode oscillations (MMOs), which are trajectories featuring an alternation of small oscillations with spikes or bursts (multiple consecutive spikes). The mechanism by which these are generated relies fundamentally on the hybrid structure of the flow: invariant manifolds of the continuous dynamics govern small oscillations, while discrete resets govern the emission of spikes or bursts, contrasting with classical MMO mechanisms in ordinary differential equations involving more than three dimensions and generally relying on a timescale separation. The decomposition of mechanisms reveals the geometrical origin of MMOs, allowing a relatively simple classification of points on the reset manifold associated to specific numbers of small oscillations. We show that the MMO pattern can be described through the study of orbits of a discrete adaptation map, which is singular as it features discrete discontinuities with unbounded left- and right-derivatives. We study orbits of the map via rotation theory for discontinuous circle maps and elucidate in detail complex behaviors arising in the case where MMOs display at most one small oscillation between each consecutive pair of spikes

Complex dynamics in simplified neuronal models: reproducing Golgi cell electroresponsiveness

Brain neurons exhibit complex electroresponsive properties – including intrinsic subthreshold oscillations and pacemaking, resonance and phase-reset – which are thought to play a critical role in controlling neural network dynamics. Although these properties emerge from detailed representations of molecular-level mechanisms in “realistic” models, they cannot usually be generated by simplified neuronal models (although these may show spike-frequency adaptation and bursting). We report here that this whole set of properties can be generated by the extended generalized leaky integrate-and-fire (E-GLIF) neuron model. E-GLIF derives from the GLIF model family and is therefore mono-compartmental, keeps the limited computational load typical of a linear low-dimensional system, admits analytical solutions and can be tuned through gradient-descent algorithms. Importantly, E-GLIF is designed to maintain a correspondence between model parameters and neuronal membrane mechanisms through a minimum set of equations. In order to test its potential, E-GLIF was used to model a specific neuron showing rich and complex electroresponsiveness, the cerebellar Golgi cell, and was validated against experimental electrophysiological data recorded from Golgi cells in acute cerebellar slices. During simulations, E-GLIF was activated by stimulus patterns, including current steps and synaptic inputs, identical to those used for the experiments. The results demonstrate that E-GLIF can reproduce the whole set of complex neuronal dynamics typical of these neurons – including intensity-frequency curves, spike-frequency adaptation, post-inhibitory rebound bursting, spontaneous subthreshold oscillations, resonance, and phase-reset – providing a new effective tool to investigate brain dynamics in large-scale simulations

Hardware implementation of a spiking neural network for fast synchronization

In this master thesis, we present two different hardware implementations of the Oscillatory Dynamic Link Matcher (ODLM). The ODLM is an algorithm which uses the synchronization in a network of spiking neurons to realize different signal processing tasks. The main objective of this work is to identify the key design choices leading to the efficient implementation of an embedded version of the ODLM. The resulting systems have been tested with image segmentation and image matching tasks. The first system is bit-slice and time-driven. The state of the whole network is updated at regular time intervals. The system uses a bit-slice architecture with a large number of processing elements. Each processing element, or slice, implements one neuron of the network and takes the form of a column on the hardware. The columns are placed side by side and they are locally connected to their 2 neighbors. This local hardware connection scheme makes the system scalable, which means that columns can be easily added to increase the capacity of the system. Each column consists of a weight vector, a synapse model unit and a membrane model unit. The system can implement any network topology, making it very flexible. The function governing the time evolution of the neurons' membrane potential is approximated by a piece-wise linear function to reduce the amount of logical resources required. With this system, a fully-connected network of 648 neurons can be implemented on a Virtex-5 Xilinx XC5VSX5OT FPGA clocked at 100 MHz. The system is designed to process simultaneous spikes in parallel, reaching a maximum processing speed of 6 Mspikes/s. It can segment a 23×23 pixel image in 2 seconds and match two pre-segmented 90×30 pixel images in 550 ms. The second system is event-driven. A single processing element sequentially processes the spikes. This processing element is a 5-stage pipeline which can process an average of 1 synapse per 7 clock cycles. The synaptic weights are not stored in memory in this system, they are computed on-the-fly as spikes are processed. The topology of the network is also resolved during operation, and the system supports various regular topologies like 8-neighbor and fully-connected. The membrane potential time evolution function is computed with high precision using a look-up table. On the Virtex-5 FPGA, a network of 65 536 neurons can be implemented and a 406×158 pixel image can be segmented in 200 ms. The FPGA can be clocked at 100 MHz. Most of the design choices made for the second system are well adapted to the hardware implementation of the ODLM. In the original ODLM, the weight values do not change over time and usually depend on a single variable. It is therefore beneficial to compute the weights on the fly rather than saving them in a huge memory bank. The event-driven approach is a very efficient strategy. It reduces the amount of computations required to run the network and the amount of data moved in and out of memory. Finally, the precise computation of the neurons' membrane potential increases the convergence speed of the network

Stochastic modeling and control of neural and small length scale dynamical systems

Recent advancements in experimental and computational techniques have created tremendous opportunities in the study of fundamental questions of science and engineering by taking the approach of stochastic modeling and control of dynamical systems. Examples include but are not limited to neural coding and emergence of behaviors in biological networks. Integrating optimal control strategies with stochastic dynamical models has ignited the development of new technologies in many emerging applications. In this direction, particular examples are brain-machine interfaces (BMIs), and systems to manipulate submicroscopic objects. The focus of this dissertation is to advance these technologies by developing optimal control strategies under various feedback scenarios and system uncertainties. Brain-machine interfaces (BMIs) establish direct communications between living brain tissue and external devices such as an artificial arm. By sensing and interpreting neuronal activity to actuate an external device, BMI-based neuroprostheses hold great promise in rehabilitating motor disabled subjects such as amputees. However, lack of the incorporation of sensory feedback, such as proprioception and tactile information, from the artificial arm back to the brain has greatly limited the widespread clinical deployment of these neuroprosthetic systems in rehabilitation. In the first part of the dissertation, we develop a systematic control-theoretic approach for a system-level rigorous analysis of BMIs under various feedback scenarios. The approach involves quantitative and qualitative analysis of single neuron and network models to the design of missing sensory feedback pathways in BMIs using optimal feedback control theory. As a part of our results, we show that the recovery of the natural performance of motor tasks in BMIs can be achieved by designing artificial sensory feedbacks in the proposed optimal control framework. The second part of the dissertation deals with developing stochastic optimal control strategies using limited feedback information for applications in neural and small length scale dynamical systems. The stochastic nature of these systems coupled with the limited feedback information has greatly restricted the direct applicability of existing control strategies in stabilizing these systems. Moreover, it has recently been recognized that the development of advanced control algorithms is essential to facilitate applications in these systems. We propose a novel broadcast stochastic optimal control strategy in a receding horizon framework to overcome existing limitations of traditional control designs. We apply this strategy to stabilize multi-agent systems and Brownian ensembles. As a part of our results, we show the optimal trapping of an ensemble of particles driven by Brownian motion in a minimum trapping region using the proposed framework