Perfect Detection of Spikes in the Linear Sub-threshold Dynamics of Point Neurons

Event-Based Update of Synapses in Voltage-Based Learning Rules

Due to the point-like nature of neuronal spiking, efficient neural network simulators often employ event-based simulation schemes for synapses. Yet many types of synaptic plasticity rely on the membrane potential of the postsynaptic cell as a third factor in addition to pre- and postsynaptic spike times. In some learning rules membrane potentials not only influence synaptic weight changes at the time points of spike events but in a continuous manner. In these cases, synapses therefore require information on the full time course of membrane potentials to update their strength which a priori suggests a continuous update in a time-driven manner. The latter hinders scaling of simulations to realistic cortical network sizes and relevant time scales for learning. Here, we derive two efficient algorithms for archiving postsynaptic membrane potentials, both compatible with modern simulation engines based on event-based synapse updates. We theoretically contrast the two algorithms with a time-driven synapse update scheme to analyze advantages in terms of memory and computations. We further present a reference implementation in the spiking neural network simulator NEST for two prototypical voltage-based plasticity rules: the Clopath rule and the Urbanczik-Senn rule. For both rules, the two event-based algorithms significantly outperform the time-driven scheme. Depending on the amount of data to be stored for plasticity, which heavily differs between the rules, a strong performance increase can be achieved by compressing or sampling of information on membrane potentials. Our results on computational efficiency related to archiving of information provide guidelines for the design of learning rules in order to make them practically usable in large-scale networks.

Computational geometry for modeling neural populations: From visualization to simulation

The importance of a mesoscopic description level of the brain has now been well established. Rate based models are widely used, but have limitations. Recently, several extremely efficient population-level methods have been proposed that go beyond the characterization of a population in terms of a single variable. Here, we present a method for simulating neural populations based on two dimensional (2D) point spiking neuron models that defines the state of the population in terms of a density function over the neural state space. Our method differs in that we do not make the diffusion approximation, nor do we reduce the state space to a single dimension (1D). We do not hard code the neural model, but read in a grid describing its state space in the relevant simulation region. Novel models can be studied without even recompiling the code. The method is highly modular: variations of the deterministic neural dynamics and the stochastic process can be investigated independently. Currently, there is a trend to reduce complex high dimensional neuron models to 2D ones as they offer a rich dynamical repertoire that is not available in 1D, such as limit cycles. We will demonstrate that our method is ideally suited to investigate noise in such systems, replicating results obtained in the diffusion limit and generalizing them to a regime of large jumps. The joint probability density function is much more informative than 1D marginals, and we will argue that the study of 2D systems subject to noise is important complementary to 1D systems.

Performance Comparison of the Digital Neuromorphic Hardware SpiNNaker and the Neural Network Simulation Software NEST for a Full-Scale Cortical Microcircuit Model

The digital neuromorphic hardware SpiNNaker has been developed with the aim of enabling large-scale neural network simulations in real time and with low power consumption. Real-time performance is achieved with 1 ms integration time steps, and thus applies to neural networks for which faster time scales of the dynamics can be neglected. By slowing down the simulation, shorter integration time steps and hence faster time scales, which are often biologically relevant, can be incorporated. We here describe the first full-scale simulations of a cortical microcircuit with biological time scales on SpiNNaker. Since about half the synapses onto the neurons arise within the microcircuit, larger cortical circuits have only moderately more synapses per neuron. Therefore, the full-scale microcircuit paves the way for simulating cortical circuits of arbitrary size. With approximately 80, 000 neurons and 0.3 billion synapses, this model is the largest simulated on SpiNNaker to date. The scale-up is enabled by recent developments in the SpiNNaker software stack that allow simulations to be spread across multiple boards. Comparison with simulations using the NEST software on a high-performance cluster shows that both simulators can reach a similar accuracy, despite the fixed-point arithmetic of SpiNNaker, demonstrating the usability of SpiNNaker for computational neuroscience applications with biological time scales and large network size. The runtime and power consumption are also assessed for both simulators on the example of the cortical microcircuit model. To obtain an accuracy similar to that of NEST with 0.1 ms time steps, SpiNNaker requires a slowdown factor of around 20 compared to real time. The runtime for NEST saturates around 3 times real time using hybrid parallelization with MPI and multi-threading. However, achieving this runtime comes at the cost of increased power and energy consumption. The lowest total energy consumption for NEST is reached at around 144 parallel threads and 4.6 times slowdown. At this setting, NEST and SpiNNaker have a comparable energy consumption per synaptic event. Our results widen the application domain of SpiNNaker and help guide its development, showing that further optimizations such as synapse-centric network representation are necessary to enable real-time simulation of large biological neural networks.