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

Abstract

Spiking neuronal networks are usually simulated with one of three main schemes: the classical time-driven and event-driven schemes, and the more recent hybrid scheme. All three schemes evolve the state of a neuron through a series of checkpoints: equally spaced in the first scheme and determined neuron-wise by spike events in the latter two. The time-driven and the hybrid scheme determine whether the membrane potential of a neuron crosses a threshold at the end of the time interval between consecutive checkpoints. Threshold crossing can, however, occur within the interval even if this test is negative. Spikes can therefore be missed. The present work offers an alternative geometric point of view on neuronal dynamics, and derives, implements, and benchmarks a method for perfect retrospective spike detection. This method can be applied to neuron models with affine or linear subthreshold dynamics. The idea behind the method is to propagate the threshold with a time-inverted dynamics, testing whether the threshold crosses the neuron state to be evolved, rather than vice versa. Algebraically this translates into a set of inequalities necessary and sufficient for threshold crossing. This test is slower than the imperfect one, but can be optimized in several ways. Comparison confirms earlier results that the imperfect tests rarely miss spikes (less than a fraction 1/108 of missed spikes) in biologically relevant settings.

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

“…The histograms for time step 1 ms contain multiple peaks due to the 1, 000 Hz rhythm imposed by the grid-constrained input spikes. The lag of grid-based NEST is due to the fact that spike times are always rounded up to the nearest grid point, not down (Morrison et al, 2008 ; Krishnan et al, 2017 ). The early spiking of SpiNNaker is likely to be due to the use of fixed-point numerical representations and the separation of the exponential decay of the synaptic inputs from the integration of the membrane equation, as shown for a single input spike in Figure 3 .…”

Computational geometry for modeling neural populations: From visualization to simulation

“…There are interesting parallels between our method and a recently proposed method for determining missing spikes in hybrid time-driven, event-driven spiking neuron simulations [ 42 ]. Here, the authors consider the problem of missing spikes: the possibility that a neuron is below threshold at the end of a simulation step, but has crossed the threshold during the step.…”

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

“…This suggests a time-driven update of neurons ( Figure 1B ). The resulting hybrid simulation scheme for neurons and synapses (Morrison et al, 2005 ; D'Haene et al, 2014 ; Krishnan et al, 2017 ) is nowadays commonly used across many spiking network simulators (for a review, see Brette et al, 2007 ).…”