Addressing the speed-accuracy simulation trade-off for adaptive spiking
  neurons
Luke Taylor Andrew J King Nicol S Harper
The adaptive leaky integrate-and-fire (ALIF) model is fundamental within
computational neuroscience and has been instrumental in studying our brains
$\textit{in silico}$. Due to the sequential nature of simulating these neural
models, a commonly faced issue is the speed-accuracy trade-off: either
accurately simulate a neuron using a small discretisation time-step (DT), which
is slow, or more quickly simulate a neuron using a larger DT and incur a loss
in simulation accuracy. Here we provide a solution to this dilemma, by
algorithmically reinterpreting the ALIF model, reducing the sequential
simulation complexity and permitting a more efficient parallelisation on GPUs.
We computationally validate our implementation to obtain over a $50\times$
training speedup using small DTs on synthetic benchmarks. We also obtained a
comparable performance to the standard ALIF implementation on different
supervised classification tasks - yet in a fraction of the training time.
Lastly, we showcase how our model makes it possible to quickly and accurately
fit real electrophysiological recordings of cortical neurons, where very fine
sub-millisecond DTs are crucial for capturing exact spike timing.