sparx.spiketrains

Statistics of and distances between spike trains, for comparing networks that cannot match spike for spike.

Spikes are [steps, neurons] arrays of 0 and 1 (or booleans) at step dt ms. These read a finished run (a sparx.graph.simulate record, a reference simulator’s output) and have no gradient. The module imports NumPy alone, so the fixture tools (tools/make_brunel_fixtures.py, tools/make_brian2_benchmarks.py) load this file in a NEST or Brian2 environment without JAX or sparx, and the statistics they record for the reference are the code the tests apply to sparx.

Van Rossum’s distance (sparx.losses.van_rossum) also compares spike trains. It lives in sparx.losses because it is written in JAX to train a network by its gradient, as sparx.objectives.ActivityFitObjective does; here it would make the tools above load JAX. The split is by use: a differentiable training target is a loss, a measurement of a finished run is here.

Contents

Name
coincidence_factor	Each neuron’s coincidence factor Γ, how well its spikes in spikes predict those in reference, both [steps, neurons] at step dt ms, with a precision of window ms.
cv_isi	The coefficient of variation of each neuron’s interspike intervals, for neurons with at least minimum intervals; 1 for a Poisson process, 0 for a clock.
population_fano	The Fano factor of the population’s spike count in windows of window ms.
rates_hz	Each neuron’s mean rate in Hz, over a run of dt ms steps.
spike_steps	Each neuron’s spike steps.
victor_purpura	Victor and Purpura’s (J. Neurophysiol. 1996) distance between two spike trains (times in ms).

coincidence_factor

def coincidence_factor(spikes: np.ndarray, reference: np.ndarray, dt: float, window: float) -> np.ndarray

sparx.spiketrains on GitHub

Each neuron’s coincidence factor Γ, how well its spikes in spikes predict those in reference, both [steps, neurons] at step dt ms, with a precision of window ms.

Γ = (N_coinc - 2 nu Δ N_ref) / (½ (N + N_ref) (1 - 2 nu Δ))

N_coinc counts the reference’s spikes with one of the neuron’s within Δ, window rounded to steps, and nu = N / duration is the rate of the neuron in spikes, so 2 nu Δ N_ref is what a Poisson train of that rate meets by chance. Γ is 1 for the same spikes, 0 on average for a Poisson train, and below 0 for fewer coincidences than chance. This is Jolivet and Gerstner’s (J. Physiol. Paris 2004, eq. 13) form of Kistler et al.’s (Neural Comput. 1997) measure, the score of spike-time prediction in Jolivet et al.’s (J. Neurosci. Methods 2008) benchmark. brian2modelfitting’s get_gamma_factor counts the same coincidences and takes nu from the reference; the two agree where the counts do. A neuron silent in both trains has none (NaN).

cv_isi

def cv_isi(spikes: np.ndarray, minimum: int = 3) -> np.ndarray

sparx.spiketrains on GitHub

The coefficient of variation of each neuron’s interspike intervals, for neurons with at least minimum intervals; 1 for a Poisson process, 0 for a clock.

population_fano

def population_fano(spikes: np.ndarray, dt: float, window: float = 1.0) -> float

sparx.spiketrains on GitHub

The Fano factor of the population’s spike count in windows of window ms.

Near 1 when neurons fire independently (Brunel’s asynchronous states), far above 1 when they fire together (his synchronous states).

rates_hz

def rates_hz(spikes: np.ndarray, dt: float) -> np.ndarray

sparx.spiketrains on GitHub

Each neuron’s mean rate in Hz, over a run of dt ms steps.

sparx.rates.firing_rates reads a different quantity during training, each layer’s mean rate in spikes per step from the sown collection.

spike_steps

def spike_steps(spikes: np.ndarray) -> list[np.ndarray]

sparx.spiketrains on GitHub

Each neuron’s spike steps.

victor_purpura

def victor_purpura(times_a: np.ndarray, times_b: np.ndarray, cost: float) -> float

sparx.spiketrains on GitHub

Victor and Purpura’s (J. Neurophysiol. 1996) distance between two spike trains (times in ms).

The cheapest way to turn one train into the other, at 1 to add or remove a spike and cost per ms to move one: cost = 0 counts the difference in spike counts, a large cost counts unmatched spikes. Computed by their dynamic program, O(len(a) len(b)); not differentiable.