Time, units and rates

sparx has two conventions for time and units, one for each half of the library, and they meet in a few places. This page lists both and where each applies.

Steps: the trainable layers

The dimensionless cells in sparx.dynamics.ml and the layers in sparx.nn count time in steps. Every model takes a step dt, 1 by default, and its time constants are in the unit of dt.

• Decay. A model stores its decay per unit of time, decay(tau) = exp(-1 / tau), and a step of dt multiplies by decay ** dt = exp(-dt / tau). LIF(tau=20.0) at the default dt=1 keeps exp(-1/20) of its membrane each step. A learned decay is stored the same way, so a checkpoint means the same at any dt.
• Input. An array input is a jump of the membrane, unitless, added unscaled each step (snnTorch’s Leaky convention). A dimensionless model refuses a current or a conductance.
• A step of real time. To bin recordings in 14 ms steps and give time constants in ms, set the layer’s dt to 14: ALIF(tau=20.0, tau_adapt=200.0, dt=14.0) decays by exp(-14/20) per step, as ALIF(tau=20/14) does at dt=1. A Recurrent layer steps at its neuron’s dt, and every layer of a SpikingMLP steps at its neuron’s dt, the readout included.
• Refractoriness. ALIF(refractory=r) is a duration in the unit of dt. The spike and the silence after it span round(r / dt) steps, Bellec et al.’s n_refractory, so r of 0 or one step leaves the neuron free to fire on the next step.
• Delays. In steps. A Sparse wiring’s per-edge delay runs from 1 to longest_delay. DelayedDense(features, max_delay) learns a delay from 0 to max_delay per connection, and SpikingMLP(delays=...) gives each synapse’s largest delay.
• Encoders. steps is the length of the time axis they add. RateEncoder fires with probability x per step, whatever the step stands for. Encoders read a uint8 field as x / 255; EventsEncoder passes counts unscaled.
• Fast weights. A Hebbian rule’s eta is a rate per unit of time: DecayingHebb keeps (1 - eta) ** dt of its trace per step, and the other rules add dt times their rate.
• Online rules. e-prop, OTTT and REINFORCE take dt and time constants in its unit, as the cells do. PulseCell has no time constant, so an RNeuralNet counts ticks and ignores dt.

Physical units: the simulator

The physical models in sparx.dynamics.neurons, the synapses and plasticity rules, and the networks of sparx.graph use one set of units, chosen so that pF * mV / ms = pA and nS * mV = pA hold without factors.

Quantity	Unit
time, dt, time constants, delays, t_ref, duration, chunk	ms
voltage	mV
current	pA
conductance	nS
capacitance	pF
rates of spiking (PoissonInput, PopulationRate)	Hz
gating rates inside Hodgkin-Huxley	1/ms

• A step. Network(dt=0.1) steps every population 0.1 ms. A physical model run by itself steps sparx.run(model, inputs, dt=...) ms, 1 by default; nn.Dynamics(AdEx(), dt=0.1) runs it as a layer at 0.1 ms.
• What reaches a membrane (SynapticInput). current in pA, held over the step. conductance in nS per receptor, held over the step at its exact mean by default (PointNeuron.hold). jump in mV, added at the end of the step before the threshold test.
• Weights. A projection’s receptor sets the unit of its weight: pA of peak current for a "current" receptor, nS of peak conductance for a "conductance" receptor, mV for a Delta synapse. A projection from a graded population weighs its synapses at full release.
• Delays. Projection(delay=...) is in ms and must be a whole number of steps, as must simulate’s duration and chunk. A delta synapse’s jump lands before the threshold test, so it needs a delay of at least one step; a kinetic synapse takes 0.
• Refractoriness. A neuron that fires holds its reset for round(t_ref / dt) steps after the step it fired in, as NEST counts it. Brian2 counts one step less (see fidelity.md).
• Inputs. PoissonInput(rate=...) is in Hz per source. CurrentInput drives in pA, as does a neuron’s constant i_e. A GapJunction’s weight is a conductance in nS.
• Neuromodulators. A Modulator’s concentration has no unit. Each spike of its source adds release, and the concentration decays with tau ms.
• Plasticity. STDP’s, triplet STDP’s, dopamine STDP’s and Tsodyks-Markram’s time constants are in ms.
• EventProp. sparx.learn.spike_times works in continuous time in ms, with the membrane in mV above rest and currents in pA.

Rates

A rate has one of two units, depending on which half reports it.

Rate	Unit
sparx.firing_rates, sparx.rate_penalty, RateBand, the rate/<layer> training metric, ActivityFitObjective’s rates, sparx.learn.run_converted	spikes per step
PopulationRate, PoissonInput.rate, sparx.spiketrains.rates_hz, a connectome’s stimulus rates	Hz

A rate per step p at steps of dt ms is 1000 p / dt Hz. RateBand(lower=0.01, upper=0.3) asks each neuron to fire on between 1% and 30% of steps.

Where the halves meet

• A physical model as a layer. nn.Dynamics(model, dt=...) takes dt in ms and its input as a current in pA (drive="current") or as a jump in mV (drive="jump"). Train it with a steep surrogate; the guide explains why.
• A dimensionless cell in a network. A Network steps every population at its dt in ms, so a dimensionless cell there decays by decay ** dt per step and its decay is per ms. Build it with decay(tau_in_ms), or give the network dt=1.0, as the tests do. Delays and PopulationRate stay in ms and Hz.
• Spike times. A spike in step n with offset o in the step happened at (n + o) * dt. A dimensionless model’s offset is 1, the end of the step.

Seconds

Two interfaces take seconds, because their formats do:

• sparx.datasets.shd(steps=100, max_time=1.4) bins the first max_time seconds of each recording into steps bins, 14 ms each by default, the binning of Zenke’s SpyTorch tutorial.
• NIR stores time constants in seconds, and sparx.nir.to_nir and from_nir take the step dt in seconds.