Spiking Neural Networks: Neurons That Talk in Timed Pulses, Not Numbers

A neuron that spikes, not a number that squashes

Standard artificial neural networks pass continuous numbers through smooth activation functions. A spiking neural network (SNN) instead models neurons much closer to biology: each unit accumulates input as a continuously evolving membrane voltage and only communicates by firing discrete, all-or-nothing spikes when that voltage crosses a threshold — information is carried in when spikes happen, not in a continuous activation level.

The standard workhorse model for the individual neuron is the leaky integrate-and-fire (LIF) neuron — a deliberately simplified model that captures the essential dynamics (integration, leak, threshold, reset) without the biophysical detail of, say, the Hodgkin-Huxley ion-channel equations:

τ dV/dt = −(V − V_rest) + R·I(t)

when V ≥ V_threshold:  neuron fires a spike, then V → V_reset (hard reset)

τ      = membrane time constant (leak rate)
V_rest  = resting potential the voltage decays back toward with no input
R·I(t)  = driving current from incoming synaptic spikes

Excitatory and inhibitory balance

Real cortical circuits, and this simulation's 40-excitatory/10-inhibitory split, are built from two functionally different populations. Excitatory neurons (releasing neurotransmitters like glutamate) push a postsynaptic neuron's voltage up toward threshold; inhibitory neurons (releasing GABA) push it down, away from threshold. A network with too much unchecked excitation runs away into synchronized, seizure-like firing; one with too little cannot sustain any activity at all. The roughly 80:20 excitatory-to-inhibitory ratio seen in real cortex, and mirrored here, sits in a regime where inhibition actively restrains and shapes excitation rather than simply damping it — producing the kind of irregular, sparse, information-rich firing patterns seen in real cortical recordings rather than either silence or synchronized bursts.

STDP: synapses that learn from timing, not from being told the answer

Spike-timing-dependent plasticity (STDP) is the leading biological model for how synapses strengthen or weaken based purely on the relative timing of pre- and postsynaptic spikes, discovered experimentally in the 1990s and directly inspired by Hebb's older, looser postulate that cells which fire together wire together.

if pre-synaptic spike arrives shortly BEFORE post-synaptic spike (Δt > 0):
    synapse strengthens (long-term potentiation, LTP)
    "this input looks like it helped cause the output — reward it"

if pre-synaptic spike arrives shortly AFTER post-synaptic spike (Δt < 0):
    synapse weakens (long-term depression, LTD)
    "this input arrived too late to have caused the output — penalize it"

Δw ~ A⁺·exp(−Δt/τ⁺)  if Δt > 0,   A⁻·exp(Δt/τ⁻)  if Δt < 0

This turns causal timing into a learning signal without ever needing an external error label or teacher: a synapse that reliably fires just before its target neuron does gets rewarded, one that fires just after gets punished, and over many spikes the network's connectivity self-organises around whichever inputs are actually predictive of downstream firing.

Reading a raster plot

The standard way to visualise spiking activity across many neurons at once is a raster plot: one row per neuron, one tick mark per spike, time running along the horizontal axis. Instead of a single continuous trace it exposes population-level structure directly — a synchronized vertical band means many neurons fired together, a diagonal streak means activity is propagating like a wave through the population, and quiet, evenly-scattered dots mean the network is in an irregular, asynchronous firing regime.

Why spikes instead of continuous activations at all

Spiking is not merely a more biologically faithful detail bolted onto an otherwise ordinary network — it changes what the network can compute and how cheaply. Because a neuron only communicates when it crosses threshold, most units in a large, sparsely-active SNN are silent at any given instant, which is the whole appeal of neuromorphic hardware (like Intel's Loihi or IBM's TrueNorth): computation and communication happen only when a spike actually occurs, so power consumption scales with activity rather than network size — a very different trade-off from a conventional neural network, which does dense matrix multiplication on every unit at every step whether or not that unit's output ends up mattering.

Frequently asked questions

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