Hebb's rule with a stopwatch. Fire the input just before the neuron does and the synapse strengthens; fire just after and it weakens. The weight change Δw is a signed, exponentially-decaying function of the pre–post timing gap Δt = tpost − tpre — "fire together, wire together," but with a direction.
source Bi & Poo, Synaptic Modifications in Cultured Hippocampal Neurons (1998), J. Neurosci. 18, 10464–10472 — jneurosci.org/content/18/24/10464 · Rendered, not quoted.
A synapse carries a scalar weight w. Each paired firing nudges it by a fixed, deterministic kernel of the timing gap alone:
Δw = +A₊·e−Δt/τ₊ for Δt > 0
Δw = −A₋·e+Δt/τ₋ for Δt < 0
Pre-before-post (Δt>0) → potentiation (LTP). Post-before-pre (Δt<0) → depression (LTD). The two lobes are independent — different amplitudes A and time constants τ.
amber τ₊=16.8 ms, τ₋=33.7 ms are Bi & Poo's fitted constants; amplitudes A are illustrative. Model of plasticity, not medical advice.
Hebb (1949) said cells that fire together wire together. Bi & Poo (1998) put a stopwatch on it: order and millisecond gap decide the sign. This is the learning rule that rides on top of spikes — the all-or-none events produced upstream by the-hodgkin-huxley. One sphere makes the spike; this one decides what the spike teaches.
Re-runs the full check live — the causal asymmetry, the exponential decay, the lobe amplitudes, and the tamper-catch. Green means the rule still flips sign at Δt=0. Trip window 6 and this flips red.
A pre–post spike pair with timing gap Δt (ms). Drag to place the input spike before (+) or after (−) the output spike.
The STDP window, computed live from the kernel. Blue lobe = strengthen, red lobe = weaken. The marker rides the curve at your Δt.
The proven result: a signed weight change whose sign is set by spike order and whose magnitude decays with the gap. Cause-before-effect is reinforced; effect-before-cause is punished.
"Just count coincidences." A symmetric coincidence detector (strengthen whenever spikes are near, regardless of order) throws away the one thing that makes STDP a causal rule. It would reward a synapse that fired after the neuron already spiked — a post-hoc bystander taking credit. The wall: symmetry is acausal and unstable; without the sign flip, runaway potentiation has no brake.
"Correlation is enough — timing is a detail."
→ Sign depends on order: a few ms decides potentiation vs depression.
"Both lobes are mirror images."
→ Asymmetric: the LTD lobe is broader (τ₋>τ₊) — A₊≠A₋.
"Distant spikes still add up."
→ Δw → 0 exponentially; spikes >100 ms apart barely interact.
Plant the disclosed void: force the rule symmetric so post-before-pre wrongly potentiates. The sign flip at Δt=0 dies — the Witness (7) catches it live.
The selfcheck plants this same void internally every boot, asserts the acausal potentiation appears, then restores — a caught bug, on purpose.