Synaptic Plasticity: How Neurons Learn (STDP)

Memory is not a photograph

Memory is not stored as a fixed pattern anywhere in the brain — it is the collective strength of billions of modifiable connections. Each synapse can be strengthened or weakened according to rules shaped by evolution, and the simplest of those rules dates to 1949, when Canadian psychologist Donald Hebb wrote: "When an axon of cell A is near enough to excite cell B and repeatedly or persistently takes part in firing it, some growth process or metabolic change takes place… such that A's efficiency… is increased." This is Hebb's postulate, usually compressed to "neurons that fire together, wire together."

In continuous form, dwij/dt = η · yi · xj — but taken literally this rule is unstable: because positive activity always increases positive weights, it produces a runaway positive-feedback loop with no ceiling. Every practical implementation of Hebbian learning adds some form of normalisation or decay. Sejnowski's 1977 covariance rule — using deviations from mean activity rather than raw firing rates — was an early fix, and it conceptually foreshadows principal component analysis in neural networks.

LTP and LTD: the experimental proof

Hebb's idea stayed theoretical until 1973, when Timothy Bliss and Terje Lømo discovered long-term potentiation (LTP) in the rabbit hippocampus: a brief burst of high-frequency stimulation produced a sustained, sometimes permanent, increase in synaptic efficacy. The complementary phenomenon, long-term depression (LTD), was confirmed by Masao Ito in 1982 in the cerebellum. Both are now understood through the NMDA receptor, a coincidence detector that opens only when presynaptic glutamate release and postsynaptic depolarisation happen together, letting Ca²⁺ flow in and activate kinases that insert AMPA receptors (LTP) or phosphatases that remove them (LTD). The direction of change tracks the size and duration of the resulting Ca²⁺ signal, not merely its presence.

Spike-timing-dependent plasticity

Tetanic stimulation is a pharmacological convenience, not how neurons behave during ordinary activity. The more physiologically relevant question, answered independently by Markram et al. (1997) and Bi & Poo (1998), is how the precise millisecond-scale order of individual spikes governs plasticity: spike-timing-dependent plasticity (STDP). If a presynaptic spike precedes the postsynaptic spike (Δt = t_post − t_pre > 0), the synapse potentiates; if it follows (Δt < 0), the synapse depresses. The classic asymmetric exponential learning window is:

Δw(Δt) =  A₊ · exp(−Δt/τ₊)   if Δt > 0   (LTP)
Δw(Δt) = −A₋ · exp(+Δt/τ₋)   if Δt < 0   (LTD)
// τ₊ ≈ τ₋ ≈ 20 ms · A₋ slightly exceeds A₊ (net depression bias)

This causal asymmetry — a synapse is strengthened only when it could plausibly have caused the postsynaptic spike — is often called a temporal Hebbian rule. Efficient implementations avoid storing raw spike times by using exponentially decaying eligibility traces for pre- and postsynaptic activity, updated on every spike, which is how online STDP runs inside real-time spiking network simulations.

The BCM sliding threshold

Pure Hebbian and STDP rules still need a stabiliser. In 1982 Bienenstock, Cooper and Munro proposed the BCM rule, which introduces a sliding modification threshold θ_M that separates LTP from LTD: dwi/dt = η·xi·y·(y − θM), where θ_M itself rises superlinearly with average postsynaptic activity. A chronically underactive neuron sees its threshold fall, making potentiation easier; a hyperactive one sees it rise, favouring depression. This single mechanism buys stability, selectivity for correlated inputs, and competition between synapses, and it correctly predicted how monocular deprivation reshapes ocular-dominance columns in visual cortex.

Homeostasis and weight distributions

A slower, complementary mechanism — synaptic scaling (Turrigiano et al., 1998) — multiplicatively rescales all of a neuron's synapses over hours to days, preserving the relative pattern of weights (the memory) while restoring the neuron's average firing rate to a target. Networks evolving under STDP for long enough tend toward a bimodal weight distribution — synapses cluster near zero or near a maximum w_max rather than settling on a continuum — which is thought to maximise storage capacity and matches the largely all-or-none potentiation observed at individual dendritic spines. Together, fast synapse-specific STDP and slow global homeostasis form a two-timescale system that can learn specific patterns without ever losing overall stability.

Frequently asked questions

Try it live

Drive two spiking neurons at adjustable rates and timing offset in Synaptic Plasticity — How Neurons Learn (STDP) and watch the synaptic weight and the empirical learning window build up in real time.