Spike Timing Dependency Plasticity (STDP)

The Last Second
I'm not talking about the last second before I die. I have no knowledge of that experience and no way to report it when it happens. I'm talking about the last second you and I experienced while reading this very sentence. What facility in your brain gives this narrow, less than one-second view of the world around you? Where is it physically located, and how does it work?

The search for this function is the culmination of my quest to understand the process in the brain that allows us to participate in the moment.

I have a strong feeling that STDP is closely tied to the last second but after a long review of papers on the field, I find that the experts are as confused as I am, not a good sign for success. A good summary is by Feldman 'The Spike-Timing Dependence of Plasticity'.

It turns out that the basis for STDP is backpropagation (bAP) - that is, when the neuron spikes and sends its output down the axon chain, it also produces a second spike that propagates back into the dendrite tree. This seems to be what effectuates STDP in the synapses. 

I found a way to modify the simulator to work with backpropagation and am moving forward with it. This solution involves sending Windows messages to various body parts during the simulation. You can see the progress on this solution in the Notes Volume 1 Chapter 5 and below.

It is amateurs who have one big bright beautiful idea that they can never abandon. Professionals know that they have to produce theory after theory before they are likely to hit the jackpot.
-Francis Crick

My Theasus:

Without self-organization, the brain would start but soon stop - Locked down at an optimum condition. To keep the brain working, you need a little noise. Enough to jolt self-satisfied neurons out of their complacency and into action but not so much that the signal gets lost in the noise.

Aside from a little noise, you need some way that the brain can organize itself into a workable whole. It cannot be done by some sort of brain-within-brain composite brain that makes the final decisions based on inputs from all other parts of the brain. That duality requires that the 'inside brain' is made out of some stuff that is 'not of this world'.

I consider STDP to be the primary candidate for this self-organization property. I believe it is the primary Neural Correlate of Consciousness.

A good look at the field is presented in STDP an Overview [Markram]

Notes from Song

These notes were taken from the sentinel paper on STDP from Song, Mill and Abbott in March 2000 (available in the reference section)

  • It must not have a global arbitrator involved. Local competition only
  • Competition can also arise locally due to synaptic modification mechanisms that equilibrate at a per-set level of total synaptic innervation or activity [9 ]
  • Spike timing provides a mechanism that can lead to competitive Hebbian learning without requiring global intracellular signaling, pre-set activity, or synaptic efficacy levels.
  • Long-term strengthening of synapses occurs if presynaptic action potentials precede postsynaptic firing by no more than about 50 ms.

The STDP function plotted.
For example a spike comming in 20 mSec 'early' will improve that synapse by about 0.18 %. A 'late' incomming spike of 20 mSec will decrease that synapse by about -0.18%

The basic function used in this simulation:

where τ+ and τ− determine the ranges of pre- to postsynaptic interspike intervals over
which synaptic strengthening and weakening occur. A+ and A− determine the maximum
amounts of synaptic modification, which occur when delta t is close to zero.

The temporal windows in the range of tens of milliseconds.

More from Song

  • The amplitude of synaptic modification, which is controlled by the parameters A+ and A−. In our simulations we use A− and A+ = 0.005
  • In our modeling studies, we examine how STDP acts on the excitatory synapses driving an integrate-and-fire model neuron with N = 1000 excitatory and 200 inhibitory synapse.
  • The excitatory synapses are activated by various types of spike trains: un-correlated spike trains generated by independent Poisson processes at various rates, bursts of action potentials with different latencies, and partially correlated spike trains. The model neuron also receives inhibitory input consisting of Poisson spike trains at a fixed rate of 10 Hz. In the simulations, excitatory synapses are modified on the basis of their pre- and postsynaptic spike timing, while inhibitory synapses are held fixed.
  • STDP will strengthen short-latency excitatory inputs while weakening those with long latencies.
  • Competition arises in a novel way, not due to a global signaling or growth factor, or to an artificially imposed balance of nonspecific synaptic decay and growth terms, but rather through a competition for control of the timing of postsynaptic action potentials
  • As Hebb suggested 1 , synapses are only strengthened if their presynaptic action potentials precede, and thus could have contributed to, the firing of the postsynaptic neuron.
  • Like any other Hebbian modification rule, STDP cannot strengthen synapses in the absence of postsynaptic firing. If for some reason the excitatory synapses to a neuron are too weak to make it fire, STDP cannot rescue them

Simulator Summary

The simulator’s STDP implementation combines:

  • Real dendritic propagation delays
  • Soma-centered timing evaluation
  • Back-propagating action potentials
  • Additive STDP learning curves
  • Nearest neghbor selection of AP for evaluation
  • End-of-run synaptic evaluation

to produce a biologically-inspired learning system in which synapses self-adjust according to their causal contribution to neuronal firing.

Basic Signal Flow

The simulator models the signal path as :

Synapse → Dendrite Tree → Soma → Axon

Each synapse injects current into a dendrite branch.
The signal then travels through the dendritic tree toward the Soma with realistic propagation delays.

When the Soma membrane potential reaches threshold, the Soma generates an Action Potential (AP).

The AP then:

  1. Travels forward down the Axon
  2. Travels backward into the dendritic tree as a Back-Propagating Action Potential (bAP)

The bAP is the critical signal used for STDP learning.

Why Timing Matters

A synapse should only be strengthened if its activity actually contributed to causing the Soma spike.

To determine this, the simulator compares:

  • The time the synapse released neurotransmitter
  • The time the Soma generated an AP

However, dendritic signals require time to travel.

A synapse located far from the Soma fires earlier than one close to the Soma if both are to influence the same AP.

Therefore the simulator evaluates timing in the Soma’s reference frame.

Dendritic Transit Delay Compensation

Each dendrite branch has an associated signal propagation delay. When a synapse fires:

Synapse release time + dendritic transit delay

This determines when that signal actually influences the Soma. Likewise, when the Soma fires an AP, the simulator sends a bAP message backward through the dendritic tree carrying:

  • Soma AP time
  • Cumulative reverse transit delay

This allows every synapse to determine Δt = SomaSpikeTime − ffectiveSynapseArrivalTime

where:

EffectiveSynapseArrivalTime =
SynapseReleaseTime + ForwardDendriticDelay

STDP Learning Rule

The simulator uses the classic additive STDP relationship described by Song, Miller, and Abbott (2000). The learning rule depends on the sign and magnitude of Δt.

Long-Term Potentiation (LTP)

If the synapse helped trigger the Soma spike Δt > 0 the synapse is strengthened. This means the Synapse fired BEFORE the Soma AP and likely contributed causally to the spike.

The closer the timing, the larger the strengthening effect.

Long-Term Depression (LTD)

If the synapse fired after the Soma AP Δt < 0 The synapse is weakened. This indicates the synapse was poorly correlated with causing the spike.

End-of-Run Evaluation

The simulator does not immediately alter synaptic weights during the run. Instead, each synapse maintains a history of:

  • Neurotransmitter release times
  • Local dendritic timing information
  • Received bAP timing information

At the end of the simulation run, the synapse evaluates all timing relationships and computes its total weight adjustment.

This approach provides:

  • Stable evaluation
  • Easier visualization
  • Full event history analysis
  • Support for nearest-neighbor timing evaluation

Synaptic Weight Representation

In the simulator, synaptic strength can be represented in several ways, including:

  • Number of effective synaptic connections
  • Current amplitude contributed by the synapse
  • Total synaptic output current

Increasing synaptic weight causes the synapse to inject more current into the dendrite, making future Soma spikes more likely. Decreasing weight reduces its future influence.

Biological Interpretation

The STDP mechanism allows the simulated neuron to learn temporal correlations automatically.

Over time:

  • Useful synapses become stronger
  • Irrelevant synapses weaken
  • Frequently co-active pathways self-organize
  • The neuron becomes selectively responsive to repeating input patterns

This creates an emergent learning behavior similar to biological neural tissue.

Back-Propagating Action Potentials (bAPs)

The simulator explicitly models bAPs because biological neurons use them as a feedback signal to indicate the Soma fired. Without a bAP, distant synapses would have no reliable way to determine whether they contributed to generating the action potential.

The bAP therefore acts as the neuron’s internal teaching signal.