Spike-Timing Dependent Plasticity (STDP)

STDP is a biologically observed synaptic learning rule in which the change in connection strength depends on the relative timing of pre- and post-synaptic spikes [6]. SpikeSEG uses the simplified STDP formulation of Kheradpisheh et al. [1].

Learning Rule

Long-Term Potentiation (LTP)

If the pre-synaptic neuron fires before or at the same time as the post-synaptic neuron, the synapse is strengthened:

$$\Delta w = a^{+} \cdot w \cdot (1 - w) \qquad \text{if } t_{\text{pre}} \leq t_{\text{post}}$$

Long-Term Depression (LTD)

If the pre-synaptic neuron fires after the post-synaptic neuron, the synapse is weakened:

$$\Delta w = -a^{-} \cdot w \cdot (1 - w) \qquad \text{if } t_{\text{pre}} > t_{\text{post}}$$

Key Properties

• The sign of the timing difference matters, not its magnitude: "The exact time difference between two spikes does not affect the weight change, but only its sign is considered." [1]
• The multiplicative term $w(1 - w)$ provides soft bounds that keep weights in $[0, 1]$ and naturally drive them toward binary values (0 or 1).
• A pre-synaptic neuron that never fires is assumed to fire later (treated as LTD).

Learning Rate Parameters

Source	$a^{+}$	$a^{-}$	Convergence speed
Kheradpisheh 2018 [1]	0.004	0.003	Standard
IGARSS 2023 [4]	0.04	0.03	10x faster

The IGARSS 2023 rates are 10x larger for faster convergence on the smaller EBSSA dataset.

Convergence Criterion

Weights converge when they polarize toward 0 or 1. The convergence metric from Equation 4 of [1]:

$$C_l = \frac{1}{n_w} \sum_{f} \sum_{i} w_{f,i} \cdot (1 - w_{f,i})$$

• $C_l = 0$: all weights are exactly 0 or 1 (fully converged).
• $C_l = 0.25$: all weights are at 0.5 (maximum uncertainty).

Training stops when $C_l < 0.01$.

Weight Initialization

Weights are drawn from $\mathcal{N}(\mu=0.8,\, \sigma=0.01)$ and clipped to $[0, 1]$. Starting near 1 accelerates STDP convergence: features that should be potentiated are already close to their final value.

Implementation

from spikeseg.learning import STDPLearner, STDPConfig

# Paper preset
config = STDPConfig.from_paper("igarss2023")
# config.lr_plus = 0.04, config.lr_minus = 0.03

learner = STDPLearner(config)

# Update weights for a WTA winner
learner.update_weights_for_winner(
    weights=layer.conv.weight,
    pre_spike_times=pre_times,
    post_spike_time=winner_time,
    winner_y=wy, winner_x=wx,
    kernel_size=5, stride=1, padding=0,
)

# Check convergence
metric = learner.get_convergence(layer.conv.weight)
if metric < 0.01:
    print("Layer converged")

See API: Learning for complete signatures and the additive STDP variant.