Hebbian Rule

A standard Hebbian learning rule that updates synaptic strengths based on the correlation between pre- and post-synaptic activities.

\[\Delta w = \epsilon \cdot (a_\text{source} \cdot a_\text{target})\]

where:

• \(\epsilon\) is the learning rate
• \(a_{\text{source}}\) is the activation of the source or pre-synaptic neuron
• \(a_{\text{target}}\) is the activation of the target or post-synaptic neuron
• \(w\) is the current synaptic strength

When a forgetting rate \(\gamma\) is applied, the update becomes:

\[w_{\text{new}} = (1 - \gamma) \cdot w + \epsilon \cdot (a_\text{source} \cdot a_\text{target})\]

Parameters

• Learning rate: Learning rate \(\epsilon\) for Hebb rule.
• Forgetting rate: The percent of strength to remove at each time step.