--- tags: - ai --- *Time-dependent, highly local, strongly interactive* - Oldest learning algorithm - Increases synaptic efficiency as a function of the correlation between presynaptic and postsynaptic activities 1. If two neurons on either side of a synapse are activated simultaneously/synchronously, then the strength of that synapse is selectively increased 2. If two neurons on either side of a synapse are activated asynchronously, then that synapse is selectively weakened or eliminated - Hebbian synapse - Time-dependent - Depends on times of pre/post-synaptic signals - Local - Interactive - Depends on both sides of synapse - True interaction between pre/post-synaptic signals - Cannot make prediction from either one by itself - Conjunctional or correlational - Based on conjunction of pre/post-synaptic signals - Conjunctional synapse - Modification classifications - Hebbian - **Increases** strength with **positively** correlated pre/post-synaptic signals - **Decreases** strength with **negatively** correlated pre/post-synaptic signals - Anti-Hebbian - **Decreases** strength with **positively** correlated pre/post-synaptic signals - **Increases** strength with **negatively** correlated pre/post-synaptic signals - Still Hebbian in nature, not in function - Non-Hebbian - Doesn't involve above correlations/time dependence etc # Mathematically $$\Delta w_{kj}(n)=F\left(y_k(n),x_j(n)\right)$$ - Generally - All Hebbian ![](../../../img/hebb-learning.png) ## Hebb's Hypothesis $$\Delta w_{kj}(n)=\eta y_k(n)x_j(n)$$ - Activity product rule - Exponential growth until saturation - No information stored - Selectivity lost ## Covariance Hypothesis $$\Delta w_{kj}(n)=\eta(x_j-\bar x)(y_k-\bar y)$$ - Characterised by perturbation from of pre/post-synaptic signals from their mean over a given time interval - Average $x$ and $y$ constitute thresholds - Intercept at y = y bar - Similar to learning in the hippocampus *Allows:* 1. Convergence to non-trivial state - When x = x bar or y = y bar 2. Prediction of both synaptic potentiation and synaptic depression