Neural Networks

Hebbian

Time-dependent, highly local, strongly interactive

Oldest learning algorithm
Increases synaptic efficiency as a function of the correlation between presynaptic and postsynaptic activities

If two neurons on either side of a synapse are activated simultaneously/synchronously, then the strength of that synapse is selectively increased
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

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:

Convergence to non-trivial state
- When x = x bar or y = y bar
Prediction of both synaptic potentiation and synaptic depression

Credit Assignment Problem Tasks