Synaptic weight

In a computational neural network, a vector or set of inputs ${\displaystyle {\textbf {x}}}$ and outputs ${\displaystyle {\textbf {y}}}$, or pre- and post-synaptic neurons respectively, are interconnected with synaptic weights represented by the matrix ${\displaystyle w}$, where for a linear neuron

${\displaystyle y_{j}=\sum _{i}w_{ij}x_{i}~~{\textrm {or}}~~{\textbf {y}}=w{\textbf {x}}}$.

where the rows of the synaptic matrix represent the vector of synaptic weights for the output indexed by ${\displaystyle j}$.

The synaptic weight is changed by using a learning rule, the most basic of which is Hebb's rule, which is usually stated in biological terms as

Neurons that fire together, wire together.

Computationally, this means that if a large signal from one of the input neurons results in a large signal from one of the output neurons, then the synaptic weight between those two neurons will increase. The rule is unstable, however, and is typically modified using such variations as Oja's rule, radial basis functions or the backpropagation algorithm.