4.23 How a network learns: the five learning rules

Work through these

• Define learning as adaptation of the free parameters by the environment

  The weights change under stimulation from outside, and the manner of that change is what names the type of learning. Holding to this definition is what keeps the five rules below comparable.

• Apply error-correction learning and the delta rule

  The difference between the desired and the actual output drives the weight change, in steps, until the correction stops. It is also called the Widrow-Hoff rule, and every supervised method later is a descendant.

• Apply memory-based learning, and the nearest neighbour and k-nearest neighbour rules

  All the examples are stored, and a new input is answered by the stored ones nearest to it. It needs a distance and a neighbourhood, and it does no work at all until a question arrives.

• State Hebb's law in its two halves, and apply the activity product rule

  Units that fire together strengthen the connection between them, and units that fire out of step weaken it. The weight change is the product of the two activities and a learning rate.

• Add a forgetting factor, and say what problem it fixes

  Hebb's rule on its own can only increase weights, so they grow without limit. Subtracting a small multiple of the current weight bounds that growth while still allowing learning.

• Work Hebbian learning through a small example step by step

  Initialise small random weights, compute the output, update the weights, repeat. Doing the arithmetic once on a tiny example is what makes the rule concrete rather than a formula on a page.

• Distinguish competitive and Boltzmann learning from the other three

  In one, units compete and only the winner adapts, which produces a division of labour among them. In the other, weights change by a stochastic rule taken from statistical physics.