The purpose of this paper(Hinton '86) is teaching NN to understand relationships between P1 and P2.
Family Tree
The family tree above can be expressed by a set of tripletts.
Person1 Relation Person2
Christopher wife Penelope
Arthur wife Margaret
James wife Victoria
Andrew wife Christine
Charles wife Jennifer
Roberto wife Maria
Pierro wife Francesca
The family tree contains 104 triplett.(FamilyTree.xlsx)
Neural Network Structure
Feed forward
There are not bias nodes.
Non-linear function(sigmoid function)
The units are arrainged in layers with a layer of input uints at the bottom, any number of intermediate layers, and a layer of output uints at the top. There no feedback connections.
Back propagation
Squared residual errors, no bias node, Batch mode
acceleration medthod : delta W(t-1)
t is incremented by 1 for each sweep through the whole set of input-output cases, and alpha is an exponential decay factor between 0 and 1 that determines the relative contribution of the current gradient and ealier gradients on the weight change.
The results.
Weights from the 24 input units for people
Weights from the 12 input units for relations
My model got 2 out of 4 test cases,
wheree "correct" means that the output unit corresponding to the right answer had an activity level above 0.5, and all the other output units were below 0.5.