2.1 The VC dimension 5 2.2 Using the growth function and the VC dimension to analyse generalization 8 2.3 VC dimension and computational learning theory 9 2.3.1 Standard PAC learning 9 2.3.2 Extended PAC learning 10 3.1 Interpolation and Micchelli's theorems 12 3.2 Networks with xed centres 16 3.3 Networks with variable centres 17 4.1 Threshold order of a boolean function 20 4.2 Further notations and denitions 21 4.3 VC dimension and independence of basis functions 22 4.4 VC dimension of PDFs 25 2 # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # 1 Linearly weighted neural networks 3 2...