# Structure Level Adaptation for Artificial Neural Networks by Tsu-Chang Lee

By Tsu-Chang Lee

63 three. 2 functionality point variation sixty four three. three Parameter point variation. sixty seven three. four constitution point model 70 three. four. 1 Neuron new release . 70 three. four. 2 Neuron Annihilation seventy two three. five Implementation . . . . . seventy four three. 6 An Illustrative instance seventy seven three. 7 precis . . . . . . . . seventy nine four aggressive sign Clustering Networks ninety three four. 1 creation. . ninety three four. 2 simple constitution ninety four four. three functionality point variation ninety six four. four Parameter point model . a hundred and one four. five constitution point model 104 four. five. 1 Neuron iteration procedure 107 four. five. 2 Neuron Annihilation and Coalition technique 114 four. five. three Structural Relation Adjustment. 116 four. 6 Implementation . . 119 four. 7 Simulation effects 122 four. eight precis . . . . . 134 five software instance: An Adaptive Neural community resource Coder one hundred thirty five five. 1 advent. . . . . . . . . . a hundred thirty five five. 2 Vector Quantization challenge 136 five. three VQ utilizing Neural community Paradigms 139 Vlll five. three. 1 easy homes . a hundred and forty five. three. 2 quickly Codebook seek process 141 five. three. three course Coding process. . . . . . . 143 five. three. four functionality comparability . . . . a hundred and forty four five. three. five Adaptive SPAN Coder/Decoder 147 five. four precis . . . . . . . . . . . . . . . . . 152 6 Conclusions a hundred and fifty five 6. 1 Contributions one hundred fifty five 6. 2 techniques 157 A Mathematical heritage 159 A. 1 Kolmogorov's Theorem . a hundred and sixty A. 2 Networks with One Hidden Layer are adequate 161 B Fluctuated Distortion degree 163 B. 1 degree development . 163 B. 2 The Relation among Fluctuation and mistake 166 C SPAN Convergence thought 171 C. 1 Asymptotic price of Wi 172 C. 2 power functionality . .

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0 The biological counterpart for F is the dendrite tree observed in biological neurons [84, 56]. The main purpose of F is to collect information from the RF and to make associations between variables in the RF through the tree structure of functions. A special function Dk' called the time index shift function, can be included in F. The following equation defines D k: 9 a[* - k] = Dk(al*]) where k, called the shift index, is an integer. A time index shift function DkO with k greater than zero is called a delay function.

E. a neural network that can adapt itself structurally), we need to specify the mechanisms to modify network structures. An S-Level neural network (S-Net) is specified by a 4-tuple E =< G, 4>, 0, J >, the components of which are defined as follows: G is a structure containing the specification of a P-Level neural net- work; 4> is a SOS (Spanning Operator Set) for the E-space £ that G belongs to. o (called the Structure Evolution Automata (SEA) for the S- Net, £) is used for two tasks: • To select a set of operators to act on Gl*], in order to generate the next P-Level network specification, G[* + 1].

This structure learning process not only happens in the long-term evolution process but also in the development process of an individual body [31,32]. If we consider gene codes as the blue-print for the final form of a living creature, this blue-print only specifies partial information for the final structure, because the chromosomes do not have enough space to specify all the structural details of a brain. Because the structure of a nerve system is evolved and developed rather than pre-specified, it would be very hard to grasp the function-structure relationship of the brain 2 and try to map it into the design of engineering artifacts.