New PDF release: Neural Networks Models: An analysis

By Philippe De Wilde (auth.)

ISBN-10: 3540199950

ISBN-13: 9783540199953

ISBN-10: 3540708197

ISBN-13: 9783540708193

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H f ( x i , t~), h f ( x i + kl,ti + h). 3) The term CO(h3) gives an estimate of the error. ,with the ai constants independent of h, but dependent on f. For an alternative definition, see page 19. For 2 neurons, there are two differential equations ic = ~1 = f(x,y,t), g(x,y,t). , C H A P T E R 4. F U N D A M E N T A L S Y S T E M 74 la = hg(xi,yi,ti), k2 = hf(xi + k l , y i + ll,ti + h), 12 = hg(xi + kl,yi + ll,ti + h). 5) For more neurons, meaning more differential equations, it is easier to generalize these formulas yourself than to write down the general equations.

5 R e m a r k s on E p o c h s a n d M u l t i p l e P a t t e r n s What has been described in the preceding subsections has the effect of changing all weights exactly once. This is called one epoch. It brings the network somewhat closer to imitating the required input-output behaviour. In general several epochs will be needed before the network makes acceptable small errors. An error criterion can be the number of output neurons that gives a wrong output. One can also choose the sum of the error signals from the output neurons.

The potential in the dendrite has the shape of Fig. 2. 59 O P E R A T I O N OF THE N E U R O N m m . . . 7: The shape of the travelling action potential at a particular moment in time. 8: The action potential is distributed over the axon branches. 60 C H A P T E R 3. 9: The potential in the dendrite. so, they have an efficacy. The number of the postsynaptic potentials can be as large as the number of dendrites, about 10000. These post-synaptic potentials diffuse, or travel, through the dendrites towards the soma.

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Neural Networks Models: An analysis by Philippe De Wilde (auth.)

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