Backpropagation: Theory, Architectures, and Applications by Yves Chauvin (ed.), David E. Rumelhart (ed.)

By Yves Chauvin (ed.), David E. Rumelhart (ed.)

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4 When the TDNN has learned its internal representation, it performs recognition by passing input speech over the TDNN units. In terms of the illustration of Fig. , the spectral coefficients. Each TDNN unit outlined in this section has the ability to encode temporal relationships within the range of the N delays. Higher layers can attend to larger time spans, so local short duration features will be formed at the lower layer and more complex longer duration features at the higher layer. The learning procedure ensures that each of the units in each layer has its weights adjusted in a way that improves the network's overall performance.

The name was coined by Geoffrey Hinton, inspired by the notion of "hidden states" in hidden Markov models. Copyrighted Material 1. BACKPROPAGATION: THE BASIC THEORY 25 4. Layers of hidden units can be viewed as a mechanism for transforming stimuli from one representation to another from layer to layer until those stimuli which are functionally similar are near one another in hidden-unit space. In the following sections we treat each of these conceptions. Sigmoidal Units as Continuous Approximations to Linear Threshold Functions Perhaps the simplest way to view sigmoidal hidden units is as continuous approximations to the linear threshold function.

It can readily b e seen that, w h e r e a s the sigmoid represents the two-alternative c a s e , the n o r m a l i z e d exponential clearly represents the multialternative c a s e . T h u s , w e d e r i v e the n o r m a l i z e d exponential in exactly the same w a y as w e derive the sigmoid: P(cj = 1| ) = e x p { Σ i [ ( x i j θi - B(θij)) + C( ) ] / a ( ) + ln P(cj Σk exp{Σi[(xiθi - B(θik)) + C( )]/a( ) + ln P(ck = 1)} = 1)} exp{Σi xij θi/a( ) - ΣiB(θij)/a( ) + ln P(cj = 1)} = = Σk exp{Σi xi θik/a( ) - B(θik)/a( ) + ln P(ck = 1)} ei xij wij +βj .

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