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From: esrmm@warwick.ac.uk (Denis Anthony)
Newsgroups: comp.ai.neural-nets
Subject: Re: Several hidden layers in feed-forward networks
Message-ID: <1991Jan8.091631.16219@warwick.ac.uk>
Date: 8 Jan 91 09:16:31 GMT
References: <7165.27885d62@abo.fi> <1991Jan7.202202.12266@murdoch.acc.Virginia.EDU>
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In article <1991Jan7.202202.12266@murdoch.acc.Virginia.EDU> aam9n@helga0.acc.Virginia.EDU (Ali Ahmad Minai) writes:
>In article <7165.27885d62@abo.fi> vt_ai@abo.fi writes:
>
>As for why more layers work "better", they often don't. But when they
>do, it is because of the greater potential "complexity" available.
>Think of each neuron in layer k as forming a distorted linear
>superposition of the outputs from the previous layer. If the neurons
>in the net have monotonic activation functions, as they usually do,
>an output layer neuron in a single hidden-layer net requires about 2n
>hidden neurons to compose a function with n modes (peaks).

Why 2n ? Is this emprical, or based on maths ? Or is it obvious,
ie. 2n to form n peaks and n troughs. Apologies if I am being
a bit dim.

Denis