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<HTML>  <HEAD>    <!--SCRIPT LANGUAGE="JavaScript" SRC="http://a1835.g.akamai.net/f/1835/276/3h/www.netlibrary.com/include/js/dictionary_library.js"></SCRIPT>    <SCRIPT LANGUAGE="JavaScript">      if (!opener){document.onkeyup=parent.turnBookPage;}    </SCRIPT!-->    <META HTTP-EQUIV="Cache-Control" CONTENT="no-cache">    <META HTTP-EQUIV="Pragma" CONTENT="no-cache">    <META HTTP-EQUIV="Expires" CONTENT="-1"><META http-equiv="Content-Type" content="text/html; charset=windows-1252"><SCRIPT>var PrevPage="Page_88";var NextPage="Page_90";var CurPage="Page_89";var PageOrder="100";</SCRIPT>  <TITLE>Document</TITLE>  </HEAD>  <BODY BGCOLOR="#FFFFFF"><CENTER><TABLE BORDER=0 WIDTH=100% CELLPADDING=0><TR><TD ALIGN=CENTER>  <TABLE BORDER=0 CELLPADDING=2 CELLSPACING=0 WIDTH=100%>  <TR>  <TD ALIGN=LEFT><A HREF='Page_88.html'>Previous</A></TD>  <TD ALIGN=RIGHT><A HREF='Page_90.html'>Next</A></TD>  </TR>  </TABLE></TD></TR><TR><TD ALIGN=LEFT><P><A NAME='JUMPDEST_Page_89'/><A NAME='{30C}'/><TABLE BORDER=0 CELLSPACING=0 CELLPADDING=0 WIDTH='100%'><TR><TD ALIGN=RIGHT><FONT FACE='Times New Roman, Times, Serif' SIZE=2 COLOR=#FF0000>Page 89</FONT></TD></TR></TABLE><A NAME='{30D}'/><TABLE BORDER=0 CELLSPACING=0 CELLPADDING=0 WIDTH='100%'><TR>  <TD ROWSPAN=5></TD>  <TD COLSPAN=3 HEIGHT=12></TD>  <TD ROWSPAN=5></TD></TR><TR>  <TD COLSPAN=3></TD></TR><TR><TD></TD>  <TD ALIGN=CENTER><FONT FACE='Times New Roman, Times, Serif' SIZE=3><IMG SRC='0089-01.GIF' BORDER=0 ALT='0089-01.gif' WIDTH=346 HEIGHT=91></FONT></TD><TD></TD></TR><TR>  <TD COLSPAN=3></TD></TR><TR>  <TD COLSPAN=3 HEIGHT=1></TD></TR></TABLE><A NAME='{30E}'/><TABLE BORDER=0 CELLSPACING=0 CELLPADDING=0 WIDTH='100%'><TR>  <TD ROWSPAN=5></TD>  <TD COLSPAN=3 HEIGHT=12></TD>  <TD ROWSPAN=5></TD></TR><TR>  <TD COLSPAN=3></TD></TR><TR><TD></TD>  <TD ALIGN=CENTER><FONT FACE='Times New Roman, Times, Serif' SIZE=2>Figure&nbsp;3-3&nbsp;<BR>This&nbsp;network&nbsp;with&nbsp;a&nbsp;hidden&nbsp;&nbsp;layer&nbsp;allows&nbsp;it&nbsp;to&nbsp;recognize&nbsp;patterns.</FONT></TD><TD></TD></TR><TR>  <TD COLSPAN=3></TD></TR><TR>  <TD COLSPAN=3 HEIGHT=1></TD></TR></TABLE><A NAME='{30F}'/><TABLE BORDER=0 CELLSPACING=0 CELLPADDING=0 WIDTH='100%'><TR>  <TD ROWSPAN=5></TD>  <TD COLSPAN=3 HEIGHT=12></TD>  <TD ROWSPAN=5></TD></TR><TR>  <TD COLSPAN=3></TD></TR><TR><TD></TD>  <TD ALIGN=CENTER><FONT FACE='Times New Roman, Times, Serif' SIZE=3><IMG SRC='0089-02.GIF' BORDER=0 ALT='0089-02.gif' WIDTH=137 HEIGHT=86></FONT></TD><TD></TD></TR><TR>  <TD COLSPAN=3></TD></TR><TR>  <TD COLSPAN=3 HEIGHT=1></TD></TR></TABLE><A NAME='{310}'/><TABLE BORDER=0 CELLSPACING=0 CELLPADDING=0 WIDTH='100%'><TR>  <TD ROWSPAN=5></TD>  <TD COLSPAN=3 HEIGHT=12></TD>  <TD ROWSPAN=5></TD></TR><TR>  <TD COLSPAN=3></TD></TR><TR><TD></TD>  <TD ALIGN=CENTER><FONT FACE='Times New Roman, Times, Serif' SIZE=2>Figure&nbsp;3-4<BR>The&nbsp;Simple&nbsp;XOR&nbsp;Function.</FONT></TD><TD></TD></TR><TR>  <TD COLSPAN=3></TD></TR><TR>  <TD COLSPAN=3 HEIGHT=1></TD></TR></TABLE><A NAME='{311}'/><TABLE BORDER=0 CELLSPACING=0 CELLPADDING=0 WIDTH='100%'><TR>  <TD ROWSPAN=5></TD>  <TD COLSPAN=3 HEIGHT=12></TD>  <TD ROWSPAN=5></TD></TR><TR>  <TD COLSPAN=3></TD></TR><TR><TD></TD>  <TD ALIGN=CENTER><FONT FACE='Times New Roman, Times, Serif' SIZE=3><IMG SRC='0089-03.GIF' BORDER=0 ALT='0089-03.gif' WIDTH=335 HEIGHT=262></FONT></TD><TD></TD></TR><TR>  <TD COLSPAN=3></TD></TR><TR>  <TD COLSPAN=3 HEIGHT=1></TD></TR></TABLE><A NAME='{312}'/><TABLE BORDER=0 CELLSPACING=0 CELLPADDING=0 WIDTH='100%'><TR>  <TD ROWSPAN=5></TD>  <TD COLSPAN=3 HEIGHT=12></TD>  <TD ROWSPAN=5></TD></TR><TR>  <TD COLSPAN=3></TD></TR><TR><TD></TD>  <TD ALIGN=CENTER><FONT FACE='Times New Roman, Times, Serif' SIZE=2>Figure&nbsp;3-5<BR>&nbsp;XOR&nbsp;function&nbsp;using&nbsp;linear&nbsp;threshold<BR>&nbsp;units&nbsp;in&nbsp;a&nbsp;backpropagation&nbsp;network.</FONT></TD><TD></TD></TR><TR>  <TD COLSPAN=3></TD></TR><TR>  <TD COLSPAN=3 HEIGHT=1></TD></TR></TABLE><A NAME='{313}'/><TABLE BORDER=0 CELLSPACING=0 CELLPADDING=0><TR>  <TD ROWSPAN=5></TD>  <TD COLSPAN=3 HEIGHT=12></TD>  <TD ROWSPAN=5></TD></TR><TR>  <TD COLSPAN=3></TD></TR><TR><TD></TD>  <TD><FONT FACE='Times New Roman, Times, Serif' SIZE=3>the neuron will output a 0, and if the sum of the inputs is less than .01, then the output will be 1. After applying a training pattern of 1 on each of the two inputs, the neurons' outputs are computed and adjusted, as Figure 3-6 shows.</FONT></TD><TD></TD></TR><TR>  <TD COLSPAN=3></TD></TR><TR>  <TD COLSPAN=3 HEIGHT=1></TD></TR></TABLE><A NAME='{314}'/><TABLE BORDER=0 CELLSPACING=0 CELLPADDING=0><TR>  <TD ROWSPAN=5></TD>  <TD COLSPAN=3 HEIGHT=12></TD>  <TD ROWSPAN=5></TD></TR><TR>  <TD COLSPAN=3></TD></TR><TR><TD></TD>  <TD><FONT FACE='Times New Roman, Times, Serif' SIZE=3>Each of the neuron's output is noted for each node along with the sum of the neuron's internal signals. Neurons <I>a</I> and <I>b</I> are both sending 1's to the next layer. Neuron <I>x</I> gets two signals, one from neuron <I>a</I> and one from neuron <I>b.</I> The weight from neurons <I>a</I> to neuron<I> x</I> is W<I>xa,</I> and its value is 

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