Neural Networks

 Revision as of 06:04, 26 February 2011 (view source)Ang (Talk | contribs)← Older edit Revision as of 06:23, 26 February 2011 (view source)Ang (Talk | contribs) Newer edit → Line 59: Line 59: In this figure, we have used circles to also denote the inputs to the network.  The circles In this figure, we have used circles to also denote the inputs to the network.  The circles - labeled +1'' are called {\bf bias units}, and correspond to the intercept term. + labeled +1'' are called '''bias units''', and correspond to the intercept term. - The leftmost layer of the network is called the {\bf input layer}, and the + The leftmost layer of the network is called the '''input layer''', and the - rightmost layer the {\bf output layer} (which, in this example, has only one + rightmost layer the '''output layer''' (which, in this example, has only one - node).  The middle layer of nodes is called the {\bf hidden layer}, because its + node).  The middle layer of nodes is called the '''hidden layer''', because its values are not observed in the training set.  We also say that our example values are not observed in the training set.  We also say that our example - neural network has 3 {\bf input units} (not counting the bias unit), 3 {\bf + neural network has 3 '''input units''' (not counting the bias unit), 3 - hidden units}, and 1 {\bf output unit}. + '''hidden units''', and 1 '''output unit'''. We will let $n_l$ We will let $n_l$ Line 79: Line 79: the value +1.  We also let $s_l$ denote the number of nodes in layer $l$ (not counting the bias unit). the value +1.  We also let $s_l$ denote the number of nodes in layer $l$ (not counting the bias unit). - We will write $a^{(l)}_i$ to denote the {\bf activation} (meaning output value) of + We will write $a^{(l)}_i$ to denote the '''activation''' (meaning output value) of unit $i$ in layer $l$.  For $l=1$, we also use $a^{(1)}_i = x_i$ to denote the $i$-th input. unit $i$ in layer $l$.  For $l=1$, we also use $a^{(1)}_i = x_i$ to denote the $i$-th input. Given a fixed setting of Given a fixed setting of