I'm looking at the cross-entropy cost function found in this tutorial:

$$C = -\frac{1}{n} \sum_x [y \ln a+(1−y)\ln(1−a)]$$

What exactly are we summing over? It is, of course, over $x$, but $y$ and $a$ don't change with $x$. All of the $x$'s are inputs into the one $a$. $a$ is even defined in the paragraph above the equation as a function of the sum of all $w$'s and $x$'s.

Also, $n$ is defined as the number of inputs into this particular neuron, correct? It is worded as "the total number of items of training data".

###Edit:

Am I correct in thinking that

$$C= -\frac{1}{n} \sum_x [y \ln a+(1−y)\ln(1−a)]$$

would be the cost function for the entire network, whereas

$$C = [y \ln a+(1−y)\ln(1−a)]$$

would be the cost for the individual neuron? Shouldn't the sum be over each output neuron?

I'm looking at the cross-entropy cost function found in this tutorial:

$$C = -\frac{1}{n} \sum_x [y \ln a+(1−y)\ln(1−a)]$$

What exactly are we summing over? It is, of course, over $x$, but $y$ and $a$ don't change with $x$. All of the $x$'s are inputs into the one $a$. $a$ is even defined in the paragraph above the equation as a function of the sum of all $w$'s and $x$'s.

Also, $n$ is defined as the number of inputs into this particular neuron, correct? It is worded as "the total number of items of training data".

Edit:

Am I correct in thinking that

$$C= -\frac{1}{n} \sum_x [y \ln a+(1−y)\ln(1−a)]$$

would be the cost function for the entire network, whereas

$$C = [y \ln a+(1−y)\ln(1−a)]$$

would be the cost for the individual neuron? Shouldn't the sum be over each output neuron?

I'm looking at the cross-entropy cost function found in this tutorial:

$$ C = -\frac{1}{n} \sum x [y \ln a+(1−y)\ln(1−a)] $$

What exactly are we summing over? It is, of course, over $x$, but $y$ and $a$ don't change with $x$. All of the $x$'s are inputs into the one $a$. $a$ is even defined in the paragraph above the equation as a function of the sum of all $w$'s and $x$'s.

Also, $n$ is defined as the number of inputs into this particular neuron, correct? It is worded as "the total number of items of training data".

###Edit:

Am I correct in thinking that

$$ C= -\frac{1}{n} \sum x [y \ln a+(1−y)\ln(1−a)] $$

would be the cost function for the entire network, whereas

$$ C = [y \ln a+(1−y)\ln(1−a)] $$

would be the cost for the individual neuron? Shouldn't the sum be over each output neuron?

I'm looking at the cross-entropy cost function found in this tutorial:

$$C = -\frac{1}{n} \sum_x [y \ln a+(1−y)\ln(1−a)]$$

What exactly are we summing over? It is, of course, over $x$, but $y$ and $a$ don't change with $x$. All of the $x$'s are inputs into the one $a$. $a$ is even defined in the paragraph above the equation as a function of the sum of all $w$'s and $x$'s.

Also, $n$ is defined as the number of inputs into this particular neuron, correct? It is worded as "the total number of items of training data".

###Edit:

Am I correct in thinking that

$$C= -\frac{1}{n} \sum_x [y \ln a+(1−y)\ln(1−a)]$$

would be the cost function for the entire network, whereas

$$C = [y \ln a+(1−y)\ln(1−a)]$$

would be the cost for the individual neuron? Shouldn't the sum be over each output neuron?

I'm looking at the cost function found here: http://neuralnetworksanddeeplearning.com/chap3.html#introducing_the_cross-entropy_cost_function

What are we summing over in: C= −1/n ∑x [ylna+(1−y)ln(1−a)]

It is of course over x, but y and a don't change with x. All of the x's are inputs into the one a.

a is even defined in the paragraph above the equation as a function of the sum of all w's and x's.

Also, n is defined as the number of inputs into this particular neuron, correct? It is worded as 'total number of training data'.

Edit: C= −1/n ∑x [ylna+(1−y)ln(1−a)] is the cost function for the entire network, whereas C= [ylna+(1−y)ln(1−a)] would be the cost for the individual neuron? Is that it? But shouldn't the sum be over each output neuron?

I'm looking at the cross-entropy cost function found in this tutorial:

$$ C = -\frac{1}{n} \sum x [y \ln a+(1−y)\ln(1−a)] $$

What exactly are we summing over? It is, of course, over $x$, but $y$ and $a$ don't change with $x$. All of the $x$'s are inputs into the one $a$. $a$ is even defined in the paragraph above the equation as a function of the sum of all $w$'s and $x$'s.

Also, $n$ is defined as the number of inputs into this particular neuron, correct? It is worded as "the total number of items of training data".

###Edit:

Am I correct in thinking that

$$ C= -\frac{1}{n} \sum x [y \ln a+(1−y)\ln(1−a)] $$

would be the cost function for the entire network, whereas

$$ C = [y \ln a+(1−y)\ln(1−a)] $$

would be the cost for the individual neuron? Shouldn't the sum be over each output neuron?