Deep Neural Networks, What is Alexnet output and loss function relationship?

Question

I am trying to understand DNN with Matconvnet DagNN. I've a question based on the following last two layers of a net which uses euclidean loss for regression

net.addLayer('fc9', dagnn.Conv('size', [1 1 4096 1], 'hasBias', true, 'stride', [1,1], 'pad', [0 0 0 0]), {'drop8'}, {'prediction'},  {'conv10f'  'conv10b'});
 net.addLayer('l2_loss', dagnn.L2Loss(), {'prediction', 'label'}, {'objective'});

where the code for L2Loss is

function Y=vl_nnL2(X,c,dzdy)
 c=reshape(c,size(X));
 if nargin == 2 || (nargin == 3 && isempty(dzdy))
    diff_xc=(bsxfun(@minus, X,(c)));
    Y=diff_xc.^2;
 elseif nargin == 3 && ~isempty(dzdy)
    Y=(X-c).*dzdy;
 end
end

X is the output of fc9 layer, which is the feature vector of length 100 (batch size), and c is the labels.

1. In the loss functions, how can the two be compared? X is an activation, a vector which is not probability.. I guess. and C is labels, integer values ranging from..0-10. So how can they be compared and subtracted, for instance? I dont know if there is any relationship between the two?
2. Also, how does backpropagation compare fc9 output and labels for minimization?

*-----------new modified L2 regression function

function Y=vl_nnL2_(X,c,dzdy)
    c=reshape(c,size(X));
    [~,chat] = max(X,[],3) ;
    [~,lchat] = max(c,[],3) ; 
if nargin == 2 || (nargin == 3 && isempty(dzdy))
      t = (chat-lchat).^ 2 ;
     Y=sum(sum(t));
elseif nargin == 3 && ~isempty(dzdy)
  ch=squeeze(chat);
  aa1=repmat(ch',35,1);
  lch=squeeze(lchat);
  aa2=repmat(lch',35,1);
  t = (chat-lchat);
  Y = dzdy.*(aa1-aa2)*2;
Y = single(reshape(Y,size(X)));

end
end

Answer 1

"if nargin == 2 || (nargin == 3 && isempty(dzdy))" checks if it's forward mode.

In the forward mode, you compute (prediction - label).^2:

diff_xc=(bsxfun(@minus, X,(c)));
Y=diff_xc.^2;

The derivative of L2 loss w.r.t. prediction is 2*(prediction - label). Thus we have

Y=(X-c).*dzdy;

in your code. Here the author of your code isn't rigorous enough to put the constant 2*. But in general it will work since it's just a constant scaling factor on your gradients. dzdy is the gradient from downstream layers. If this layer is the last one, dzdy=1, which manually provided by MatConvnet.

c must be of the same size as X since its' regression.

More comments coming. Let me know if you have other questions. I'm pretty familiar with MatConvNet.