criterion = ClassNLLCriterion()

The negative log likelihood criterion. It is useful to train a classication problem with n classes. The input given through a forward() is expected to contain log-probabilities of each class: input has to be a 1D tensor of size n. Obtaining log-probabilities in a neural network is easily achieved by adding a LogSoftMax layer in the last layer of your neural network.

This criterion expect a class index (1 to the number of class) as target when calling forward(input, target) and backward(input, target).

The loss can be described as: 

loss(x, class) = forward(x, class) = -x[class]

The following is a code fragment showing how to make a gradient step given an input x, a desired output y (an integer 1 to n, in this case n = 2 classes), a network mlp and a learning rate learningRate: 

function gradUpdate(mlp,x,y,learningRate)
  local criterion = nn.ClassNLLCriterion()
  pred = mlp:forward(x)
  local err = criterion:forward(pred, y); 
  mlp:zeroGradParameters();
  local t = criterion:backward(pred, y);
  mlp:backward(x, t);
  mlp:updateParameters(learningRate);
end