Is it possible to have a negative output using only ReLU activation functions, but not in the final layer? I know that if you use an ReLU activation function at a node in the neural network, the output of that node will be non-negative. I am wondering if it is possible to have a negative output in the final layer, provided that you do not use any activation functions in the final layer, and all the activation functions in the previous hidden layers are ReLU?
Yes, if there's no activation function in the last layer, the weights could simply be negative there, so the network would multiply a positive value with a negative weight, therefore outputting a negative value.
There is still an activation function, but it is the identity.