I am solving multi-label classification problem (assigning each image 1 to N labels) and want to use neural network (like in this post). Does this approach take correlations between class labels into account? Or are the predictions for individual labels completely independent (like in the binary relevance approach)?
For sure correlation is taken into account since your hidden layer mixing all signals from input together via fully connected layer. Your network will learn about co-occurrence of labels, however it's done in not-random way, I meant your network would find some deterministic rules for generating the best output. Be aware that this only 'projection' of statistical correlation into NN's linear space forced by your NN's optimization function. You won't have any direct influence on that