Multi-label classification with neural networks: Are correlations between class labels taken into account? 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)?
 A: 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
A: As stated by @podludek as long as you have a hidden layer your neural network should be able to learn label correlations.
There is also indeed a risk that your neural network learns deterministic rules of label co-occurence, by "assigning" some hidden units to some particular label sets. One way to alleviate this would be to use dropout, to force your neural network to learn general representations of your examples rather than making a deterministic encoding of some specific training data points.
You can for instance refer to this paper investigating this label correlation with NNs on text data.
So in a nutshell: yes NNs can inherently capture some multilabel correlations. Still, there exist several methods to help them capture the correlations better, and as always in ML, there's no free lunch and you will have to try and check what works best for your setting.
