The objective learning formulation is essential for the success of convolutional neural networks. In this work, we analyse thoroughly the standard learning objective functions for multi-class classification CNNs: softmax regression (SR) for single-label scenario and logistic regression (LR) for multi-label scenario. Our analyses lead to an inspiration of exploiting LR for single-label classification learning, and then the disclosing of the negative class distraction problem in LR. To address this problem, we develop two novel LR based objective functions that not only generalise the conventional LR but importantly turn out to be competitive alternatives to SR in single label classification. Extensive comparative evaluations demonstrate the model learning advantages of the proposed LR functions over the commonly adopted SR in single-label coarse-grained object categorisation and cross-class fine-grained person instance identification tasks. We also show the performance superiority of our method on clothing attribute classification in comparison to the vanilla LR function.