Deep convolutional neural networks are widely used to learn feature spaces for image classification tasks. We propose cam-softmax, a generalisation of the final layer activations and softmax function, that encourages deep feature spaces to exhibit high intra-class compactness and high inter-class separability. We provide an algorithm to automatically adapt the method's main hyperparameter so that it gradually diverges from the standard activations and softmax method during training. We report experiments using CASIA-Webface, LFW, and YTF face datasets demonstrating that cam-softmax leads to representations well suited to open-set face recognition and face pair matching. Furthermore, we provide empirical evidence that cam-softmax provides some robustness to class labelling errors in training data, making it of potential use for deep learning from large datasets with poorly verified labels.