In real-life scenarios, there are many variations in sizes of objects of the same category and the objects are not always placed at a fixed distance from the camera. This results in objects taking up an arbitrary size of pixels in the image. Vanilla CNNs are by design only translation equivariant and thus have to learn separate filters for scaled variants of the same objects. Recently, scale-equivariant approaches have been developed that share features across a set of pre-determined fixed scales. We further refer to this set of scales as the internal scales. Existing work gives little information about how to best choose the internal scales when the underlying distribution of sizes, or scale distribution, in the dataset, is known. In this work, we develop a model of how the features at different internal scales are used for samples containing differently-sized objects. The proposed model return comparable internal scales to the best-performing internal scales for different data scale distribution of various width. However, in most cases, the scale distribution is not known. Compared to previous scale-equivariant methods, we do not treat the internal scales as a fixed set but directly optimise them with regard to the loss, removing the need for prior knowledge about the data scale distribution. We parameterise the internal scales by the smallest scale which we refer to as σbasis, and the Internal Scale Range (ISR) that models the ratio between the smallest and largest scale. By varying the ISR, we learn the range of the scales the model is equivariant to. We show that our method can learn the internal scales on various data scale distributions and can better adapt the internal scales than other parameterisations. Finally, we compare our scale learning approach and other parameterisations to current State-of-the-art scale-equivariant approaches on the MNIST-Scale dataset.

Multi-label learning is becoming more and moreimportant as real-world data often contains multi-ple labels. The dataset used for learning such aclassifier is of great importance. Acquiring a cor-rectly labelled dataset is however a difficult task.Active learning is a method which can, given anoisy dataset, identify important instances for anexpert to label. This greatly reduces the amountof instances needed to train an accurate classi-fier, and thus reduces the cost of cleaning a noisydataset. Therefore, this paper aims to present an ac-tive learning algorithm, focused on wrongly labeleddata, combined with a deep neural network formulti-label image classification. The proposed ac-tive learning solution is divided into two measures;a mislabelling likelihood and an informativenessmeasure together with an option to identify anduse highly probable clean instances in the dataset.Experiments performed on the real world dataset,called Microsoft COCO, with 20, 40 and 60% in-jected label noise show that Multi-AL outperformsthe current state-of-the-art multi-label learning al-gorithm called ASL by 28% while only using 600labelled instances in total and 250 extracted ’clean’instances. Multi-AL additionally outperforms ran-dom sampling by 3% on average for 20 and 40%random label noise when sampling from a wronglylabelled dataset of 23k instances.