Nearest Neighbour Radial Basis Function Solvers for Deep Neural Networks

We present a radial basis function solver for convolutional neural networks that can be directly applied to both distance metric learning and classification problems. Our method treats all training features from a deep neural network as radial basis function centres and computes loss by summing the influence of a feature's nearby centres in the embedding space. Having a radial basis function centred on each training feature is made scalable by treating it as an approximate nearest neighbour search problem. End-to-end learning of the network and solver is carried out, mapping high dimensional features into clusters of the same class. This results in a well formed embedding space, where semantically related instances are likely to be located near one another, regardless of whether or not the network was trained on those classes. The same loss function is used for both the metric learning and classification problems. We show that our radial basis function solver outperforms state-of-the-art embedding approaches on the Stanford Cars196 and CUB-200-2011 datasets. Additionally, we show that when used as a classifier, our method outperforms a conventional softmax classifier on the CUB-200-2011, Stanford Cars196, Oxford 102 Flowers and Leafsnap fine-grained classification datasets.