text: The authors propose a loss that is based on a RBF loss for metric learning and incorporates additional per exemplar weights in the index for classification.  Significant improvements over softmax are shown on several datasets. IMHO, this could be a worthwhile paper,  but the framing of the paper into existing literature is lacking  and thus it appears as if the authors are re-inventing the wheel (NCA loss) under a different name (RBF solver). The specific problems are: - The authors completely miss the connection to NCA loss (https://papers.nips.cc/paper/2566-neighbourhood-components-analysis.pdf)  and thus appear to be re-inventing the wheel.   - The proposed metric learning scenario is exactly as proposed in the NCA loss works,  while the classification approach adds an interesting twist by learning per exemplar weights.  I haven't encountered this before and it could make an interesting proposal.  Of course the benefit of this should be evaluated in ablation studies ( Tab 3 shows one experiment with marginal improvements). - The authors' use of 'solver' seems uncommon and confusing.  What is proposed is a loss in addition to building a weighted index in the case of classification. - In the metric learning comparison with softmax (end of page 9) the authors mentions that a Gaussian standard deviation for softmax is learned.  It appears as if the authors use the softmax logits as embedding  whereas the more common approach is to use the bottleneck layer.  This is also indicated by the discussion at the end of page 10 where the authors mention that softmax is restricted to axis aligned embeddings.  All softmax metric learning experiments should be carried out on appropriately sized bottleneck layers. - Some of the motivations of what the various methods learn seem flawed,  e.g. triplet loss CAN learn multiple modes per class and there is nothing in the Softmax loss that encourages the classes to fill a large region of the space. - Why don't the authors compare on ImageNet? Some positive points: - The authors mention in Sec 3.3 that updating the RBF centres is not required.  This is a crucial point that should be made a centerpiece of this work,  as there are many metric learning works that struggle with this.  Additional experiments that can investigate this point would greatly contribute to a well rounded paper. - The numbers reported in Tab 1 show very significant improvements If the paper was re-framed and builds on top of the already existing NCA loss, there could be valuable contributions in this paper.  The experimental comparisons are lacking in some respect,  as the comparison with Softmax as a metric learning method seems uncommon, i.e. using the logits instead of the bottleneck layer.  I encourage the authors to extend the paper and flesh out some of the experiments and then submit it again.