Self-Supervised Learning (SSL) frameworks became the standard for learning robust class representations by benefiting from large unlabeled datasets. For Speaker Verification (SV), most SSL systems rely on contrastive-based loss functions. We explore different ways to improve the performance of these techniques by revisiting the NT-Xent contrastive loss. Our main contribution is the definition of the NT-Xent-AM loss and the study of the importance of Additive Margin (AM) in SimCLR and MoCo SSL methods to further separate positive from negative pairs. Despite class collisions, we show that AM enhances the compactness of same-speaker embeddings and reduces the number of false negatives and false positives on SV. Additionally, we demonstrate the effectiveness of the symmetric contrastive loss, which provides more supervision for the SSL task. Implementing these two modifications to SimCLR improves performance and results in 7.85% EER on VoxCeleb1-O, outperforming other equivalent methods.

Most state-of-the-art self-supervised speaker verification systems rely on a contrastive-based objective function to learn speaker representations from unlabeled speech data. We explore different ways to improve the performance of these methods by: (1) revisiting how positive and negative pairs are sampled through a "symmetric" formulation of the contrastive loss; (2) introducing margins similar to AM-Softmax and AAM-Softmax that have been widely adopted in the supervised setting. We demonstrate the effectiveness of the symmetric contrastive loss which provides more supervision for the self-supervised task. Moreover, we show that Additive Margin and Additive Angular Margin allow reducing the overall number of false negatives and false positives by improving speaker separability. Finally, by combining both techniques and training a larger model we achieve 7.50% EER and 0.5804 minDCF on the VoxCeleb1 test set, which outperforms other contrastive self supervised methods on speaker verification.

Aiming towards the development of a general clustering theory, we discuss abstract axiomatization for clustering. In this respect, we follow up on the work of Kelinberg, (Kleinberg) that showed an impossibility result for such axiomatization. We argue that an impossibility result is not an inherent feature of clustering, but rather, to a large extent, it is an artifact of the specific formalism used in Kleinberg. As opposed to previous work focusing on clustering functions, we propose to address clustering quality measures as the primitive object to be axiomatized. We show that principles like those formulated in Kleinberg's axioms can be readily expressed in the latter framework without leading to inconsistency. A clustering-quality measure is a function that, given a data set and its partition into clusters, returns a non-negative real number representing how `strong' or `conclusive' the clustering is. We analyze what clustering-quality measures should look like and introduce a set of requirements (`axioms') that express these requirement and extend the translation of Kleinberg's axioms to our framework. We propose several natural clustering quality measures, all satisfying the proposed axioms. In addition, we show that the proposed clustering quality can be computed in polynomial time.