Meshes are ubiquitous in visual computing and simulation, yet most existing machine learning techniques represent meshes only indirectly, e.g. as the level set of a scalar field or deformation of a template, or as a disordered triangle soup lacking local structure. This work presents a scheme to directly generate manifold, polygonal meshes of complex connectivity as the output of a neural network. Our key innovation is to define a continuous latent connectivity space at each mesh vertex, which implies the discrete mesh. In particular, our vertex embeddings generate cyclic neighbor relationships in a halfedge mesh representation, which gives a guarantee of edge-manifoldness and the ability to represent general polygonal meshes. This representation is well-suited to machine learning and stochastic optimization, without restriction on connectivity or topology. We first explore the basic properties of this representation, then use it to fit distributions of meshes from large datasets. The resulting models generate diverse meshes with tessellation structure learned from the dataset population, with concise details and high-quality mesh elements. In applications, this approach not only yields high-quality outputs from generative models, but also enables directly learning challenging geometry processing tasks such as mesh repair.

Few-shot classification is the task of predicting the category of an example from a set of few labeled examples. The number of labeled examples per category is called the number of shots (or shot number). Recent works tackle this task through meta-learning, where a meta-learner extracts information from observed tasks during meta-training to quickly adapt to new tasks during meta-testing. In this formulation, the number of shots exploited during meta-training has an impact on the recognition performance at meta-test time. Generally, the shot number used in meta-training should match the one used in meta-testing to obtain the best performance. We introduce a theoretical analysis of the impact of the shot number on Prototypical Networks, a state-of-the-art few-shot classification method. From our analysis, we propose a simple method that is robust to the choice of shot number used during meta-training, which is a crucial hyperparameter. The performance of our model trained for an arbitrary meta-training shot number shows great performance for different values of meta-testing shot numbers. We experimentally demonstrate our approach on different few-shot classification benchmarks.

Then, a PLDA model is trained to measure thesimilarity of i-vectors. Replacing traditional i-vectors with speaker embedding models based on deep neural networks haslead to improvement in SV [4, 3]. Nonetheless, a PLDA classifier is still needed to compare the similarity of embeddings. More recently, end-to-end training of an embedding networkthat makes decision by comparing distance in the embedding to a cross-validated threshold outperformed traditional methods. For detailed comparison between embedding networksand i-vector based methods, we refer the reader to [6, 4, 3]. Building on top of these studies, our work focuses on the comparison between two different approaches for deep metric learning (TL [5, 6, 7, 8] and PNL [10]) for end-to-end speaker embedding models. Deep metric learning: End-to-end speaker embedding models can be seen as a form of deep metric learning, which has been widely studied in the machine learning literature. Early examples of metric learning with neural networks include signature[11] and face verification [12]. Both compare pairs of examples with standard similarity functions (e.g.