When training a variational autoencoder (VAE) on a given dataset, determining the optimal number of latent variables is mostly done by grid search -- a costly process in terms of computational time and carbon footprint. In this paper, we explore the intrinsic dimension estimation (IDE) of the data and latent representations learned by VAEs. We show that the discrepancies between the IDE of the mean and sampled representations of a VAE after only a few steps of training reveal the presence of passive variables in the latent space, which, in well-behaved VAEs, indicates a superfluous number of dimensions. Using this property, we propose FONDUE: an algorithm which quickly finds the number of latent dimensions after which the mean and sampled representations start to diverge (i.e., when passive variables are introduced), providing a principled method for selecting the number of latent dimensions for VAEs and autoencoders. "How many latent variables should I use for this model?" is a question that many practitioners using variational autoencoders (VAEs) or autoencoders (AEs) have to deal with. When the task has been studied before, this information is available in the literature for the specific architecture and dataset used. However, when it has not, answering this question becomes more complicated.

Real-world data often presents itself in the form of a network. Examples include social networks, citation networks, biological networks, and knowledge graphs. In their simplest form, networks represent real-life entities (e.g. people, papers, proteins, concepts) as nodes, and describe them in terms of their relations with other entities by means of edges between these nodes. This can be valuable for a range of purposes from the study of information diffusion to bibliographic analysis, bioinformatics research, and question-answering. The quality of networks is often problematic though, affecting downstream tasks. This paper focuses on the common problem where a node in the network in fact corresponds to multiple real-life entities. In particular, we introduce FONDUE, an algorithm based on network embedding for node disambiguation. Given a network, FONDUE identifies nodes that correspond to multiple entities, for subsequent splitting. Extensive experiments on twelve benchmark datasets demonstrate that FONDUE is substantially and uniformly more accurate for ambiguous node identification compared to the existing state-of-the-art, at a comparable computational cost, while less optimal for determining the best way to split ambiguous nodes.