Work in deep clustering focuses on finding a single partition of data. However, high-dimensional data, such as images, typically feature multiple interesting characteristics one could cluster over. For example, images of objects against a background
could be clustered over the shape of the object and separately by the colour of the background. In this paper, we introduce Multi-Facet Clustering Variational Autoencoders (MFCVAE), a novel class of variational autoencoders with a hierarchy of latent variables, each with a Mixture-of-Gaussians prior, that learns multiple clusterings simultaneously, and is trained fully unsupervised and end-to-end. MFCVAE uses a progressively-trained ladder architecture which leads to highly stable performance. We provide novel theoretical results for optimising the ELBO analytically with respect to the categorical variational posterior distribution, and corrects earlier influential theoretical work. On image benchmarks, we demonstrate that our approach separates out and clusters over different aspects of the data in a disentangled manner. We also show other advantages of our model: the compositionality of its latent space and that it provides controlled generation of samples.
We introduce Ivy, a templated Deep Learning (DL) framework which abstracts existing DL frameworks. Ivy unifies the core functions of these frameworks to exhibit consistent call signatures, syntax and input-output behaviour. New high-level framework-a
gnostic functions and classes, which are usable alongside framework-specific code, can then be implemented as compositions of the unified low-level Ivy functions. Ivy currently supports TensorFlow, PyTorch, MXNet, Jax and NumPy. We also release four pure-Ivy libraries for mechanics, 3D vision, robotics, and differentiable environments. Through our evaluations, we show that Ivy can significantly reduce lines of code with a runtime overhead of less than 1% in most cases. We welcome developers to join the Ivy community by writing their own functions, layers and libraries in Ivy, maximizing their audience and helping to accelerate DL research through inter-framework codebases. More information can be found at https://ivy-dl.org.
