Geometry of Deep Generative Models for Disentangled Representations

Deep generative models like variational autoencoders approximate the intrinsic geometry of high dimensional data manifolds by learning low-dimensional latent-space variables and an embedding function. The geometric properties of these latent spaces has been studied under the lens of Riemannian geometry; via analysis of the non-linearity of the generator function. In new developments, deep generative models have been used for learning semantically meaningful `disentangled' representations; that capture task relevant attributes while being invariant to other attributes. In this work, we explore the geometry of popular generative models for disentangled representation learning. We use several metrics to compare the properties of latent spaces of disentangled representation models in terms of class separability and curvature of the latent-space. The results we obtain establish that the class distinguishable features in the disentangled latent space exhibits higher curvature as opposed to a variational autoencoder. We evaluate and compare the geometry of three such models with variational autoencoder on two different datasets. Further, our results show that distances and interpolation in the latent space are significantly improved with Riemannian metrics derived from the curvature of the space. We expect these results will have implications on understanding how deep-networks can be made more robust, generalizable, as well as interpretable.Comment: Accepted at ICVGIP, 201

Disentangling Multiple Features in Video Sequences using Gaussian Processes in Variational Autoencoders

We introduce MGP-VAE (Multi-disentangled-features Gaussian Processes Variational AutoEncoder), a variational autoencoder which uses Gaussian processes (GP) to model the latent space for the unsupervised learning of disentangled representations in video sequences. We improve upon previous work by establishing a framework by which multiple features, static or dynamic, can be disentangled. Specifically we use fractional Brownian motions (fBM) and Brownian bridges (BB) to enforce an inter-frame correlation structure in each independent channel, and show that varying this structure enables one to capture different factors of variation in the data. We demonstrate the quality of our representations with experiments on three publicly available datasets, and also quantify the improvement using a video prediction task. Moreover, we introduce a novel geodesic loss function which takes into account the curvature of the data manifold to improve learning. Our experiments show that the combination of the improved representations with the novel loss function enable MGP-VAE to outperform the baselines in video prediction

Product of Orthogonal Spheres Parameterization for Disentangled Representation Learning

Learning representations that can disentangle explanatory attributes underlying the data improves interpretabilty as well as provides control on data generation. Various learning frameworks such as VAEs, GANs and auto-encoders have been used in the literature to learn such representations. Most often, the latent space is constrained to a partitioned representation or structured by a prior to impose disentangling. In this work, we advance the use of a latent representation based on a product space of Orthogonal Spheres PrOSe. The PrOSe model is motivated by the reasoning that latent-variables related to the physics of image-formation can under certain relaxed assumptions lead to spherical-spaces. Orthogonality between the spheres is motivated via physical independence models. Imposing the orthogonal-sphere constraint is much simpler than other complicated physical models, is fairly general and flexible, and extensible beyond the factors used to motivate its development. Under further relaxed assumptions of equal-sized latent blocks per factor, the constraint can be written down in closed form as an ortho-normality term in the loss function. We show that our approach improves the quality of disentanglement significantly. We find consistent improvement in disentanglement compared to several state-of-the-art approaches, across several benchmarks and metrics.Comment: Accepted at British Machine Vision Conference (BMVC) 201

Mixing Consistent Deep Clustering

Finding well-defined clusters in data represents a fundamental challenge for many data-driven applications, and largely depends on good data representation. Drawing on literature regarding representation learning, studies suggest that one key characteristic of good latent representations is the ability to produce semantically mixed outputs when decoding linear interpolations of two latent representations. We propose the Mixing Consistent Deep Clustering method which encourages interpolations to appear realistic while adding the constraint that interpolations of two data points must look like one of the two inputs. By applying this training method to various clustering (non-)specific autoencoder models we found that using the proposed training method systematically changed the structure of learned representations of a model and it improved clustering performance for the tested ACAI, IDEC, and VAE models on the MNIST, SVHN, and CIFAR-10 datasets. These outcomes have practical implications for numerous real-world clustering tasks, as it shows that the proposed method can be added to existing autoencoders to further improve clustering performance

Dimensionality compression and expansion in Deep Neural Networks

Datasets such as images, text, or movies are embedded in high-dimensional spaces. However, in important cases such as images of objects, the statistical structure in the data constrains samples to a manifold of dramatically lower dimensionality. Learning to identify and extract task-relevant variables from this embedded manifold is crucial when dealing with high-dimensional problems. We find that neural networks are often very effective at solving this task and investigate why. To this end, we apply state-of-the-art techniques for intrinsic dimensionality estimation to show that neural networks learn low-dimensional manifolds in two phases: first, dimensionality expansion driven by feature generation in initial layers, and second, dimensionality compression driven by the selection of task-relevant features in later layers. We model noise generated by Stochastic Gradient Descent and show how this noise balances the dimensionality of neural representations by inducing an effective regularization term in the loss. We highlight the important relationship between low-dimensional compressed representations and generalization properties of the network. Our work contributes by shedding light on the success of deep neural networks in disentangling data in high-dimensional space while achieving good generalization. Furthermore, it invites new learning strategies focused on optimizing measurable geometric properties of learned representations, beginning with their intrinsic dimensionality.Comment: Submitted to NeurIPS 2019. First two authors contributed equall