We examine the problem of controlling divergences for latent space regularisation in variational autoencoders. Specifically, when aiming to reconstruct example $x\in\mathbb{R}^{m}$ via latent space $z\in\mathbb{R}^{n}$ ($n\leq m$), while balancing this against the need for generalisable latent representations. We present a regularisation mechanism based on the skew-geometric Jensen-Shannon divergence $\left(\textrm{JS}^{\textrm{G}_{\alpha}}\right)$. We find a variation in $\textrm{JS}^{\textrm{G}_{\alpha}}$, motivated by limiting cases, which leads to an intuitive interpolation between forward and reverse KL in the space of both distributions and divergences. We motivate its potential benefits for VAEs through low-dimensional examples, before presenting quantitative and qualitative results. Our experiments demonstrate that skewing our variant of $\textrm{JS}^{\textrm{G}_{\alpha}}$, in the context of $\textrm{JS}^{\textrm{G}_{\alpha}}$-VAEs, leads to better reconstruction and generation when compared to several baseline VAEs. Our approach is entirely unsupervised and utilises only one hyperparameter which can be easily interpreted in latent space.

In this paper, we introduce a novel form of value function, $Q(s, s')$, that expresses the utility of transitioning from a state $s$ to a neighboring state $s'$ and then acting optimally thereafter. In order to derive an optimal policy, we develop a forward dynamics model that learns to make next-state predictions that maximize this value. This formulation decouples actions from values while still learning off-policy. We highlight the benefits of this approach in terms of value function transfer, learning within redundant action spaces, and learning off-policy from state observations generated by sub-optimal or completely random policies. Code and videos are available at \url{sites.google.com/view/qss-paper}.

Measuring the similarity between data points often requires domain knowledge. This can in parts be compensated by relying on unsupervised methods such as latent-variable models, where similarity/distance is estimated in a more compact latent space. Prevalent is the use of the Euclidean metric, which has the drawback of ignoring information about similarity of data stored in the decoder, as captured by the framework of Riemannian geometry. Alternatives---such as approximating the geodesic---are often computationally inefficient, rendering the methods impractical. We propose an extension to the framework of variational auto-encoders allows learning flat latent manifolds, where the Euclidean metric is a proxy for the similarity between data points. This is achieved by defining the latent space as a Riemannian manifold and by regularising the metric tensor to be a scaled identity matrix. Additionally, we replace the compact prior typically used in variational auto-encoders with a recently presented, more expressive hierarchical one---and formulate the learning problem as a constrained optimisation problem. We evaluate our method on a range of data-sets, including a video-tracking benchmark, where the performance of our unsupervised approach nears that of state-of-the-art supervised approaches, while retaining the computational efficiency of straight-line-based approaches.

Generative Adversarial networks (GANs) have obtained remarkable success in many unsupervised learning tasks and unarguably, clustering is an important unsupervised learning problem. While one can potentially exploit the latent-space back-projection in GANs to cluster, we demonstrate that the cluster structure is not retained in the GAN latent space. In this paper, we propose ClusterGAN as a new mechanism for clustering using GANs. By sampling latent variables from a mixture of one-hot encoded variables and continuous latent variables, coupled with an inverse network (which projects the data to the latent space) trained jointly with a clustering specific loss, we are able to achieve clustering in the latent space. Our results show a remarkable phenomenon that GANs can preserve latent space interpolation across categories, even though the discriminator is never exposed to such vectors. We compare our results with various clustering baselines and demonstrate superior performance on both synthetic and real datasets.

In the field of machine learning, it is still a critical issue to identify and supervise the learned representation without manually intervention or intuition assistance to extract useful knowledge or serve for the latter tasks in machine learning. In this work, we focus on supervising the influential factors extracted by the variational autoencoder(VAE). The VAE is proposed to learn independent low dimension representation while facing the problem that sometimes pre-set factors are ignored. We argue that the mutual information of the input and each learned factor of the representation plays a necessary indicator. We find the VAE objective inclines to induce mutual information sparsity in factor dimension over the data intrinsic dimension and results in some non-influential factors whose function on data reconstruction could be ignored. We show mutual information also influences the lower bound of VAE's reconstruction error and latter classification task. To make such indicator applicable, we design an algorithm on calculating the mutual information for VAE and prove its consistency. Experimental results on Mnist, CelebA and Deap datasets show that mutual information can help determine influential factors, of which some are interpretable and can be used to further generation and classification tasks, and help discover the variant that connects with emotion on Deap dataset.