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Modern generative models are usually designed to match target distributions directly in the data space, where the intrinsic dimension of data can be much lower than the ambient dimension. We argue that this discrepancy may contribute to the difficulties in training generative models. We therefore propose to map both the generated and target distributions to a latent space using the encoder of a standard autoencoder, and train the generator (or decoder) to match the target distribution in the latent space. Specifically, we enforce the consistency in both the data space and the latent space with theoretically justified data and latent reconstruction losses. The resulting generative model, which we call a perceptual generative autoencoder (PGA), is then trained with a maximum likelihood or variational autoencoder (VAE) objective. With maximum likelihood, PGAs generalize the idea of reversible generative models to unrestricted neural network architectures and arbitrary number of latent dimensions. When combined with VAEs, PGAs substantially improve over the baseline VAEs in terms of sample quality. Compared to other autoencoder-based generative models using simple priors, PGAs achieve state-of-the-art FID scores on CIFAR-10 and CelebA.
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High dimensional data is often assumed to be concentrated on or near a low-dimensional manifold. Autoencoders (AE) is a popular technique to learn representations of such data by pushing it through a neural network with a low dimension bottleneck while minimizing a reconstruction error. Using high capacity AE often leads to a large collection of minimizers, many of which represent a low dimensional manifold that fits the data well but generalizes poorly. Two sources of bad generalization are: extrinsic, where the learned manifold possesses extraneous parts that are far from the data; and intrinsic, where the encoder and decoder introduce arbitrary distortion in the low dimensional parameterization. An approach taken to alleviate these issues is to add a regularizer that favors a particular solution; common regularizers promote sparsity, small derivatives, or robustness to noise. In this paper, we advocate an isometry (i.e., local distance preserving) regularizer. Specifically, our regularizer encourages: (i) the decoder to be an isometry; and (ii) the encoder to be the decoders pseudo-inverse, that is, the encoder extends the inverse of the decoder to the ambient space by orthogonal projection. In a nutshell, (i) and (ii) fix both intrinsic and extrinsic degrees of freedom and provide a non-linear generalization to principal component analysis (PCA). Experimenting with the isometry regularizer on dimensionality reduction tasks produces useful low-dimensional data representations.
Graphon is a nonparametric model that generates graphs with arbitrary sizes and can be induced from graphs easily. Based on this model, we propose a novel algorithmic framework called textit{graphon autoencoder} to build an interpretable and scalable graph generative model. This framework treats observed graphs as induced graphons in functional space and derives their latent representations by an encoder that aggregates Chebshev graphon filters. A linear graphon factorization model works as a decoder, leveraging the latent representations to reconstruct the induced graphons (and the corresponding observed graphs). We develop an efficient learning algorithm to learn the encoder and the decoder, minimizing the Wasserstein distance between the model and data distributions. This algorithm takes the KL divergence of the graph distributions conditioned on different graphons as the underlying distance and leads to a reward-augmented maximum likelihood estimation. The graphon autoencoder provides a new paradigm to represent and generate graphs, which has good generalizability and transferability.
A standard Variational Autoencoder, with a Euclidean latent space, is structurally incapable of capturing topological properties of certain datasets. To remove topological obstructions, we introduce Diffusion Variational Autoencoders with arbitrary manifolds as a latent space. A Diffusion Variational Autoencoder uses transition kernels of Brownian motion on the manifold. In particular, it uses properties of the Brownian motion to implement the reparametrization trick and fast approximations to the KL divergence. We show that the Diffusion Variational Autoencoder is capable of capturing topological properties of synthetic datasets. Additionally, we train MNIST on spheres, tori, projective spaces, SO(3), and a torus embedded in R3. Although a natural dataset like MNIST does not have latent variables with a clear-cut topological structure, training it on a manifold can still highlight topological and geometrical properties.
Variational autoencoders (VAE) are a powerful and widely-used class of models to learn complex data distributions in an unsupervised fashion. One important limitation of VAEs is the prior assumption that latent sample representations are independent and identically distributed. However, for many important datasets, such as time-series of images, this assumption is too strong: accounting for covariances between samples, such as those in time, can yield to a more appropriate model specification and improve performance in downstream tasks. In this work, we introduce a new model, the Gaussian Process (GP) Prior Variational Autoencoder (GPPVAE), to specifically address this issue. The GPPVAE aims to combine the power of VAEs with the ability to model correlations afforded by GP priors. To achieve efficient inference in this new class of models, we leverage structure in the covariance matrix, and introduce a new stochastic backpropagation strategy that allows for computing stochastic gradients in a distributed and low-memory fashion. We show that our method outperforms conditional VAEs (CVAEs) and an adaptation of standard VAEs in two image data applications.
Learning a model of perceptual similarity from a collection of objects is a fundamental task in machine learning underlying numerous applications. A common way to learn such a model is from relative comparisons in the form of triplets: responses to queries of the form Is object a more similar to b than it is to c?. If no consideration is made in the determination of which queries to ask, existing similarity learning methods can require a prohibitively large number of responses. In this work, we consider the problem of actively learning from triplets -finding which queries are most useful for learning. Different from previous active triplet learning approaches, we incorporate auxiliary information into our similarity model and introduce an active learning scheme to find queries that are informative for quickly learning both the relevant aspects of auxiliary data and the directly-learned similarity components. Compared to prior approaches, we show that we can learn just as effectively with much fewer queries. For evaluation, we introduce a new dataset of exhaustive triplet comparisons obtained from humans and demonstrate improved performance for different types of auxiliary information.
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