arXiv subjects

Ricky T. Q. Chen

Publications and source records attributed to Ricky T. Q. Chen.

59 records · Page 4Linked to original sources

arXiv2019

Neural Networks with Cheap Differential Operators

Gradients of neural networks can be computed efficiently for any architecture, but some applications require differential operators with higher time complexity. We describe a family of restricted neural network architectures that allow efficient computation of a family of differential operators involving dimension-wise derivatives, used in cases such as computing the divergence. Our proposed architecture has a Jacobian matrix composed of diagonal and hollow (non-diagonal) components. We can then modify the backward computation graph to extract dimension-wise derivatives efficiently with automatic differentiation. We demonstrate these cheap differential operators for solving root-finding subproblems in implicit ODE solvers, exact density evaluation for continuous normalizing flows, and evaluating the Fokker--Planck equation for training stochastic differential equation models.

cs.LG↗

arXiv2019

Latent ODEs for Irregularly-Sampled Time Series

Time series with non-uniform intervals occur in many applications, and are difficult to model using standard recurrent neural networks (RNNs). We generalize RNNs to have continuous-time hidden dynamics defined by ordinary differential equations (ODEs), a model we call ODE-RNNs. Furthermore, we use ODE-RNNs to replace the recognition network of the recently-proposed Latent ODE model. Both ODE-RNNs and Latent ODEs can naturally handle arbitrary time gaps between observations, and can explicitly model the probability of observation times using Poisson processes. We show experimentally that these ODE-based models outperform their RNN-based counterparts on irregularly-sampled data.

cs.LG↗

arXiv2019

Invertible Residual Networks

We show that standard ResNet architectures can be made invertible, allowing the same model to be used for classification, density estimation, and generation. Typically, enforcing invertibility requires partitioning dimensions or restricting network architectures. In contrast, our approach only requires adding a simple normalization step during training, already available in standard frameworks. Invertible ResNets define a generative model which can be trained by maximum likelihood on unlabeled data. To compute likelihoods, we introduce a tractable approximation to the Jacobian log-determinant of a residual block. Our empirical evaluation shows that invertible ResNets perform competitively with both state-of-the-art image classifiers and flow-based generative models, something that has not been previously achieved with a single architecture.

cs.LG↗

arXiv2019

Isolating Sources of Disentanglement in Variational Autoencoders

We decompose the evidence lower bound to show the existence of a term measuring the total correlation between latent variables. We use this to motivate our $β$-TCVAE (Total Correlation Variational Autoencoder), a refinement of the state-of-the-art $β$-VAE objective for learning disentangled representations, requiring no additional hyperparameters during training. We further propose a principled classifier-free measure of disentanglement called the mutual information gap (MIG). We perform extensive quantitative and qualitative experiments, in both restricted and non-restricted settings, and show a strong relation between total correlation and disentanglement, when the latent variables model is trained using our framework.

cs.LG↗

arXiv2018

FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models

A promising class of generative models maps points from a simple distribution to a complex distribution through an invertible neural network. Likelihood-based training of these models requires restricting their architectures to allow cheap computation of Jacobian determinants. Alternatively, the Jacobian trace can be used if the transformation is specified by an ordinary differential equation. In this paper, we use Hutchinson's trace estimator to give a scalable unbiased estimate of the log-density. The result is a continuous-time invertible generative model with unbiased density estimation and one-pass sampling, while allowing unrestricted neural network architectures. We demonstrate our approach on high-dimensional density estimation, image generation, and variational inference, achieving the state-of-the-art among exact likelihood methods with efficient sampling.

cs.LG↗