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 latentspace 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. 1

The design of codes for communicating reliably over a statistically well defined channel is an important endeavor involving deep mathematical research and wide-ranging practical applications. In this work, we present the first family of codes obtained via deep learning, which significantly beats state-of-the-art codes designed over several decades of research. The communication channel under consideration is the Gaussian noise channel with feedback, whose study was initiated by Shannon; feedback is known theoretically to improve reliability of communication, but no practical codes that do so have ever been successfully constructed.We break this logjam by integrating information theoretic insights harmoniously with recurrent-neural-network based encoders and decoders to create novel codes that outperform known codes by 3 orders of magnitude in reliability. We also demonstrate several desirable properties of the codes: (a) generalization to larger block lengths, (b) composability with known codes, (c) adaptation to practical constraints. This result also has broader ramifications for coding theory: even when the channel has a clear mathematical model, deep learning methodologies, when combined with channel-specific information-theoretic insights, can potentially beat state-of-the-art codes constructed over decades of mathematical research.

Singlecell transcriptome sequencing now routinely samples thousands of cells, potentially providing enough data to reconstruct causal gene regulatory networks from observational data. Here, we present Scribe, a toolkit for detecting and visualizing causal regulatory interactions between genes and explore the potential for singlecell experiments to power network reconstruction. Scribe employs Restricted Directed Information to determine causality by estimating the strength of information transferred from a potential regulator to its downstream target. We apply Scribe and other leading approaches for causal network reconstruction to several types of singlecell measurements and show that there is a dramatic drop in performance for "pseudotime" ordered singlecell data compared to true time series data. We demonstrate that performing causal inference requires temporal coupling between measurements. We show that methods such as "RNA velocity" restore some degree of coupling through an analysis of chromaffin cell fate commitment. These analyses therefore highlight an important shortcoming in experimental and computational methods for analyzing gene regulation at singlecell resolution and point the way towards overcoming it..

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