In this work, we present new theoretical results on convolutional generative neural networks, in particular their invertibility (i.e., the recovery of input latent code given the network output). The study of network inversion problem is motivated by image inpainting and the mode collapse problem in training GAN. Network inversion is highly non-convex, and thus is typically computationally intractable and without optimality guarantees. However, we rigorously prove that, under some mild technical assumptions, the input of a two-layer convolutional generative network can be deduced from the network output efficiently using simple gradient descent. This new theoretical finding implies that the mapping from the low-dimensional latent space to the high-dimensional image space is bijective (i.e., one-to-one). In addition, the same conclusion holds even when the network output is only partially observed (i.e., with missing pixels). Our theorems hold for 2-layer convolutional generative network with ReLU as the activation function, but we demonstrate empirically that the same conclusion extends to multi-layer networks and networks with other activation functions, including the leaky ReLU, sigmoid and tanh.

This paper proposes a stochastic variant of a classic algorithm---the cubic-regularized Newton method [Nesterov and Polyak]. The proposed algorithm efficiently escapes saddle points and finds approximate local minima for general smooth, nonconvex functions in only $\mathcal{\tilde{O}}(\epsilon^{-3.5})$ stochastic gradient and stochastic Hessian-vector product evaluations. The latter can be computed as efficiently as stochastic gradients. This improves upon the $\mathcal{\tilde{O}}(\epsilon^{-4})$ rate of stochastic gradient descent. Our rate matches the best-known result for finding local minima without requiring any delicate acceleration or variance-reduction techniques.

Population risk is always of primary interest in machine learning; however, learning algorithms only have access to the empirical risk. Even for applications with nonconvex non-smooth losses (such as modern deep networks), the population risk is generally significantly more well behaved from an optimization point of view than the empirical risk. In particular, sampling can create many spurious local minima. We consider a general framework which aims to optimize a smooth nonconvex function $F$ (population risk) given only access to an approximation $f$ (empirical risk) that is pointwise close to $F$ (i.e., $\norm{F-f}_{\infty} \le \nu$). Our objective is to find the $\epsilon$-approximate local minima of the underlying function $F$ while avoiding the shallow local minima---arising because of the tolerance $\nu$---which exist only in $f$. We propose a simple algorithm based on stochastic gradient descent (SGD) on a smoothed version of $f$ that is guaranteed to achieve our goal as long as $\nu \le O(\epsilon^{1.5}/d)$. We also provide an almost matching lower bound showing that our algorithm achieves optimal error tolerance $\nu$ among all algorithms making a polynomial number of queries of $f$. As a concrete example, we show that our results can be directly used to give sample complexities for learning a ReLU unit.

We study the problem of video-to-video synthesis, whose goal is to learn a mapping function from an input source video (e.g., a sequence of semantic segmentation masks) to an output photorealistic video that precisely depicts the content of the source video. While its image counterpart, the image-to-image translation problem, is a popular topic, the video-to-video synthesis problem is less explored in the literature. Without modeling temporal dynamics, directly applying existing image synthesis approaches to an input video often results in temporally incoherent videos of low visual quality. In this paper, we propose a video-to-video synthesis approach under the generative adversarial learning framework. Through carefully-designed generators and discriminators, coupled with a spatio-temporal adversarial objective, we achieve high-resolution, photorealistic, temporally coherent video results on a diverse set of input formats including segmentation masks, sketches, and poses. Experiments on multiple benchmarks show the advantage of our method compared to strong baselines. In particular, our model is capable of synthesizing 2K resolution videos of street scenes up to 30 seconds long, which significantly advances the state-of-the-art of video synthesis. Finally, we apply our method to future video prediction, outperforming several competing systems. Code, models, and more results are available at our website: https://github.com/NVIDIA/vid2vid. (Please use Adobe Reader to see the embedded videos in the paper.)

Model-free reinforcement learning (RL) algorithms directly parameterize and update value functions or policies, bypassing the modeling of the environment. They are typically simpler, more flexible to use, and thus more prevalent in modern deep RL than model-based approaches. However, empirical work has suggested that they require large numbers of samples to learn. The theoretical question of whether not model-free algorithms are in fact \emph{sample efficient} is one of the most fundamental questions in RL. The problem is unsolved even in the basic scenario with finitely many states and actions. We prove that, in an episodic MDP setting, Q-learning with UCB exploration achieves regret $\tlO(\sqrt{H^3 SAT})$ where $S$ and $A$ are the numbers of states and actions, $H$ is the number of steps per episode, and $T$ is the total number of steps. Our regret matches the optimal regret up to a single $\sqrt{H}$ factor. Thus we establish the sample efficiency of a classical model-free approach. Moreover, to the best of our knowledge, this is the first model-free analysis to establish $\sqrt{T}$ regret \emph{without} requiring access to a ``simulator.''

Recent years have witnessed substantial progress in understanding the behavior of EM for mixture models that are correctly specified. Given that model misspecification is common in practice, it is important to understand EM in this more general setting. We provide non-asymptotic guarantees for population and sample-based EM for parameter estimation under a few specific univariate settings of misspecified Gaussian mixture models. Due to misspecification, the EM iterates no longer converge to the true model and instead converge to the projection of the true model over the set of models being searched over. We provide two classes of theoretical guarantees: first, we characterize the bias introduced due to the misspecification; and second, we prove that population EM converges at a geometric rate to the model projection under a suitable initialization condition. This geometric convergence rate for population EM imply a statistical complexity of order $1/\sqrt{n}$ when running EM with $n$ samples.

Adversarial learning has been embedded into deep networks to learn disentangled and transferable representations for domain adaptation. Existing adversarial domain adaptation methods may struggle to align different domains of multimodal distributions that are native in classification problems. In this paper, we present conditional adversarial domain adaptation, a principled framework that conditions the adversarial adaptation models on discriminative information conveyed in the classifier predictions. Conditional domain adversarial networks (CDANs) are designed with two novel conditioning strategies: multilinear conditioning that captures the cross-covariance between feature representations and classifier predictions to improve the discriminability, and entropy conditioning that controls the uncertainty of classifier predictions to guarantee the transferability. Experiments testify that the proposed approach exceeds the state-of-the-art results on five benchmark datasets.

Parameterizing the approximate posterior of a generative model with neural networks has become a common theme in recent machine learning research. While providing appealing flexibility, this approach makes it difficult to impose or assess structural constraints such as conditional independence. We propose a framework for learning representations that relies on Auto-Encoding Variational Bayes and whose search space is constrained via kernel-based measures of independence. In particular, our method employs the $d$-variable Hilbert-Schmidt Independence Criterion (dHSIC) to enforce independence between the latent representations and arbitrary nuisance factors. We show how to apply this method to a range of problems, including the problems of learning invariant representations and the learning of interpretable representations. We also present a full-fledged application to single-cell RNA sequencing (scRNA-seq).

Your Out-of-Distribution Detection Method is Not Robust!

Extreme multi-label classification (XMLC) is a problem of tagging an instance with a small subset of relevant labels chosen from an extremely large pool of possible labels. Large label spaces can be efficiently handled by organizing labels as a tree, like in the hierarchical softmax (HSM) approach commonly used for multi-class problems. In this paper, we investigate probabilistic label trees (PLTs) that have been recently devised for tackling XMLC problems. We show that PLTs are a no-regret multi-label generalization of HSM when precision@$k$ is used as a model evaluation metric. Critically, we prove that pick-one-label heuristic---a reduction technique from multi-label to multi-class that is routinely used along with HSM---is not consistent in general. We also show that our implementation of PLTs, referred to as extremeText (XT), obtains significantly better results than HSM with the pick-one-label heuristic and XML-CNN, a deep network specifically designed for XMLC problems. Moreover, XT is competitive to many state-of-the-art approaches in terms of statistical performance, model size and prediction time which makes it amenable to deploy in an online system.