We study randomly initialized residual networks using mean field theory and the theory of difference equations.

Adaptive optimization methods, which perform local optimization with a metric constructed from the history of iterates, are becoming increasingly popular for training deep neural networks. Examples include AdaGrad, RMSProp, and Adam. We show that for simple overparameterized problems, adaptive methods often find drastically different solutions than gradient descent (GD) or stochastic gradient descent (SGD). We construct an illustrative binary classification problem where the data is linearly separable, GD and SGD achieve zero test error, and AdaGrad, Adam, and RMSProp attain test errors arbitrarily close to half. We additionally study the empirical generalization capability of adaptive methods on several state-of-the-art deep learning models. We observe that the solutions found by adaptive methods generalize worse (often significantly worse) than SGD, even when these solutions have better training performance. These results suggest that practitioners should reconsider the use of adaptive methods to train neural networks.

Many image-to-image translation problems are ambiguous, as a single input image may correspond to multiple possible outputs. In this work, we aim to model a distribution of possible outputs in a conditional generative modeling setting. The ambiguity of the mapping is distilled in a low-dimensional latent vector, which can be randomly sampled at test time. A generator learns to map the given input, combined with this latent code, to the output. We explicitly encourage the connection between output and the latent code to be invertible. This helps prevent a many-to-one mapping from the latent code to the output during training, also known as the problem of mode collapse, and produces more diverse results. We explore several variants of this approach by employing different training objectives, network architectures, and methods of injecting the latent code. Our proposed method encourages bijective consistency between the latent encoding and output modes. We present a systematic comparison of our method and other variants on both perceptual realism and diversity.

We study the generalization error of randomized learning algorithms -- focusing on stochastic gradient descent (SGD) -- using a novel combination of PAC-Bayes and algorithmic stability. Importantly, our generalization bounds hold for all posterior distributions on an algorithm's random hyperparameters, including distributions that depend on the training data.

In the online multiple testing problem, p-values corresponding to different null hypotheses are presented one by one, and the decision of whether to reject a hypothesis must be made immediately, after which the next p-value is presented. Alpha-investing algorithms to control the false discovery rate were first formulated by Foster and Stine and have since been generalized and applied to various settings, varying from quality-preserving databases for science to multiple A/B tests for internet commerce. This paper improves the class of generalized alpha-investing algorithms (GAI) in four ways: (a) we show how to uniformly improve the power of the entire class of GAI procedures under independence by awarding more alpha-wealth for each rejection, giving a near win-win resolution to a dilemma raised by Javanmard and Montanari, (b) we demonstrate how to incorporate prior weights to indicate domain knowledge of which hypotheses are likely to be null or non-null, (c) we allow for differing penalties for false discoveries to indicate that some hypotheses may be more meaningful/important than others, (d) we define a new quantity called the \emph{decaying memory false discovery rate, or $\memfdr$} that may be more meaningful for applications with an explicit time component, using a discount factor to incrementally forget past decisions and alleviate some potential problems that we describe and name ``piggybacking'' and ``alpha-death''. Our GAI++ algorithms incorporate all four generalizations (a, b, c, d) simulatenously, and reduce to more powerful variants of earlier algorithms when the weights and decay are all set to unity.

In this paper, we describe the PixelGAN autoencoder, a generative autoencoder in which the generative path is a convolutional autoregressive neural network on pixels (PixelCNN) that is conditioned on a latent code, and the recognition path uses a generative adversarial network (GAN) to impose a prior distribution on the latent code. We show that different priors result in different decompositions of information between the latent code and the autoregressive decoder. For example, by imposing a Gaussian distribution as the prior, we can achieve a global vs. local decomposition, or by imposing a categorical distribution as the prior, we can disentangle the style and content information of images in an unsupervised fashion. We further show how the PixelGAN autoencoder with a categorical prior can be directly used in semi-supervised settings and achieve competitive semi-supervised classification results on the MNIST, SVHN and NORB datasets.

Despite the growing prominence of generative adversarial networks (GANs), optimization in GANs is still a poorly understood topic. In this paper, we analyze the ``gradient descent'' form of GAN optimization, i.e., the natural setting where we simultaneously take small gradient steps in both generator and discriminator parameters. We show that even though GAN optimization does \emph{not} correspond to a convex-concave game (even for simple parameterizations), under proper conditions, equilibrium points of this optimization procedure are still \emph{locally asymptotically stable} for the traditional GAN formulation. On the other hand, we show that the recently proposed Wasserstein GAN can have non-convergent limit cycles near equilibrium. Motivated by this stability analysis, we propose an additional regularization term for gradient descent GAN updates, which \emph{is} able to guarantee local stability for both the WGAN and the traditional GAN, and also shows practical promise in speeding up convergence and addressing mode collapse.

The sparse matrix estimation problem consists of estimating the distribution of an $n\times n$ matrix $Y$, from a sparsely observed single instance of this matrix where the entries of $Y$ are independent random variables. This captures a wide array of problems; special instances include matrix completion in the context of recommendation systems, graphon estimation, and community detection in (mixed membership) stochastic block models. Inspired by classical collaborative filtering for recommendation systems, we propose a novel iterative, collaborative filtering-style algorithm for matrix estimation in this generic setting. We show that the mean squared error (MSE) of our estimator converges to $0$ at the rate of $O(d^2 (pn)^{-2/5})$ as long as $\omega(d^5 n)$ random entries from a total of $n^2$ entries of $Y$ are observed (uniformly sampled), $\E[Y]$ has rank $d$, and the entries of $Y$ have bounded support. The maximum squared error across all entries converges to $0$ with high probability as long as we observe a little more, $\Omega(d^5 n \ln^5(n))$ entries. Our results are the best known sample complexity results in this generality.

Synthesizing realistic profile faces is promising for more efficiently training deep pose-invariant models for large-scale unconstrained face recognition, by populating samples with extreme poses and avoiding tedious annotations. However, learning from synthetic faces may not achieve the desired performance due to the discrepancy between distributions of the synthetic and real face images. To narrow this gap, we propose a Dual-Agent Generative Adversarial Network (DA-GAN) model, which can improve the realism of a face simulator's output using unlabeled real faces, while preserving the identity information during the realism refinement. The dual agents are specifically designed for distinguishing real v.s.

Why can't language models write well? I n a certain, strange way, generative AI peaked with OpenAI's GPT-2 seven years ago. Little known to anyone outside of tech circles, GPT-2 excelled at producing unexpected answers. "You could be like, 'Continue this story:,' and GPT-2 would be like, ','" Katy Gero, a poet and computer scientist who has been experimenting with language models since 2017, told me. "The models won't do that anymore." AI leaders boast about their models' superhuman technical abilities.