A Theory of Output-Side Unsupervised Domain Adaptation

When learning a mapping from an input space to an output space, the assumption that the sample distribution of the training data is the same as that of the test data is often violated. Unsupervised domain shift methods adapt the learned function in order to correct for this shift. Previous work has focused on utilizing unlabeled samples from the target distribution. We consider the complementary problem in which the unlabeled samples are given post mapping, i.e., we are given the outputs of the mapping of unknown samples from the shifted domain. Two other variants are also studied: the two sided version, in which unlabeled samples are give from both the input and the output spaces, and the Domain Transfer problem, which was recently formalized. In all cases, we derive generalization bounds that employ discrepancy terms

The Role of Minimal Complexity Functions in Unsupervised Learning of Semantic Mappings

We discuss the feasibility of the following learning problem: given unmatched samples from two domains and nothing else, learn a mapping between the two, which preserves semantics. Due to the lack of paired samples and without any definition of the semantic information, the problem might seem ill-posed. Specifically, in typical cases, it seems possible to build infinitely many alternative mappings from every target mapping. This apparent ambiguity stands in sharp contrast to the recent empirical success in solving this problem. We identify the abstract notion of aligning two domains in a semantic way with concrete terms of minimal relative complexity. A theoretical framework for measuring the complexity of compositions of functions is developed in order to show that it is reasonable to expect the minimal complexity mapping to be unique. The measured complexity used is directly related to the depth of the neural networks being learned and a semantically aligned mapping could then be captured simply by learning using architectures that are not much bigger than the minimal architecture. Various predictions are made based on the hypothesis that semantic alignment can be captured by the minimal mapping. These are verified extensively. In addition, a new mapping algorithm is proposed and shown to lead to better mapping results

Estimating the Success of Unsupervised Image to Image Translation

While in supervised learning, the validation error is an unbiased estimator of the generalization (test) error and complexity-based generalization bounds are abundant, no such bounds exist for learning a mapping in an unsupervised way. As a result, when training GANs and specifically when using GANs for learning to map between domains in a completely unsupervised way, one is forced to select the hyperparameters and the stopping epoch by subjectively examining multiple options. We propose a novel bound for predicting the success of unsupervised cross domain mapping methods, which is motivated by the recently proposed Simplicity Principle. The bound can be applied both in expectation, for comparing hyperparameters and for selecting a stopping criterion, or per sample, in order to predict the success of a specific cross-domain translation. The utility of the bound is demonstrated in an extensive set of experiments employing multiple recent algorithms. Our code is available at https://github.com/sagiebenaim/gan_bound .Comment: The first and second authors contributed equall

Generalization Bounds for Unsupervised Cross-Domain Mapping with WGANs

The recent empirical success of unsupervised cross-domain mapping algorithms, between two domains that share common characteristics, is not well-supported by theoretical justifications. This lacuna is especially troubling, given the clear ambiguity in such mappings. We work with the adversarial training method called the Wasserstein GAN and derive a novel generalization bound, which limits the risk between the learned mapping $h$ and the target mapping $y$, by a sum of two terms: (i) the risk between $h$ and the most distant alternative mapping that was learned by the same cross-domain mapping algorithm, and (ii) the minimal Wasserstein GAN divergence between the target domain and the domain obtained by applying a hypothesis $h^*$ on the samples of the source domain, where $h^*$ is a hypothesis selected by the same algorithm. The bound is directly related to Occam's razor and encourages the selection of the minimal architecture that supports a small Wasserstein GAN divergence. The bound leads to multiple algorithmic consequences, including a method for hyperparameters selection and for an early stopping in cross-domain mapping GANs. We also demonstrate a novel capability for unsupervised learning of estimating confidence in the mapping of every specific sample. Lastly, we show how non-minimal architectures can be effectively trained by an inverted knowledge distillation, in which a minimal architecture is used to train a larger one, leading to higher quality outputs.Comment: arXiv admin note: text overlap with arXiv:1709.0007

Unsupervised Learning of the Set of Local Maxima

This paper describes a new form of unsupervised learning, whose input is a set of unlabeled points that are assumed to be local maxima of an unknown value function v in an unknown subset of the vector space. Two functions are learned: (i) a set indicator c, which is a binary classifier, and (ii) a comparator function h that given two nearby samples, predicts which sample has the higher value of the unknown function v. Loss terms are used to ensure that all training samples x are a local maxima of v, according to h and satisfy c(x)=1. Therefore, c and h provide training signals to each other: a point x' in the vicinity of x satisfies c(x)=-1 or is deemed by h to be lower in value than x. We present an algorithm, show an example where it is more efficient to use local maxima as an indicator function than to employ conventional classification, and derive a suitable generalization bound. Our experiments show that the method is able to outperform one-class classification algorithms in the task of anomaly detection and also provide an additional signal that is extracted in a completely unsupervised way.Comment: ICLR 201

On Random Kernels of Residual Architectures

We derive finite width and depth corrections for the Neural Tangent Kernel (NTK) of ResNets and DenseNets. Our analysis reveals that finite size residual architectures are initialized much closer to the "kernel regime" than their vanilla counterparts: while in networks that do not use skip connections, convergence to the NTK requires one to fix the depth, while increasing the layers' width. Our findings show that in ResNets, convergence to the NTK may occur when depth and width simultaneously tend to infinity, provided with a proper initialization. In DenseNets, however, convergence of the NTK to its limit as the width tends to infinity is guaranteed, at a rate that is independent of both the depth and scale of the weights. Our experiments validate the theoretical results and demonstrate the advantage of deep ResNets and DenseNets for kernel regression with random gradient features

Evaluation Metrics for Conditional Image Generation

We present two new metrics for evaluating generative models in the class-conditional image generation setting. These metrics are obtained by generalizing the two most popular unconditional metrics: the Inception Score (IS) and the Fre'chet Inception Distance (FID). A theoretical analysis shows the motivation behind each proposed metric and links the novel metrics to their unconditional counterparts. The link takes the form of a product in the case of IS or an upper bound in the FID case. We provide an extensive empirical evaluation, comparing the metrics to their unconditional variants and to other metrics, and utilize them to analyze existing generative models, thus providing additional insights about their performance, from unlearned classes to mode collapse.Comment: To be published in "INTERNATIONAL JOURNAL OF COMPUTER VISION

Domain Intersection and Domain Difference

We present a method for recovering the shared content between two visual domains as well as the content that is unique to each domain. This allows us to map from one domain to the other, in a way in which the content that is specific for the first domain is removed and the content that is specific for the second is imported from any image in the second domain. In addition, our method enables generation of images from the intersection of the two domains as well as their union, despite having no such samples during training. The method is shown analytically to contain all the sufficient and necessary constraints. It also outperforms the literature methods in an extensive set of experiments. Our code is available at https://github.com/sagiebenaim/DomainIntersectionDifference

On Infinite-Width Hypernetworks

{\em Hypernetworks} are architectures that produce the weights of a task-specific {\em primary network}. A notable application of hypernetworks in the recent literature involves learning to output functional representations. In these scenarios, the hypernetwork learns a representation corresponding to the weights of a shallow MLP, which typically encodes shape or image information. While such representations have seen considerable success in practice, they remain lacking in the theoretical guarantees in the wide regime of the standard architectures. In this work, we study wide over-parameterized hypernetworks. We show that unlike typical architectures, infinitely wide hypernetworks do not guarantee convergence to a global minima under gradient descent. We further show that convexity can be achieved by increasing the dimensionality of the hypernetwork's output, to represent wide MLPs. In the dually infinite-width regime, we identify the functional priors of these architectures by deriving their corresponding GP and NTK kernels, the latter of which we refer to as the {\em hyperkernel}. As part of this study, we make a mathematical contribution by deriving tight bounds on high order Taylor expansion terms of standard fully connected ReLU networks.Comment: The first two authors contributed equall

Emerging Disentanglement in Auto-Encoder Based Unsupervised Image Content Transfer

We study the problem of learning to map, in an unsupervised way, between domains A and B, such that the samples b in B contain all the information that exists in samples a in A and some additional information. For example, ignoring occlusions, B can be people with glasses, A people without, and the glasses, would be the added information. When mapping a sample a from the first domain to the other domain, the missing information is replicated from an independent reference sample b in B. Thus, in the above example, we can create, for every person without glasses a version with the glasses observed in any face image. Our solution employs a single two-pathway encoder and a single decoder for both domains. The common part of the two domains and the separate part are encoded as two vectors, and the separate part is fixed at zero for domain A. The loss terms are minimal and involve reconstruction losses for the two domains and a domain confusion term. Our analysis shows that under mild assumptions, this architecture, which is much simpler than the literature guided-translation methods, is enough to ensure disentanglement between the two domains. We present convincing results in a few visual domains, such as no-glasses to glasses, adding facial hair based on a reference image, etc