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Register a new userForward Super-Resolution: How Can GANs Learn Hierarchical Generative Models for Real-World Distributions
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Added by
Zeyuan Allen-Zhu
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Generative adversarial networks (GANs) are among the most successful models for learning high-complexity, real-world distributions. However, in theory, due to the highly non-convex, non-concave landscape of the minmax training objective, GAN remains one of the least understood deep learning models. In this work, we formally study how GANs can efficiently learn certain hierarchically generated distributions that are close to the distribution of images in practice. We prove that when a distribution has a structure that we refer to as Forward Super-Resolution, then simply training generative adversarial networks using gradient descent ascent (GDA) can indeed learn this distribution efficiently, both in terms of sample and time complexities. We also provide concrete empirical evidence that not only our assumption forward super-resolution is very natural in practice, but also the underlying learning mechanisms that we study in this paper (to allow us efficiently train GAN via GDA in theory) simulates the actual learning process of GANs in practice on real-world problems.
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How can neural networks such as ResNet efficiently learn CIFAR-10 with test accuracy more than 96%, while other methods, especially kernel methods, fall relatively behind? Can we more provide theoretical justifications for this gap? Recently, there is an influential line of work relating neural networks to kernels in the over-parameterized regime, proving they can learn certain concept class that is also learnable by kernels with similar test error. Yet, can neural networks provably learn some concept class BETTER than kernels? We answer this positively in the distribution-free setting. We prove neural networks can efficiently learn a notable class of functions, including those defined by three-layer residual networks with smooth activations, without any distributional assumption. At the same time, we prove there are simple functions in this class such that with the same number of training examples, the test error obtained by neural networks can be MUCH SMALLER than ANY kernel method, including neural tangent kernels (NTK). The main intuition is that multi-layer neural networks can implicitly perform hierarchical learning using different layers, which reduces the sample complexity comparing to one-shot learning algorithms such as kernel methods. In a follow-up work [2], this theory of hierarchical learning is further strengthened to incorporate the backward feature correction process when training deep networks. In the end, we also prove a computation complexity advantage of ResNet with respect to other learning methods including linear regression over arbitrary feature mappings.
Recurrent Neural Networks (RNNs) are among the most popular models in sequential data analysis. Yet, in the foundational PAC learning language, what concept class can it learn? Moreover, how can the same recurrent unit simultaneously learn functions from different input tokens to different output tokens, without affecting each other? Existing generalization bounds for RNN scale exponentially with the input length, significantly limiting their practical implications. In this paper, we show using the vanilla stochastic gradient descent (SGD), RNN can actually learn some notable concept class efficiently, meaning that both time and sample complexity scale polynomially in the input length (or almost polynomially, depending on the concept). This concept class at least includes functions where each output token is generated from inputs of earlier tokens using a smooth two-layer neural network.
In real-world single image super-resolution (SISR) task, the low-resolution image suffers more complicated degradations, not only downsampled by unknown kernels. However, existing SISR methods are generally studied with the synthetic low-resolution generation such as bicubic interpolation (BI), which greatly limits their performance. Recently, some researchers investigate real-world SISR from the perspective of the camera and smartphone. However, except the acquisition equipment, the display device also involves more complicated degradations. In this paper, we focus on the camera-screen degradation and build a real-world dataset (Cam-ScreenSR), where HR images are original ground truths from the previous DIV2K dataset and corresponding LR images are camera-captur
Most image super-resolution (SR) methods are developed on synthetic low-resolution (LR) and high-resolution (HR) image pairs that are constructed by a predetermined operation, e.g., bicubic downsampling. As existing methods typically learn an inverse mapping of the specific function, they produce blurry results when applied to real-world images whose exact formulation is different and unknown. Therefore, several methods attempt to synthesize much more diverse LR samples or learn a realistic downsampling model. However, due to restrictive assumptions on the downsampling process, they are still biased and less generalizable. This study proposes a novel method to simulate an unknown downsampling process without imposing restrictive prior knowledge. We propose a generalizable low-frequency loss (LFL) in the adversarial training framework to imitate the distribution of target LR images without using any paired examples. Furthermore, we design an adaptive data loss (ADL) for the downsampler, which can be adaptively learned and updated from the data during the training loops. Extensive experiments validate that our downsampling model can facilitate existing SR methods to perform more accurate reconstructions on various synthetic and real-world examples than the conventional approaches.
Deep generative models (e.g. GANs and VAEs) have been developed quite extensively in recent years. Lately, there has been an increased interest in the inversion of such a model, i.e. given a (possibly corrupted) signal, we wish to recover the latent vector that generated it. Building upon sparse representation theory, we define conditions that are applicable to any inversion algorithm (gradient descent, deep encoder, etc.), under which such generative models are invertible with a unique solution. Importantly, the proposed analysis is applicable to any trained model, and does not depend on Gaussian i.i.d. weights. Furthermore, we introduce two layer-wise inversion pursuit algorithms for trained generative networks of arbitrary depth, and accompany these with recovery guarantees. Finally, we validate our theoretical results numerically and show that our method outperforms gradient descent when inverting such generators, both for clean and corrupted signals.
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