The Low-Rank Simplicity Bias in Deep Networks

Modern deep neural networks are highly over-parameterized compared to the data on which they are trained, yet they often generalize remarkably well. A flurry of recent work has asked: why do deep networks not overfit to their training data? We investigate the hypothesis that deeper nets are implicitly biased to find lower rank solutions and that these are the solutions that generalize well. We prove for the asymptotic case that the percent volume of low effective-rank solutions increases monotonically as linear neural networks are made deeper. We then show empirically that our claim holds true on finite width models. We further empirically find that a similar result holds for non-linear networks: deeper non-linear networks learn a feature space whose kernel has a lower rank. We further demonstrate how linear over-parameterization of deep non-linear models can be used to induce low-rank bias, improving generalization performance without changing the effective model capacity. We evaluate on various model architectures and demonstrate that linearly over-parameterized models outperform existing baselines on image classification tasks, including ImageNet.

Anycost GANs for Interactive Image Synthesis and Editing

Generative adversarial networks (GANs) have enabled photorealistic image synthesis and editing. However, due to the high computational cost of large-scale generators (e.g., StyleGAN2), it usually takes seconds to see the results of a single edit on edge devices, prohibiting interactive user experience. In this paper, we take inspirations from modern rendering software and propose Anycost GAN for interactive natural image editing. We train the Anycost GAN to support elastic resolutions and channels for faster image generation at versatile speeds. Running subsets of the full generator produce outputs that are perceptually similar to the full generator, making them a good proxy for preview. By using sampling-based multi-resolution training, adaptive-channel training, and a generator-conditioned discriminator, the anycost generator can be evaluated at various configurations while achieving better image quality compared to separately trained models. Furthermore, we develop new encoder training and latent code optimization techniques to encourage consistency between the different sub-generators during image projection. Anycost GAN can be executed at various cost budgets (up to 10x computation reduction) and adapt to a wide range of hardware and latency requirements. When deployed on desktop CPUs and edge devices, our model can provide perceptually similar previews at 6-12x speedup, enabling interactive image editing. The code and demo are publicly available: https://github.com/mit-han-lab/anycost-gan.

CDPAM: Contrastive learning for perceptual audio similarity

Many speech processing methods based on deep learning require an automatic and differentiable audio metric for the loss function. The DPAM approach of Manocha et al. learns a full-reference metric trained directly on human judgments, and thus correlates well with human perception. However, it requires a large number of human annotations and does not generalize well outside the range of perturbations on which it was trained. This paper introduces CDPAM, a metric that builds on and advances DPAM. The primary improvement is to combine contrastive learning and multi-dimensional representations to build robust models from limited data. In addition, we collect human judgments on triplet comparisons to improve generalization to a broader range of audio perturbations. CDPAM correlates well with human responses across nine varied datasets. We also show that adding this metric to existing speech synthesis and enhancement methods yields significant improvement, as measured by objective and subjective tests.

Spatially-Adaptive Pixelwise Networks for Fast Image Translation

We introduce a new generator architecture, aimed at fast and efficient high-resolution image-to-image translation. We design the generator to be an extremely lightweight function of the full-resolution image. In fact, we use pixel-wise networks; that is, each pixel is processed independently of others, through a composition of simple affine transformations and nonlinearities. We take three important steps to equip such a seemingly simple function with adequate expressivity. First, the parameters of the pixel-wise networks are spatially varying so they can represent a broader function class than simple 1x1 convolutions. Second, these parameters are predicted by a fast convolutional network that processes an aggressively low-resolution representation of the input; Third, we augment the input image with a sinusoidal encoding of spatial coordinates, which provides an effective inductive bias for generating realistic novel high-frequency image content. As a result, our model is up to 18x faster than state-of-the-art baselines. We achieve this speedup while generating comparable visual quality across different image resolutions and translation domains.

Few-shot Image Generation with Elastic Weight Consolidation

Few-shot image generation seeks to generate more data of a given domain, with only few available training examples. As it is unreasonable to expect to fully infer the distribution from just a few observations (e.g., emojis), we seek to leverage a large, related source domain as pretraining (e.g., human faces). Thus, we wish to preserve the diversity of the source domain, while adapting to the appearance of the target. We adapt a pretrained model, without introducing any additional parameters, to the few examples of the target domain. Crucially, we regularize the changes of the weights during this adaptation, in order to best preserve the information of the source dataset, while fitting the target. We demonstrate the effectiveness of our algorithm by generating high-quality results of different target domains, including those with extremely few examples (e.g., <10). We also analyze the performance of our method with respect to some important factors, such as the number of examples and the dissimilarity between the source and target domain.

Contrastive Learning for Unpaired Image-to-Image Translation

In image-to-image translation, each patch in the output should reflect the content of the corresponding patch in the input, independent of domain. We propose a straightforward method for doing so -- maximizing mutual information between the two, using a framework based on contrastive learning. The method encourages two elements (corresponding patches) to map to a similar point in a learned feature space, relative to other elements (other patches) in the dataset, referred to as negatives. We explore several critical design choices for making contrastive learning effective in the image synthesis setting. Notably, we use a multilayer, patch-based approach, rather than operate on entire images. Furthermore, we draw negatives from within the input image itself, rather than from the rest of the dataset. We demonstrate that our framework enables one-sided translation in the unpaired image-to-image translation setting, while improving quality and reducing training time. In addition, our method can even be extended to the training setting where each "domain" is only a single image.

Swapping Autoencoder for Deep Image Manipulation

Deep generative models have become increasingly effective at producing realistic images from randomly sampled seeds, but using such models for controllable manipulation of existing images remains challenging. We propose the Swapping Autoencoder, a deep model designed specifically for image manipulation, rather than random sampling. The key idea is to encode an image with two independent components and enforce that any swapped combination maps to a realistic image. In particular, we encourage the components to represent structure and texture, by enforcing one component to encode co-occurrent patch statistics across different parts of an image. As our method is trained with an encoder, finding the latent codes for a new input image becomes trivial, rather than cumbersome. As a result, it can be used to manipulate real input images in various ways, including texture swapping, local and global editing, and latent code vector arithmetic. Experiments on multiple datasets show that our model produces better results and is substantially more efficient compared to recent generative models.

How Many Samples is a Good Initial Point Worth?

Given a sufficiently large amount of labeled data, the non-convex low-rank matrix recovery problem contains no spurious local minima, so a local optimization algorithm is guaranteed to converge to a global minimum starting from any initial guess. However, the actual amount of data needed by this theoretical guarantee is very pessimistic, as it must prevent spurious local minima from existing anywhere, including at adversarial locations. In contrast, prior work based on good initial guesses have more realistic data requirements, because they allow spurious local minima to exist outside of a neighborhood of the solution. In this paper, we quantify the relationship between the quality of the initial guess and the corresponding reduction in data requirements. Using the restricted isometry constant as a surrogate for sample complexity, we compute a sharp threshold number of samples needed to prevent each specific point on the optimization landscape from becoming a spurious local minima. Optimizing the threshold over regions of the landscape, we see that, for initial points not too close to the ground truth, a linear improvement in the quality of the initial guess amounts to a constant factor improvement in the sample complexity.