Small data challenges have emerged in many learning problems, since the success of deep neural networks often relies on the availability of a huge amount of labeled data that is expensive to collect. To address it, many efforts have been made on training complex models with small data in an unsupervised and semi-supervised fashion. In this paper, we will review the recent progresses on these two major categories of methods. A wide spectrum of small data models will be categorized in a big picture, where we will show how they interplay with each other to motivate explorations of new ideas. We will review the criteria of learning the transformation equivariant, disentangled, self-supervised and semi-supervised representations, which underpin the foundations of recent developments. Many instantiations of unsupervised and semi-supervised generative models have been developed on the basis of these criteria, greatly expanding the territory of existing autoencoders, generative adversarial nets (GANs) and other deep networks by exploring the distribution of unlabeled data for more powerful representations. While we focus on the unsupervised and semi-supervised methods, we will also provide a broader review of other emerging topics, from unsupervised and semi-supervised domain adaptation to the fundamental roles of transformation equivariance and invariance in training a wide spectrum of deep networks. It is impossible for us to write an exclusive encyclopedia to include all related works. Instead, we aim at exploring the main ideas, principles and methods in this area to reveal where we are heading on the journey towards addressing the small data challenges in this big data era.
Existing neural architecture search (NAS) methods often return an architecture with good search performance but generalizes poorly to the test setting. To achieve better generalization, we propose a novel neighborhood-aware NAS formulation to identify flat-minima architectures in the search space, with the assumption that flat minima generalize better than sharp minima. The phrase "flat-minima architecture" refers to architectures whose performance is stable under small perturbations in the architecture (e.g., replacing a convolution with a skip connection). Our formulation takes the "flatness" of an architecture into account by aggregating the performance over the neighborhood of this architecture. We demonstrate a principled way to apply our formulation to existing search algorithms, including sampling-based algorithms and gradient-based algorithms. To facilitate the application to gradient-based algorithms, we also propose a differentiable representation for the neighborhood of architectures. Based on our formulation, we propose neighborhood-aware random search (NA-RS) and neighborhood-aware differentiable architecture search (NA-DARTS). Notably, by simply augmenting DARTS with our formulation, NA-DARTS finds architectures that perform better or on par with those found by state-of-the-art NAS methods on established benchmarks, including CIFAR-10, CIFAR-100 and ImageNet.