In this paper, we give a formalization of this shared pattern, which we call G IMLI, prove its general requirements, and derive a general-purpose algorithm for implementing similar approaches. Based on this analysis and algorithm, we describe a library of our design, higher, which we share with the community to assist and enable future research into these kinds of meta-learning approaches. We end the paper by showcasing the practical applications of this framework and library through illustrative experiments and ablation studies which they facilitate. 1 I NTRODUCTION Although it is by no means a new subfield of machine learning research (see e.g. Schmidhuber, 1987; Bengio, 2000; Hochreiter et al., 2001), there has recently been a surge of interest in meta-learning (e.g. This is due to the methods meta-learning provides, amongst other things, for producing models that perform well beyond the confines of a single task, outside the constraints of a static dataset, or simply with greater data efficiency or sample complexity. Due to the wealth of options in what could be considered "meta-" to a learning problem, the term itself may have been used with some degree of underspecification. However, it turns out that many meta-learning approaches, in particular in the recent literature, follow the pattern of optimizing the "meta-parameters" of the training process by nesting one or more inner loops in an outer training loop. Such nesting enables training a model for several steps, evaluating it, calculating or approximating the gradients of that evaluation with respect to the meta-parameters, and subsequently updating these meta-parameters.

We introduce a new algorithm named WGAN, an alternative to traditional GAN training. In this new model, we show that we can improve the stability of learning, get rid of problems like mode collapse, and provide meaningful learning curves useful for debugging and hyperparameter searches. Furthermore, we show that the corresponding optimization problem is sound, and provide extensive theoretical work highlighting the deep connections to other distances between distributions.

This paper establishes the existence of observable footprints that reveal the "causal dispositions" of the object categories appearing in collections of images. We achieve this goal in two steps. First, we take a learning approach to observational causal discovery, and build a classifier that achieves state-of-the-art performance on finding the causal direction between pairs of random variables, given samples from their joint distribution. Second, we use our causal direction classifier to effectively distinguish between features of objects and features of their contexts in collections of static images. Our experiments demonstrate the existence of a relation between the direction of causality and the difference between objects and their contexts, and by the same token, the existence of observable signals that reveal the causal dispositions of objects.

This paper introduces MazeBase: an environment for simple 2D games, designed as a sandbox for machine learning approaches to reasoning and planning. Within it, we create 10 simple games embodying a range of algorithmic tasks (e.g. if-then statements or set negation). A variety of neural models (fully connected, convolutional network, memory network) are deployed via reinforcement learning on these games, with and without a procedurally generated curriculum. Despite the tasks' simplicity, the performance of the models is far from optimal, suggesting directions for future development. We also demonstrate the versatility of MazeBase by using it to emulate small combat scenarios from StarCraft. Models trained on the MazeBase version can be directly applied to StarCraft, where they consistently beat the in-game AI.

In this paper we introduce a generative model capable of producing high quality samples of natural images. Our approach uses a cascade of convolutional networks (convnets) within a Laplacian pyramid framework to generate images in a coarse-to-fine fashion. At each level of the pyramid a separate generative convnet model is trained using the Generative Adversarial Nets (GAN) approach. Samples drawn from our model are of significantly higher quality than existing models. In a quantitive assessment by human evaluators our CIFAR10 samples were mistaken for real images around 40% of the time, compared to 10% for GAN samples. We also show samples from more diverse datasets such as STL10 and LSUN.

A complex-valued convolutional network (convnet) implements the repeated application of the following composition of three operations, recursively applying the composition to an input vector of nonnegative real numbers: (1) convolution with complex-valued vectors followed by (2) taking the absolute value of every entry of the resulting vectors followed by (3) local averaging. For processing real-valued random vectors, complex-valued convnets can be viewed as "data-driven multiscale windowed power spectra," "data-driven multiscale windowed absolute spectra," "data-driven multiwavelet absolute values," or (in their most general configuration) "data-driven nonlinear multiwavelet packets." Indeed, complex-valued convnets can calculate multiscale windowed spectra when the convnet filters are windowed complex-valued exponentials. Standard real-valued convnets, using rectified linear units (ReLUs), sigmoidal (for example, logistic or tanh) nonlinearities, max. pooling, etc., do not obviously exhibit the same exact correspondence with data-driven wavelets (whereas for complex-valued convnets, the correspondence is much more than just a vague analogy). Courtesy of the exact correspondence, the remarkably rich and rigorous body of mathematical analysis for wavelets applies directly to (complex-valued) convnets.