Deep convolutional neural networks have been shown to be able to fit a labeling over random data while still being able to generalize well on normal datasets. Describing deep convolutional neural network capacity through the measure of spectral complexity has been recently proposed to tackle this apparent paradox. Spectral complexity correlates with GE and can distinguish networks trained on normal and random labels. We propose the first GE bound based on spectral complexity for deep convolutional neural networks and provide tighter bounds by orders of magnitude from the previous estimate. We then investigate theoretically and empirically the insensitivity of spectral complexity to invariances of modern deep convolutional neural networks, and show several limitations of spectral complexity that occur as a result.

Neural network training is usually accomplished by solving a non-convex optimization problem using stochastic gradient descent. Although one optimizes over the networks parameters, the loss function generally only depends on the realization of a neural network, i.e. the function it computes. Studying the functional optimization problem over the space of realizations can open up completely new ways to understand neural network training. In particular, usual loss functions like the mean squared error are convex on sets of neural network realizations, which themselves are non-convex. Note, however, that each realization has many different, possibly degenerate, parametrizations. In particular, a local minimum in the parametrization space needs not correspond to a local minimum in the realization space. To establish such a connection, inverse stability of the realization map is required, meaning that proximity of realizations must imply proximity of corresponding parametrizations. In this paper we present pathologies which prevent inverse stability in general, and proceed to establish a restricted set of parametrizations on which we have inverse stability w.r.t. to a Sobolev norm. Furthermore, we show that by optimizing over such restricted sets, it is still possible to learn any function, which can be learned by optimization over unrestricted sets. While most of this paper focuses on shallow networks, none of methods used are, in principle, limited to shallow networks, and it should be possible to extend them to deep neural networks.

State-of-the-art deep learning methods have shown a remarkable capacity to model complex data domains, but struggle with geospatial data. In this paper, we introduce SpaceGAN, a novel generative model for geospatial domains that learns neighbourhood structures through spatial conditioning. We propose to enhance spatial representation beyond mere spatial coordinates, by conditioning each data point on feature vectors of its spatial neighbours, thus allowing for a more flexible representation of the spatial structure. To overcome issues of training convergence, we employ a metric capturing the loss in local spatial autocorrelation between real and generated data as stopping criterion for SpaceGAN parametrization. This way, we ensure that the generator produces synthetic samples faithful to the spatial patterns observed in the input. SpaceGAN is successfully applied for data augmentation and outperforms compared to other methods of synthetic spatial data generation. Finally, we propose an ensemble learning framework for the geospatial domain, taking augmented SpaceGAN samples as training data for a set of ensemble learners. We empirically show the superiority of this approach over conventional ensemble learning approaches and rivaling spatial data augmentation methods, using synthetic and real-world prediction tasks. Our findings suggest that SpaceGAN can be used as a tool for (1) artificially inflating sparse geospatial data and (2) improving generalization of geospatial models.

Generative Adversarial Networks (GANs) enjoy great success at image generation, but have proven difficult to train in the domain of natural language. Challenges with gradient estimation, optimization instability, and mode collapse have lead practitioners to resort to maximum likelihood pre-training, followed by small amounts of adversarial fine-tuning. The benefits of GAN fine-tuning for language generation are unclear, as the resulting models produce comparable or worse samples than traditional language models. We show it is in fact possible to train a language GAN from scratch -- without maximum likelihood pre-training. We combine existing techniques such as large batch sizes, dense rewards and discriminator regularization to stabilize and improve language GANs. The resulting model, ScratchGAN, performs comparably to maximum likelihood training on EMNLP2017 News and WikiText-103 corpora according to quality and diversity metrics.

The wide and rapid adoption of deep learning by practitioners brought unintended consequences in many situations such as in the infamous case of Google Photos' racist image recognition algorithm; thus, necessitated the utilization of the quantified uncertainty for each prediction. There have been recent efforts towards quantifying uncertainty in conventional deep learning methods (e.g., dropout as Bayesian approximation); however, their optimal use in decision making is often overlooked and understudied. In this study, we propose a mixed-integer programming framework for classification with reject option (also known as selective classification), that investigates and combines model uncertainty and predictive mean to identify optimal classification and rejection regions. Our results indicate superior performance of our framework both in non-rejected accuracy and rejection quality on several publicly available datasets. Moreover, we extend our framework to cost-sensitive settings and show that our approach outperforms industry standard methods significantly for online fraud management in real-world settings.

Despite recent innovations in network architectures and loss functions, training RNNs to learn long-term dependencies remains difficult due to challenges with gradient-based optimisation methods. Inspired by the success of Deep Neuroevolution in reinforcement learning (Such et al. 2017), we explore the use of gradient-free population-based global optimisation (PBO) techniques -- training RNNs to capture long-term dependencies in time-series data. Testing evolution strategies (ES) and particle swarm optimisation (PSO) on an application in volatility forecasting, we demonstrate that PBO methods lead to performance improvements in general, with ES exhibiting the most consistent results across a variety of architectures.

Lossless compression methods shorten the expected representation size of data without loss of information, using a statistical model. Flow-based models are attractive in this setting because they admit exact likelihood optimization, which is equivalent to minimizing the expected number of bits per message. However, conventional flows assume continuous data, which may lead to reconstruction errors when quantized for compression. For that reason, we introduce a flow-based generative model for ordinal discrete data called Integer Discrete Flow (IDF): a bijective integer map that can learn rich transformations on high-dimensional data. As building blocks for IDFs, we introduce a flexible transformation layer called integer discrete coupling. Our experiments show that IDFs are competitive with other flow-based generative models. Furthermore, we demonstrate that IDF based compression achieves state-of-the-art lossless compression rates on CIFAR10, ImageNet32, and ImageNet64. To the best of our knowledge, this is the first lossless compression method that uses invertible neural networks.

Recent progress in machine learning techniques have revived interest in building artificial general intelligence using these particular tools. There has been a tremendous success in applying them for narrow intellectual tasks such as pattern recognition, natural language processing and playing Go. The latter application vastly outperforms the strongest human player in recent years. However, these tasks are formalized by people in such ways that it has become "easy" for automated recipes to find better solutions than humans do. In the sense of John Searle's Chinese Room Argument, the computer playing Go does not actually understand anything from the game. Thinking like a human mind requires to go beyond the curve fitting paradigm of current systems. There is a fundamental limit to what they can achieve currently as only very specific problem formalization can increase their performances in particular tasks. In this paper, we argue than one of the most important aspects of the human mind is its capacity for logical thinking, which gives rise to many intellectual expressions that differentiate us from animal brains. We propose to model the emergence of logical thinking based on Piaget's theory of cognitive development.

The creation of social ties is largely determined by the entangled effects of people's similarities in terms of individual characters and friends. However, feature and structural characters of people usually appear to be correlated, making it difficult to determine which has greater responsibility in the formation of the emergent network structure. We propose \emph{AN2VEC}, a node embedding method which ultimately aims at disentangling the information shared by the structure of a network and the features of its nodes. Building on the recent developments of Graph Convolutional Networks (GCN), we develop a multitask GCN Variational Autoencoder where different dimensions of the generated embeddings can be dedicated to encoding feature information, network structure, and shared feature-network information. We explore the interaction between these disentangled characters by comparing the embedding reconstruction performance to a baseline case where no shared information is extracted. We use synthetic datasets with different levels of interdependency between feature and network characters and show (i) that shallow embeddings relying on shared information perform better than the corresponding reference with unshared information, (ii) that this performance gap increases with the correlation between network and feature structure, and (iii) that our embedding is able to capture joint information of structure and features. Our method can be relevant for the analysis and prediction of any featured network structure ranging from online social systems to network medicine.

Stochastic methods with coordinate-wise adaptive stepsize (such as RMSprop and Adam) have been widely used in training deep neural networks. Despite their fast convergence, they can generalize worse than stochastic gradient descent. In this paper, by revisiting the design of Adagrad, we propose to split the network parameters into blocks, and use a blockwise adaptive stepsize. Intuitively, blockwise adaptivity is less aggressive than adaptivity to individual coordinates, and can have a better balance between adaptivity and generalization. We show theoretically that the proposed blockwise adaptive gradient descent has comparable convergence rate as its counterpart with coordinate-wise adaptive stepsize, but is faster up to some constant. We also study its uniform stability and show that blockwise adaptivity can lead to lower generalization error than coordinate-wise adaptivity. Experimental results show that blockwise adaptive gradient descent converges faster and improves generalization performance over Nesterov's accelerated gradient and Adam.