Universal Transformer
Self-attentive feed-forward sequence models have been shown to achieve impressive results on sequence modeling tasks, thereby presenting a compelling alternative to recurrent neural networks (RNNs) which has remained the de-facto standard architecture for many sequence modeling problems to date. Despite these successes, however, feed-forward sequence models like the Transformer fail to generalize in many tasks that recurrent models handle with ease (e.g. copying when the string lengths exceed those observed at training time). Moreover, and in contrast to RNNs, the Transformer model is not computationally universal, limiting its theoretical expressivity. In this paper we propose the Universal Transformer which addresses these practical and theoretical shortcomings and we show that it leads to improved performance on several tasks. Instead of recurring over the individual symbols of sequences like RNNs, the Universal Transformer repeatedly revises its representations of all symbols in the sequence with each recurrent step. In order to combine information from different parts of a sequence, it employs a self-attention mechanism in every recurrent step. Assuming sufficient memory, its recurrence makes the Universal Transformer computationally universal. We further employ an adaptive computation time (ACT) mechanism to allow the model to dynamically adjust the number of times the representation of each position in a sequence is revised. Beyond saving computation, we show that ACT can improve the accuracy of the model. Our experiments show that on various algorithmic tasks and a diverse set of large-scale language understanding tasks the Universal Transformer generalizes significantly better and outperforms both a vanilla Transformer and an LSTM in machine translation, and achieves a new state of the art on the bAbI linguistic reasoning task and the challenging LAMBADA language modeling task. …

Pixel-Adaptive Convolutional Neural Network
Convolutions are the fundamental building block of CNNs. The fact that their weights are spatially shared is one of the main reasons for their widespread use, but it also is a major limitation, as it makes convolutions content agnostic. We propose a pixel-adaptive convolution (PAC) operation, a simple yet effective modification of standard convolutions, in which the filter weights are multiplied with a spatially-varying kernel that depends on learnable, local pixel features. PAC is a generalization of several popular filtering techniques and thus can be used for a wide range of use cases. Specifically, we demonstrate state-of-the-art performance when PAC is used for deep joint image upsampling. PAC also offers an effective alternative to fully-connected CRF (Full-CRF), called PAC-CRF, which performs competitively, while being considerably faster. In addition, we also demonstrate that PAC can be used as a drop-in replacement for convolution layers in pre-trained networks, resulting in consistent performance improvements. …

Monte Carlo Dependency Estimation (MCDE)
Estimating the dependency of variables is a fundamental task in data analysis. Identifying the relevant attributes in databases leads to better data understanding and also improves the performance of learning algorithms, both in terms of runtime and quality. In data streams, dependency monitoring provides key insights into the underlying process, but is challenging. In this paper, we propose Monte Carlo Dependency Estimation (MCDE), a theoretical framework to estimate multivariate dependency in static and dynamic data. MCDE quantifies dependency as the average discrepancy between marginal and conditional distributions via Monte Carlo simulations. Based on this framework, we present Mann-Whitney P (MWP), a novel dependency estimator. We show that MWP satisfies a number of desirable properties and can accommodate any kind of numerical data. We demonstrate the superiority of our estimator by comparing it to the state-of-the-art multivariate dependency measures. …

Nonlinear Collaborative Scheme
Conventional research attributes the improvements of generalization ability of deep neural networks either to powerful optimizers or the new network design. Different from them, in this paper, we aim to link the generalization ability of a deep network to optimizing a new objective function. To this end, we propose a \textit{nonlinear collaborative scheme} for deep network training, with the key technique as combining different loss functions in a nonlinear manner. We find that after adaptively tuning the weights of different loss functions, the proposed objective function can efficiently guide the optimization process. What is more, we demonstrate that, from the mathematical perspective, the nonlinear collaborative scheme can lead to (i) smaller KL divergence with respect to optimal solutions; (ii) data-driven stochastic gradient descent; (iii) tighter PAC-Bayes bound. We also prove that its advantage can be strengthened by nonlinearity increasing. To some extent, we bridge the gap between learning (i.e., minimizing the new objective function) and generalization (i.e., minimizing a PAC-Bayes bound) in the new scheme. We also interpret our findings through the experiments on Residual Networks and DenseNet, showing that our new scheme performs superior to single-loss and multi-loss schemes no matter with randomization or not. …