We describe a new software framework for fast training of generalized linear models. The framework, named Snap Machine Learning (Snap ML), combines recent advances in machine learning systems and algorithms in a nested manner to reflect the hierarchical architecture of modern computing systems. We prove theoretically that such a hierarchical system can accelerate training in distributed environments where intra-node communication is cheaper than inter-node communication. Additionally, we provide a review of the implementation of Snap ML in terms of GPU acceleration, pipelining, communication patterns and software architecture, highlighting aspects that were critical for achieving high performance. We evaluate the performance of Snap ML in both single-node and multi-node environments, quantifying the benefit of the hierarchical scheme and the data streaming functionality, and comparing with other widely-used machine learning software frameworks. Finally, we present a logistic regression benchmark on the Criteo Terabyte Click Logs dataset and show that Snap ML achieves the same test loss an order of magnitude faster than any of the previously reported results, including those obtained using TensorFlow and scikit-learn.

Nonlocal neural networks have been proposed and shown to be effective in several computer vision tasks, where the nonlocal operations can directly capture long-range dependencies in the feature space. In this paper, we study the nature of diffusion and damping effect of nonlocal networks by doing spectrum analysis on the weight matrices of the well-trained networks, and then propose a new formulation of the nonlocal block. The new block not only learns the nonlocal interactions but also has stable dynamics, thus allowing deeper nonlocal structures. Moreover, we interpret our formulation from the general nonlocal modeling perspective, where we make connections between the proposed nonlocal network and other nonlocal models, such as nonlocal diffusion process and Markov jump process.

Graph matching has received persistent attention over several decades, which can be formulated as a quadratic assignment problem (QAP). We show that a large family of functions, which we define as Separable Functions, can approximate discrete graph matching in the continuous domain asymptotically by varying the approximation controlling parameters. We also study the properties of global optimality and devise convex/concave-preserving extensions to the widely used Lawler's QAP form. Our theoretical findings show the potential for deriving new algorithms and techniques for graph matching. We deliver solvers based on two specific instances of Separable Functions, and the state-of-the-art performance of our method is verified on popular benchmarks.

We present a formulation of deep learning that aims at producing a large margin classifier. The notion of \emc{margin}, minimum distance to a decision boundary, has served as the foundation of several theoretically profound and empirically successful results for both classification and regression tasks. However, most large margin algorithms are applicable only to shallow models with a preset feature representation; and conventional margin methods for neural networks only enforce margin at the output layer. Such methods are therefore not well suited for deep networks. In this work, we propose a novel loss function to impose a margin on any chosen set of layers of a deep network (including input and hidden layers). Our formulation allows choosing any $l_p$ norm ($p \geq 1$) on the metric measuring the margin. We demonstrate that the decision boundary obtained by our loss has nice properties compared to standard classification loss functions. Specifically, we show improved empirical results on the MNIST, CIFAR-10 and ImageNet datasets on multiple tasks: generalization from small training sets, corrupted labels, and robustness against adversarial perturbations. The resulting loss is general and complementary to existing data augmentation (such as random/adversarial input transform) and regularization techniques such as weight decay, dropout, and batch norm. \footnote{Code for the large margin loss function is released at \url{https://github.com/google-research/google-research/tree/master/large_margin}}

We address the problem of learning semantic representation of questions to measure similarity between pairs as a continuous distance metric. Our work naturally extends Word Mover's Distance (WMD) [1] by representing text documents as normal distributions instead of bags of embedded words. Our learned metric measures the dissimilarity between two questions as the minimum amount of distance the intent (hidden representation) of one question needs to "travel" to match the intent of another question. We first learn to repeat, reformulate questions to infer intents as normal distributions with a deep generative model [2] (variational auto encoder). Semantic similarity between pairs is then learned discriminatively as an optimal transport distance metric (Wasserstein 2) with our novel variational siamese framework. Among known models that can read sentences individually, our proposed framework achieves competitive results on Quora duplicate questions dataset. Our work sheds light on how deep generative models can approximate distributions (semantic representations) to effectively measure semantic similarity with meaningful distance metrics from Information Theory.

Multiplicative noise, including dropout, is widely used to regularize deep neural networks (DNNs), and is shown to be effective in a wide range of architectures and tasks. From an information perspective, we consider injecting multiplicative noise into a DNN as training the network to solve the task with noisy information pathways, which leads to the observation that multiplicative noise tends to increase the correlation between features, so as to increase the signal-to-noise ratio of information pathways. However, high feature correlation is undesirable, as it increases redundancy in representations. In this work, we propose non-correlating multiplicative noise (NCMN), which exploits batch normalization to remove the correlation effect in a simple yet effective way. We show that NCMN significantly improves the performance of standard multiplicative noise on image classification tasks, providing a better alternative to dropout for batch-normalized networks. Additionally, we present a unified view of NCMN and shake-shake regularization, which explains the performance gain of the latter.

Convolutional neural networks (CNNs) are inherently subject to invariable filters that can only aggregate local inputs with the same topological structures. It causes that CNNs are allowed to manage data with Euclidean or grid-like structures (e.g., images), not ones with non-Euclidean or graph structures (e.g., traffic networks). To broaden the reach of CNNs, we develop structure-aware convolution to eliminate the invariance, yielding a unified mechanism of dealing with both Euclidean and non-Euclidean structured data. Technically, filters in the structure-aware convolution are generalized to univariate functions, which are capable of aggregating local inputs with diverse topological structures. Since infinite parameters are required to determine a univariate function, we parameterize these filters with numbered learnable parameters in the context of the function approximation theory. By replacing the classical convolution in CNNs with the structure-aware convolution, Structure-Aware Convolutional Neural Networks (SACNNs) are readily established. Extensive experiments on eleven datasets strongly evidence that SACNNs outperform current models on various machine learning tasks, including image classification and clustering, text categorization, skeleton-based action recognition, molecular activity detection, and taxi flow prediction.

As machine learning becomes more widely used in practice, we need new methods to build complex intelligent systems that integrate learning with existing software, and with domain knowledge encoded as rules. As a case study, we present such a system that learns to parse Newtonian physics problems in textbooks. This system, Nuts&Bolts, learns a pipeline process that incorporates existing code, pre-learned machine learning models, and human engineered rules. It jointly trains the entire pipeline to prevent propagation of errors, using a combination of labelled and unlabelled data. Our approach achieves a good performance on the parsing task, outperforming the simple pipeline and its variants. Finally, we also show how Nuts&Bolts can be used to achieve improvements on a relation extraction task and on the end task of answering Newtonian physics problems.

In this paper, we consider the problem of linear regression with heavy-tailed distributions. Different from previous studies that use the squared loss to measure the performance, we choose the absolute loss, which is capable of estimating the conditional median. To address the challenge that both the input and output could be heavy-tailed, we propose a truncated minimization problem, and demonstrate that it enjoys an $O(\sqrt{d/n})$ excess risk, where $d$ is the dimensionality and $n$ is the number of samples. Compared with traditional work on $\ell_1$-regression, the main advantage of our result is that we achieve a high-probability risk bound without exponential moment conditions on the input and output. Furthermore, if the input is bounded, we show that the classical empirical risk minimization is competent for $\ell_1$-regression even when the output is heavy-tailed.

Convolutional neural networks (CNNs) have recently achieved great success in single-image super-resolution (SISR). However, these methods tend to produce over-smoothed outputs and miss some textural details. To solve these problems, we propose the Super-Resolution CliqueNet (SRCliqueNet) to reconstruct the high resolution (HR) image with better textural details in the wavelet domain. The proposed SRCliqueNet firstly extracts a set of feature maps from the low resolution (LR) image by the clique blocks group. Then we send the set of feature maps to the clique up-sampling module to reconstruct the HR image. The clique up-sampling module consists of four sub-nets which predict the high resolution wavelet coefficients of four sub-bands. Since we consider the edge feature properties of four sub-bands, the four sub-nets are connected to the others so that they can learn the coefficients of four sub-bands jointly. Finally we apply inverse discrete wavelet transform (IDWT) to the output of four sub-nets at the end of the clique up-sampling module to increase the resolution and reconstruct the HR image. Extensive quantitative and qualitative experiments on benchmark datasets show that our method achieves superior performance over the state-of-the-art methods.