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Group synchronization refers to estimating a collection of group elements from the noisy pairwise measurements. Such a nonconvex problem has received much attention from numerous scientific fields including computer vision, robotics, and cryo-electron microscopy. In this paper, we focus on the orthogonal group synchronization problem with general additive noise models under incomplete measurements, which is much more general than the commonly considered setting of complete measurements. Characterizations of the orthogonal group synchronization problem are given from perspectives of optimality conditions as well as fixed points of the projected gradient ascent method which is also known as the generalized power method (GPM). It is well worth noting that these results still hold even without generative models. In the meantime, we derive the local error bound property for the orthogonal group synchronization problem which is useful for the convergence rate analysis of different algorithms and can be of independent interest. Finally, we prove the linear convergence result of the GPM to a global maximizer under a general additive noise model based on the established local error bound property. Our theoretical convergence result holds under several deterministic conditions which can cover certain cases with adversarial noise, and as an example we specialize it to the setting of the Erd\"os-R\'enyi measurement graph and Gaussian noise.

Machine learning models are critically susceptible to evasion attacks from adversarial examples. Generally, adversarial examples, modified inputs deceptively similar to the original input, are constructed under whitebox settings by adversaries with full access to the model. However, recent attacks have shown a remarkable reduction in query numbers to craft adversarial examples using blackbox attacks. Particularly, alarming is the ability to exploit the classification decision from the access interface of a trained model provided by a growing number of Machine Learning as a Service providers including Google, Microsoft, IBM and used by a plethora of applications incorporating these models. The ability of an adversary to exploit only the predicted label from a model to craft adversarial examples is distinguished as a decision-based attack. In our study, we first deep dive into recent state-of-the-art decision-based attacks in ICLR and SP to highlight the costly nature of discovering low distortion adversarial employing gradient estimation methods. We develop a robust query efficient attack capable of avoiding entrapment in a local minimum and misdirection from noisy gradients seen in gradient estimation methods. The attack method we propose, RamBoAttack, exploits the notion of Randomized Block Coordinate Descent to explore the hidden classifier manifold, targeting perturbations to manipulate only localized input features to address the issues of gradient estimation methods. Importantly, the RamBoAttack is more robust to the different sample inputs available to an adversary and the targeted class. Overall, for a given target class, RamBoAttack is demonstrated to be more robust at achieving a lower distortion within a given query budget. We curate our extensive results using the large-scale high-resolution ImageNet dataset and open-source our attack, test samples and artifacts on GitHub.

In this article, we study the Adjacent Quadratic Shortest Path Problem (AQSPP), which consists in finding the shortest path on a directed graph when its total weight component also includes the impact of consecutive arcs. We provide a formal description of the AQSPP and propose an extension of Dijkstra's algorithm (that we denote aqD) for solving AQSPPs in polynomial-time and provide a proof for its correctness under some mild assumptions. Furthermore, we introduce an adjacent quadratic A* algorithm (that we denote aqA*) with a backward search for cost-to-go estimation to speed up the search. We assess the performance of both algorithms by comparing their relative performance with benchmark algorithms from the scientific literature and carry out a thorough collection of sensitivity analysis of the methods on a set of problem characteristics using randomly generated graphs. Numerical results suggest that: (i) aqA* outperforms all other algorithms, with a performance being about 75 times faster than aqD and the fastest alternative; (ii) the proposed solution procedures do not lose efficiency when the magnitude of quadratic costs vary; (iii) aqA* and aqD are fastest on random graph instances, compared with benchmark algorithms from scientific literature. We conclude the numerical experiments by presenting a stress test of the AQSPP in the context of real grid graph instances, with sizes up to $16 \times 10^6$ nodes, $64 \times 10^6$ arcs, and $10^9$ quadratic arcs.

Neural networks are popular and useful in many fields, but they have the problem of giving high confidence responses for examples that are away from the training data. This makes the neural networks very confident in their prediction while making gross mistakes, thus limiting their reliability for safety-critical applications such as autonomous driving, space exploration, etc. This paper introduces a novel neuron generalization that has the standard dot-product-based neuron and the {\color{black} radial basis function (RBF)} neuron as two extreme cases of a shape parameter. Using a rectified linear unit (ReLU) as the activation function results in a novel neuron that has compact support, which means its output is zero outside a bounded domain. To address the difficulties in training the proposed neural network, it introduces a novel training method that takes a pretrained standard neural network that is fine-tuned while gradually increasing the shape parameter to the desired value. The theoretical findings of the paper are a bound on the gradient of the proposed neuron and a proof that a neural network with such neurons has the universal approximation property. This means that the network can approximate any continuous and integrable function with an arbitrary degree of accuracy. The experimental findings on standard benchmark datasets show that the proposed approach has smaller test errors than state-of-the-art competing methods and outperforms the competing methods in detecting out-of-distribution samples on two out of three datasets.

Tensor decomposition is one of the fundamental technique for model compression of deep convolution neural networks owing to its ability to reveal the latent relations among complex structures. However, most existing methods compress the networks layer by layer, which cannot provide a satisfactory solution to achieve global optimization. In this paper, we proposed a model reduction method to compress the pre-trained networks using low-rank tensor decomposition of the convolution layers. Our method is based on the optimization techniques to select the proper ranks of decomposed network layers. A new regularization method, called funnel function, is proposed to suppress the unimportant factors during the compression, so the proper ranks can be revealed much easier. The experimental results show that our algorithm can reduce more model parameters than other tensor compression methods. For ResNet18 with ImageNet2012, our reduced model can reach more than twi times speed up in terms of GMAC with merely 0.7% Top-1 accuracy drop, which outperforms most existing methods in both metrics.

Learning low-dimensional topological representation of a network in dynamic environments is attracting much attention due to the time-evolving nature of many real-world networks. The main and common objective of Dynamic Network Embedding (DNE) is to efficiently update node embeddings while preserving network topology at each time step. The idea of most existing DNE methods is to capture the topological changes at or around the most affected nodes (instead of all nodes) and accordingly update node embeddings. Unfortunately, this kind of approximation, although can improve efficiency, cannot effectively preserve the global topology of a dynamic network at each time step, due to not considering the inactive sub-networks that receive accumulated topological changes propagated via the high-order proximity. To tackle this challenge, we propose a novel node selecting strategy to diversely select the representative nodes over a network, which is coordinated with a new incremental learning paradigm of Skip-Gram based embedding approach. The extensive experiments show GloDyNE, with a small fraction of nodes being selected, can already achieve the superior or comparable performance w.r.t. the state-of-the-art DNE methods in three typical downstream tasks. Particularly, GloDyNE significantly outperforms other methods in the graph reconstruction task, which demonstrates its ability of global topology preservation. The source code is available at //github.com/houchengbin/GloDyNE

Co-evolving time series appears in a multitude of applications such as environmental monitoring, financial analysis, and smart transportation. This paper aims to address the following challenges, including (C1) how to incorporate explicit relationship networks of the time series; (C2) how to model the implicit relationship of the temporal dynamics. We propose a novel model called Network of Tensor Time Series, which is comprised of two modules, including Tensor Graph Convolutional Network (TGCN) and Tensor Recurrent Neural Network (TRNN). TGCN tackles the first challenge by generalizing Graph Convolutional Network (GCN) for flat graphs to tensor graphs, which captures the synergy between multiple graphs associated with the tensors. TRNN leverages tensor decomposition to model the implicit relationships among co-evolving time series. The experimental results on five real-world datasets demonstrate the efficacy of the proposed method.

Most algorithms for representation learning and link prediction in relational data have been designed for static data. However, the data they are applied to usually evolves with time, such as friend graphs in social networks or user interactions with items in recommender systems. This is also the case for knowledge bases, which contain facts such as (US, has president, B. Obama, [2009-2017]) that are valid only at certain points in time. For the problem of link prediction under temporal constraints, i.e., answering queries such as (US, has president, ?, 2012), we propose a solution inspired by the canonical decomposition of tensors of order 4. We introduce new regularization schemes and present an extension of ComplEx (Trouillon et al., 2016) that achieves state-of-the-art performance. Additionally, we propose a new dataset for knowledge base completion constructed from Wikidata, larger than previous benchmarks by an order of magnitude, as a new reference for evaluating temporal and non-temporal link prediction methods.

The monitoring and management of numerous and diverse time series data at Alibaba Group calls for an effective and scalable time series anomaly detection service. In this paper, we propose RobustTAD, a Robust Time series Anomaly Detection framework by integrating robust seasonal-trend decomposition and convolutional neural network for time series data. The seasonal-trend decomposition can effectively handle complicated patterns in time series, and meanwhile significantly simplifies the architecture of the neural network, which is an encoder-decoder architecture with skip connections. This architecture can effectively capture the multi-scale information from time series, which is very useful in anomaly detection. Due to the limited labeled data in time series anomaly detection, we systematically investigate data augmentation methods in both time and frequency domains. We also introduce label-based weight and value-based weight in the loss function by utilizing the unbalanced nature of the time series anomaly detection problem. Compared with the widely used forecasting-based anomaly detection algorithms, decomposition-based algorithms, traditional statistical algorithms, as well as recent neural network based algorithms, RobustTAD performs significantly better on public benchmark datasets. It is deployed as a public online service and widely adopted in different business scenarios at Alibaba Group.

Self-attention network (SAN) has recently attracted increasing interest due to its fully parallelized computation and flexibility in modeling dependencies. It can be further enhanced with multi-headed attention mechanism by allowing the model to jointly attend to information from different representation subspaces at different positions (Vaswani et al., 2017). In this work, we propose a novel convolutional self-attention network (CSAN), which offers SAN the abilities to 1) capture neighboring dependencies, and 2) model the interaction between multiple attention heads. Experimental results on WMT14 English-to-German translation task demonstrate that the proposed approach outperforms both the strong Transformer baseline and other existing works on enhancing the locality of SAN. Comparing with previous work, our model does not introduce any new parameters.