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Great advances in deep neural networks (DNNs) have led to state-of-the-art performance on a wide range of tasks. However, recent studies have shown that DNNs are vulnerable to adversarial attacks, which have brought great concerns when deploying these models to safety-critical applications such as autonomous driving. Different defense approaches have been proposed against adversarial attacks, including: a) empirical defenses, which usually can be adaptively attacked again without providing robustness certification; and b) certifiably robust approaches which consist of robustness verification providing the lower bound of robust accuracy against any attacks under certain conditions and corresponding robust training approaches. In this paper, we systematize the certifiably robust approaches and related practical and theoretical implications and findings. We also provide the first comprehensive benchmark on existing robustness verification and training approaches on different datasets. In particular, we 1) provide a taxonomy for the robustness verification and training approaches, as well as summarize the methodologies for representative algorithms, 2) reveal the characteristics, strengths, limitations, and fundamental connections among these approaches, 3) discuss current research progresses, theoretical barriers, main challenges, and future directions for certifiably robust approaches for DNNs, and 4) provide an open-sourced unified platform to evaluate over 20 representative certifiably robust approaches for a wide range of DNNs.

Synthetic control (SC) methods have been widely applied to estimate the causal effect of large-scale interventions, e.g., the state-wide effect of a change in policy. The idea of synthetic controls is to approximate one unit's counterfactual outcomes using a weighted combination of some other units' observed outcomes. The motivating question of this paper is: how does the SC strategy lead to valid causal inferences? We address this question by re-formulating the causal inference problem targeted by SC with a more fine-grained model, where we change the unit of the analysis from "large units" (e.g., states) to "small units" (e.g., individuals in states). Under this re-formulation, we derive sufficient conditions for the non-parametric causal identification of the causal effect. We highlight two implications of the reformulation: (1) it clarifies where "linearity" comes from, and how it falls naturally out of the more fine-grained and flexible model, and (2) it suggests new ways of using available data with SC methods for valid causal inference, in particular, new ways of selecting observations from which to estimate the counterfactual.

We consider structured optimisation problems defined in terms of the sum of a smooth and convex function, and a proper, l.s.c., convex (typically non-smooth) one in reflexive variable exponent Lebesgue spaces $L_{p(\cdot)}(\Omega)$. Due to their intrinsic space-variant properties, such spaces can be naturally used as solution space and combined with space-variant functionals for the solution of ill-posed inverse problems. For this purpose, we propose and analyse two instances (primal and dual) of proximal gradient algorithms in $L_{p(\cdot)}(\Omega)$, where the proximal step, rather than depending on the natural (non-separable) $L_{p(\cdot)}(\Omega)$ norm, is defined in terms of its modular function, which, thanks to its separability, allows for the efficient computation of algorithmic iterates. Convergence in function values is proved for both algorithms, with convergence rates depending on problem/space smoothness. To show the effectiveness of the proposed modelling, some numerical tests highlighting the flexibility of the space $L_{p(\cdot)}(\Omega)$ are shown for exemplar deconvolution and mixed noise removal problems. Finally, a numerical verification on the convergence speed and computational costs of both algorithms in comparison with analogous ones defined in standard $L_{p}(\Omega)$ spaces is presented.

Identifying the most influential nodes in information networks has been the focus of many research studies. This problem has crucial applications in various contexts including biology, medicine, and social science, such as controlling the propagation of viruses or rumours in real world networks. While existing methods mostly employ local neighbourhood features which heavily rely on the network structure and disregard the underlying diffusion dynamics, in this work we present a randomized sampling algorithm that not only takes into account the local and global structural features of the network but also considers the underlying diffusion dynamics and its parameters. The main idea is to compute the influentiality of a node through reachability from that node in a set of random graphs. We use a hyper-graph to capture the reachability from nodes in the original network, and theoretically argue that the hypergraph can be used to approximate the theoretical influentiality of nodes in the original graph with a factor of 1 - epsilon. The performance of the proposed model is also evaluated empirically by measuring the correlation between the ranking generated by the proposed method and the ground truth ranking. Our results show that the proposed method substantially outperforms state of the art methods and achieves the highest correlation with the ground-truth ranking, while the generated ranking has a high level of uniqueness and uniformity. Theoretical and practical analysis of the running time of the algorithm also confirms that the proposed method maintains a competitive running time in comparison to the state of the art methods.

Bio-inspired sensorimotor control systems may be appealing to roboticists who try to solve problems of multiDOF humanoids and human-robot interactions. This paper presents a simple posture control concept from neuroscience, called disturbance estimation and compensation, DEC concept [1]. It provides human-like mechanical compliance due to low loop gain, tolerance of time delays, and automatic adjustment to changes in external disturbance scenarios. Its outstanding feature is that it uses feedback of multisensory disturbance estimates rather than 'raw' sensory signals for disturbance compensation. After proof-of-principle tests in 1 and 2 DOF posture control robots, we present here a generalized DEC control module for multi-DOF robots. In the control layout, one DEC module controls one DOF (modular control architecture). Modules of neighboring joints are synergistically interconnected using vestibular information in combination with joint angle and torque signals. These sensory interconnections allow each module to control the kinematics of the more distal links as if they were a single link. This modular design makes the complexity of the robot control scale linearly with the DOFs and error robustness high compared to monolithic control architectures. The presented concept uses Matlab/Simulink (The MathWorks, Natick, USA) for both, model simulation and robot control and will be available as open library

Due to their increasing spread, confidence in neural network predictions became more and more important. However, basic neural networks do not deliver certainty estimates or suffer from over or under confidence. Many researchers have been working on understanding and quantifying uncertainty in a neural network's prediction. As a result, different types and sources of uncertainty have been identified and a variety of approaches to measure and quantify uncertainty in neural networks have been proposed. This work gives a comprehensive overview of uncertainty estimation in neural networks, reviews recent advances in the field, highlights current challenges, and identifies potential research opportunities. It is intended to give anyone interested in uncertainty estimation in neural networks a broad overview and introduction, without presupposing prior knowledge in this field. A comprehensive introduction to the most crucial sources of uncertainty is given and their separation into reducible model uncertainty and not reducible data uncertainty is presented. The modeling of these uncertainties based on deterministic neural networks, Bayesian neural networks, ensemble of neural networks, and test-time data augmentation approaches is introduced and different branches of these fields as well as the latest developments are discussed. For a practical application, we discuss different measures of uncertainty, approaches for the calibration of neural networks and give an overview of existing baselines and implementations. Different examples from the wide spectrum of challenges in different fields give an idea of the needs and challenges regarding uncertainties in practical applications. Additionally, the practical limitations of current methods for mission- and safety-critical real world applications are discussed and an outlook on the next steps towards a broader usage of such methods is given.

Deep neural networks (DNN) have achieved unprecedented success in numerous machine learning tasks in various domains. However, the existence of adversarial examples has raised concerns about applying deep learning to safety-critical applications. As a result, we have witnessed increasing interests in studying attack and defense mechanisms for DNN models on different data types, such as images, graphs and text. Thus, it is necessary to provide a systematic and comprehensive overview of the main threats of attacks and the success of corresponding countermeasures. In this survey, we review the state of the art algorithms for generating adversarial examples and the countermeasures against adversarial examples, for the three popular data types, i.e., images, graphs and text.

Visual Question Answering (VQA) models should have both high robustness and accuracy. Unfortunately, most of the current VQA research only focuses on accuracy because there is a lack of proper methods to measure the robustness of VQA models. There are two main modules in our algorithm. Given a natural language question about an image, the first module takes the question as input and then outputs the ranked basic questions, with similarity scores, of the main given question. The second module takes the main question, image and these basic questions as input and then outputs the text-based answer of the main question about the given image. We claim that a robust VQA model is one, whose performance is not changed much when related basic questions as also made available to it as input. We formulate the basic questions generation problem as a LASSO optimization, and also propose a large scale Basic Question Dataset (BQD) and Rscore (novel robustness measure), for analyzing the robustness of VQA models. We hope our BQD will be used as a benchmark for to evaluate the robustness of VQA models, so as to help the community build more robust and accurate VQA models.

Recent years have witnessed significant progresses in deep Reinforcement Learning (RL). Empowered with large scale neural networks, carefully designed architectures, novel training algorithms and massively parallel computing devices, researchers are able to attack many challenging RL problems. However, in machine learning, more training power comes with a potential risk of more overfitting. As deep RL techniques are being applied to critical problems such as healthcare and finance, it is important to understand the generalization behaviors of the trained agents. In this paper, we conduct a systematic study of standard RL agents and find that they could overfit in various ways. Moreover, overfitting could happen "robustly": commonly used techniques in RL that add stochasticity do not necessarily prevent or detect overfitting. In particular, the same agents and learning algorithms could have drastically different test performance, even when all of them achieve optimal rewards during training. The observations call for more principled and careful evaluation protocols in RL. We conclude with a general discussion on overfitting in RL and a study of the generalization behaviors from the perspective of inductive bias.

Classifying large scale networks into several categories and distinguishing them according to their fine structures is of great importance with several applications in real life. However, most studies of complex networks focus on properties of a single network but seldom on classification, clustering, and comparison between different networks, in which the network is treated as a whole. Due to the non-Euclidean properties of the data, conventional methods can hardly be applied on networks directly. In this paper, we propose a novel framework of complex network classifier (CNC) by integrating network embedding and convolutional neural network to tackle the problem of network classification. By training the classifiers on synthetic complex network data and real international trade network data, we show CNC can not only classify networks in a high accuracy and robustness, it can also extract the features of the networks automatically.