Driven by the outstanding performance of neural networks in the structured Euclidean domain, recent years have seen a surge of interest in developing neural networks for graphs and data supported on graphs. The graph is leveraged as a parameterization to capture detail at the node level with a reduced number of parameters and complexity. Following this rationale, this paper puts forth a general framework that unifies state-of-the-art graph neural networks (GNNs) through the concept of EdgeNet. An EdgeNet is a GNN architecture that allows different nodes to use different parameters to weigh the information of different neighbors. By extrapolating this strategy to more iterations between neighboring nodes, the EdgeNet learns edge- and neighbor-dependent weights to capture local detail. This is the most general local operation that a node can do and encompasses under one formulation all graph convolutional neural networks (GCNNs) as well as graph attention networks (GATs). In writing different GNN architectures with a common language, EdgeNets highlight specific architecture advantages and limitations, while providing guidelines to improve their capacity without compromising their local implementation. For instance, we show that GCNNs have a parameter sharing structure that induces permutation equivariance. This can be an advantage or a limitation, depending on the application. When it is a limitation, we propose hybrid approaches and provide insights to develop several other solutions that promote parameter sharing without enforcing permutation equivariance. Another interesting conclusion is the unification of GCNNs and GATs -approaches that have been so far perceived as separate. In particular, we show that GATs are GCNNs on a graph that is learned from the features. This particularization opens the doors to develop alternative attention mechanisms for improving discriminatory power.

Adversarial attacks on deep neural networks (DNNs) have been found for several years. However, the existing adversarial attacks have high success rates only when the information of the attacked DNN is well-known or could be estimated by structure similarity or massive queries. In this paper, we propose an \emph{Attack on Attention} (AoA), a semantic feature commonly shared by DNNs. The transferability of AoA is quite high. With no more than 10 queries of the decision only, AoA can achieve almost 100\% success rate when attacking on many popular DNNs. Even without query, AoA could keep a surprisingly high attack performance. We apply AoA to generate 96020 adversarial samples from ImageNet to defeat many neural networks, and thus name the dataset as \emph{DAmageNet}. 20 well-trained DNNs are tested on DAmageNet. Without adversarial training, most of the tested DNNs have an error rate over 90\%. DAmageNet is the first universal adversarial dataset and it could serve as a benchmark for robustness testing and adversarial training.

Deep Neural Networks (DNNs) are finding important applications in safety-critical systems such as Autonomous Vehicles (AVs), where perceiving the environment correctly and robustly is necessary for safe operation. Raising unique challenges for assurance due to their black-box nature, DNNs pose a fundamental problem for regulatory acceptance of these types of systems. Robust training --- training to minimize excessive sensitivity to small changes in input --- has emerged as one promising technique to address this challenge. However, existing robust training tools are inconvenient to use or apply to existing codebases and models: they typically only support a small subset of model elements and require users to extensively rewrite the training code. In this paper we introduce a novel framework, PaRoT, developed on the popular TensorFlow platform, that greatly reduces the barrier to entry. Our framework enables robust training to be performed on arbitrary DNNs without any rewrites to the model. We demonstrate that our framework's performance is comparable to prior art, and exemplify its ease of use on off-the-shelf, trained models and on a real-world industrial application: training a robust traffic light detection network.

A deep neural network (DNN) with piecewise linear activatio ns can partition the input space into numerous small linear regions, where diffe rent linear functions are fitted. It is believed that the number of these regions rep resents the expressivity of the DNN. This paper provides a novel and meticulous perspe ctive to look into DNNs: Instead of just counting the number of the linear regio ns, we study their local properties, such as the inspheres, the directions of t he corresponding hyper-planes, the decision boundaries, and the relevance of the su rrounding regions. W e empirically observed that different optimization techniq ues lead to completely different linear regions, even though they result in similar cl assification accuracies. W e hope our study can inspire the design of novel optimizatio n techniques, and help discover and analyze the behaviors of DNNs. In the past few decades, deep neural networks (DNNs) have ach ieved remarkable success in various difficult tasks of machine learning (Krizhevsky et al., 2012; Graves et al., 2013; Goodfellow et al., 2014; He et al., 2016; Silver et al., 2017; Devlin et al., 2019). Albeit the great progress DNNs have made, there are still many problems which have not been thoro ughly studied, such as the expressivity and optimization of DNNs. High expressivity is believed to be one of the most important reasons for the success of DNNs. It is well known that a standard deep feedforward network with pie cewise linear activations can partition the input space into many linear regions, where different li near functions are fitted (Pascanu et al., 2014; Montufar et al., 2014). More specifically, the activat ion states are in one-to-one correspondence with the linear regions, i.e., all points in the same li near region activate the same nodes of the DNN, and hence the hidden layers serve as a series of affine transformations of these points.

Data-based discovery of effective, coarse-grained (CG) models of high-dimensional dynamical systems presents a unique challenge in computational physics and particularly in the context of multiscale problems. The present paper offers a data-based, probablistic perspective that enables the quantification of predictive uncertainties. One of the outstanding problems has been the introduction of physical constraints in the probabilistic machine learning objectives. The primary utility of such constraints stems from the undisputed physical laws such as conservation of mass, energy etc that they represent. Furthermore and apart from leading to physically realistic predictions, they can significantly reduce the requisite amount of training data which for high-dimensional, multiscale systems are expensive to obtain (Small Data regime). We formulate the coarse-graining process by employing a probabilistic state-space model and account for the aforementioned equality constraints as virtual observables in the associated densities. We demonstrate how probabilistic inference tools can be employed to identify the coarse-grained variables in combination with deep neural nets and their evolution model without ever needing to define a fine-to-coarse (restriction) projection and without needing time-derivatives of state variables. The formulation adopted enables the quantification of a crucial, and often neglected, component in the CG process, i.e. the predictive uncertainty due to information loss. Furthermore, it is capable of reconstructing the evolution of the full, fine-scale system and therefore the observables of interest need not be selected a priori. We demonstrate the efficacy of the proposed framework by applying it to systems of interacting particles and an image series of a nonlinear pendulum. In both cases we identify the underlying coarse dynamics and can generate extrap-olative predicitions including the forming and propagation of a shock for the particle systems and a stable trajectory in the phase space for the pendulum. Keywords: Bayesian machine learning, virtual observables, multiscale modeling, reduced order modeling, coarse graining1. Introduction High-dimensional, nonlinear dynamical systems are ubiquitous in applied physics and engineering. The computational resources needed for their solution can grow exponentially with the dimension of the state-space as well as with the smallest timescale that needs to be resolved as this determines the discretization time-step.

A brain-computer interface (BCI) system usually needs a long calibration session for each new subject/task to adjust its parameters, which impedes its transition from the laboratory to real-world applications. Domain adaptation, which leverages labeled data from auxiliary subjects/tasks (source domains), has demonstrated its effectiveness in reducing such calibration effort. Currently, most domain adaptation approaches require the source domains to have the same feature space and label space as the target domain, which limits their applications, as the auxiliary data may have different feature spaces and/or different label spaces. This paper considers different set domain adaptation for BCIs, i.e., the source and target domains have different label spaces. We introduce a practical setting of different label sets for BCIs, and propose a novel label alignment (LA) approach to align the source label space with the target label space. It has three desirable properties: 1) LA only needs as few as one labeled sample from each class of the target subject; 2) LA can be used as a preprocessing step before different feature extraction and classification algorithms; and, 3) LA can be integrated with other domain adaptation approaches to achieve even better performance. Experiments on two motor imagery datasets demonstrated the effectiveness of LA.

During training, the weights of a Deep Neural Network (DNN) are optimized from a random initialization towards a nearly optimum value minimizing a loss function. Only this final state of the weights is typically kept for testing, while the wealth of information on the geometry of the weight space, accumulated over the descent towards the minimum is discarded. In this work we propose to make use of this knowledge and leverage it for computing the distributions of the weights of the DNN. This can be further used for estimating the epistemic uncertainty of the DNN by sampling an ensemble of networks from these distributions. T o this end we introduce a method for tracking the trajectory of the weights during optimization, that does not require any changes in the architecture nor on the training procedure. W e evaluate our method on standard classification and regression benchmarks, and on out-of-distribution detection for classification and semantic segmentation. W e achieve competitive results, while preserving computational efficiency in comparison to other popular approaches.

We present an attention mechanism inspired from definition of screened Coulomb potential. This attention mechanism was used to interpret the Graph Attention (GAT) model layers and training dataset by using a flexible and scalable framework (CoulGAT) developed for this purpose. Using CoulGAT, a forest of plain and resnet models were trained and characterized using this attention mechanism against CHAMPS dataset. The learnable variables of the attention mechanism are used to extract node-node and node-feature interactions to define an empirical standard model for the graph structure and hidden layer. This representation of graph and hidden layers can be used as a tool to compare different models, optimize hidden layers and extract a compact definition of graph structure of the dataset.

This paper studies the fundamental problem of learning deep generative models that consist of one or more layers of latent variables organized in top-down architectures. Learning such a generative model requires inferring the latent variables for each training example based on the posterior distribution of these latent variables. The inference typically requires Markov chain Monte Caro (MCMC) that can be time consuming. In this paper, we propose to use short run inference dynamics guided by the log-posterior, such as finite-step gradient descent algorithm initialized from the prior distribution of the latent variables, as an approximate sampler of the posterior distribution, where the step size of the gradient descent dynamics is optimized by minimizing the Kullback-Leibler divergence between the distribution produced by the short run inference dynamics and the posterior distribution. Our experiments show that the proposed method outperforms variational auto-encoder (VAE) in terms of reconstruction error and synthesis quality. The advantage of the proposed method is that it is natural and automatic, even for models with multiple layers of latent variables.

Graph Convolutional Networks (GCNs) have gained significant developments in representation learning on graphs. However, current GCNs suffer from two common challenges: 1) GCNs are only effective with shallow structures; stacking multiple GCN layers will lead to over-smoothing. 2) GCNs do not scale well with large, dense graphs due to the recursive neighborhood expansion. We generalize the propagation strategies of current GCNs as a \emph{"Sink$\to$Source"} mode, which seems to be an underlying cause of the two challenges. To address these issues intrinsically, in this paper, we study the information propagation mechanism in a \emph{"Source$\to$Sink"} mode. We introduce a new concept "information flow path" that explicitly defines where information originates and how it diffuses. Then a novel framework, namely Flow Graph Network (FlowGN), is proposed to learn node representations. FlowGN is computationally efficient and flexible in propagation strategies. Moreover, FlowGN decouples the layer structure from the information propagation process, removing the interior constraint of applying deep structures in traditional GCNs. Further experiments on public datasets demonstrate the superiority of FlowGN against state-of-the-art GCNs.