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Real-life applications of deep neural networks are hindered by their unsteady predictions when faced with noisy inputs and adversarial attacks. The certified radius in this context is a crucial indicator of the robustness of models. However how to design an efficient classifier with an associated certified radius? Randomized smoothing provides a promising framework by relying on noise injection into the inputs to obtain a smoothed and robust classifier. In this paper, we first show that the variance introduced by the Monte-Carlo sampling in the randomized smoothing procedure estimate closely interacts with two other important properties of the classifier, \textit{i.e.} its Lipschitz constant and margin. More precisely, our work emphasizes the dual impact of the Lipschitz constant of the base classifier, on both the smoothed classifier and the empirical variance. To increase the certified robust radius, we introduce a different way to convert logits to probability vectors for the base classifier to leverage the variance-margin trade-off. We leverage the use of Bernstein's concentration inequality along with enhanced Lipschitz bounds for randomized smoothing. Experimental results show a significant improvement in certified accuracy compared to current state-of-the-art methods. Our novel certification procedure allows us to use pre-trained models with randomized smoothing, effectively improving the current certification radius in a zero-shot manner.

Most work on the formal verification of neural networks has focused on bounding the set of outputs that correspond to a given set of inputs (for example, bounded perturbations of a nominal input). However, many use cases of neural network verification require solving the inverse problem, or over-approximating the set of inputs that lead to certain outputs. We present the INVPROP algorithm for verifying properties over the preimage of a linearly constrained output set, which can be combined with branch-and-bound to increase precision. Contrary to other approaches, our efficient algorithm is GPU-accelerated and does not require a linear programming solver. We demonstrate our algorithm for identifying safe control regions for a dynamical system via backward reachability analysis, verifying adversarial robustness, and detecting out-of-distribution inputs to a neural network. Our results show that in certain settings, we find over-approximations over 2500x tighter than prior work while being 2.5x faster. By strengthening robustness verification with output constraints, we consistently verify more properties than the previous state-of-the-art on multiple benchmarks, including a large model with 167k neurons in VNN-COMP 2023. Our algorithm has been incorporated into the $\alpha,\!\beta$-CROWN verifier, available at //abcrown.org.

Next-generation wireless networks need to handle massive user access effectively. This paper addresses the problem of joint group scheduling and multicast beamforming for downlink multicast with many active groups. Aiming to maximize the minimum user throughput, we propose a three-phase approach to tackle this difficult joint optimization problem efficiently. In Phase 1, we utilize the optimal multicast beamforming structure obtained recently to find the group-channel directions for all groups. We propose two low-complexity scheduling algorithms in Phase 2, which determine the subset of groups in each time slot sequentially and the total number of time slots required for all groups. The first algorithm measures the level of spatial separation among groups and selects the dissimilar groups that maximize the minimum user rate into the same time slot. In contrast, the second algorithm first identifies the spatially correlated groups via a learning-based clustering method based on the group-channel directions, and then separates spatially similar groups into different time slots. Finally, the multicast beamformers for the scheduled groups are obtained in each time slot by a computationally efficient method. Simulation results show that our proposed approaches can effectively capture the level of spatial separation among groups for scheduling to improve the minimum user throughput over the conventional approach that serves all groups in a single time slot or one group per time slot, and can be executed with low computational complexity.

The problem of distributed optimization requires a group of networked agents to compute a parameter that minimizes the average of their local cost functions. While there are a variety of distributed optimization algorithms that can solve this problem, they are typically vulnerable to "Byzantine" agents that do not follow the algorithm. Recent attempts to address this issue focus on single dimensional functions, or assume certain statistical properties of the functions at the agents. In this paper, we provide two resilient, scalable, distributed optimization algorithms for multi-dimensional functions. Our schemes involve two filters, (1) a distance-based filter and (2) a min-max filter, which each remove neighborhood states that are extreme (defined precisely in our algorithms) at each iteration. We show that these algorithms can mitigate the impact of up to $F$ (unknown) Byzantine agents in the neighborhood of each regular agent. In particular, we show that if the network topology satisfies certain conditions, all of the regular agents' states are guaranteed to converge to a bounded region that contains the minimizer of the average of the regular agents' functions.

Graph neural networks (GNNs) have attracted significant attention for their outstanding performance in graph learning and node classification tasks. However, their vulnerability to adversarial attacks, particularly through susceptible nodes, poses a challenge in decision-making. The need for robust graph summarization is evident in adversarial challenges resulting from the propagation of attacks throughout the entire graph. In this paper, we address both performance and adversarial robustness in graph input by introducing the novel technique SHERD (Subgraph Learning Hale through Early Training Representation Distances). SHERD leverages information from layers of a partially trained graph convolutional network (GCN) to detect susceptible nodes during adversarial attacks using standard distance metrics. The method identifies "vulnerable (bad)" nodes and removes such nodes to form a robust subgraph while maintaining node classification performance. Through our experiments, we demonstrate the increased performance of SHERD in enhancing robustness by comparing the network's performance on original and subgraph inputs against various baselines alongside existing adversarial attacks. Our experiments across multiple datasets, including citation datasets such as Cora, Citeseer, and Pubmed, as well as microanatomical tissue structures of cell graphs in the placenta, highlight that SHERD not only achieves substantial improvement in robust performance but also outperforms several baselines in terms of node classification accuracy and computational complexity.

We address the problem of user association in a dense millimeter wave (mmWave) network, in which each arriving user brings a file containing a random number of packets and each time slot is divided into multiple mini-slots. This problem is an instance of the restless multi-armed bandit problem, and is provably hard to solve. Using a technique introduced by Whittle, we relax the hard per-stage constraint that each arriving user must be associated with exactly one mmWave base station (mBS) to a long-term constraint and then use the Lagrangian multiplier technique to convert the problem into an unconstrained problem. This decouples the process governing the system into separate Markov Decision Processes at different mBSs. We prove that the problem is Whittle indexable, present a scheme for computing the Whittle indices of different mBSs, and propose an association scheme under which, each arriving user is associated with the mBS with the smallest value of the Whittle index. Using extensive simulations, we show that the proposed Whittle index based scheme outperforms several user association schemes proposed in prior work in terms of various performance metrics such as average cost, delay, throughput, and Jain's fairness index.

A large number of real-world graphs or networks are inherently heterogeneous, involving a diversity of node types and relation types. Heterogeneous graph embedding is to embed rich structural and semantic information of a heterogeneous graph into low-dimensional node representations. Existing models usually define multiple metapaths in a heterogeneous graph to capture the composite relations and guide neighbor selection. However, these models either omit node content features, discard intermediate nodes along the metapath, or only consider one metapath. To address these three limitations, we propose a new model named Metapath Aggregated Graph Neural Network (MAGNN) to boost the final performance. Specifically, MAGNN employs three major components, i.e., the node content transformation to encapsulate input node attributes, the intra-metapath aggregation to incorporate intermediate semantic nodes, and the inter-metapath aggregation to combine messages from multiple metapaths. Extensive experiments on three real-world heterogeneous graph datasets for node classification, node clustering, and link prediction show that MAGNN achieves more accurate prediction results than state-of-the-art baselines.

Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such a graph-structure is available. In practice, however, real-world graphs are often noisy and incomplete or might not be available at all. With this work, we propose to jointly learn the graph structure and the parameters of graph convolutional networks (GCNs) by approximately solving a bilevel program that learns a discrete probability distribution on the edges of the graph. This allows one to apply GCNs not only in scenarios where the given graph is incomplete or corrupted but also in those where a graph is not available. We conduct a series of experiments that analyze the behavior of the proposed method and demonstrate that it outperforms related methods by a significant margin.

Deep neural networks (DNNs) have been found to be vulnerable to adversarial examples resulting from adding small-magnitude perturbations to inputs. Such adversarial examples can mislead DNNs to produce adversary-selected results. Different attack strategies have been proposed to generate adversarial examples, but how to produce them with high perceptual quality and more efficiently requires more research efforts. In this paper, we propose AdvGAN to generate adversarial examples with generative adversarial networks (GANs), which can learn and approximate the distribution of original instances. For AdvGAN, once the generator is trained, it can generate adversarial perturbations efficiently for any instance, so as to potentially accelerate adversarial training as defenses. We apply AdvGAN in both semi-whitebox and black-box attack settings. In semi-whitebox attacks, there is no need to access the original target model after the generator is trained, in contrast to traditional white-box attacks. In black-box attacks, we dynamically train a distilled model for the black-box model and optimize the generator accordingly. Adversarial examples generated by AdvGAN on different target models have high attack success rate under state-of-the-art defenses compared to other attacks. Our attack has placed the first with 92.76% accuracy on a public MNIST black-box attack challenge.

The dominant sequence transduction models are based on complex recurrent or convolutional neural networks in an encoder-decoder configuration. The best performing models also connect the encoder and decoder through an attention mechanism. We propose a new simple network architecture, the Transformer, based solely on attention mechanisms, dispensing with recurrence and convolutions entirely. Experiments on two machine translation tasks show these models to be superior in quality while being more parallelizable and requiring significantly less time to train. Our model achieves 28.4 BLEU on the WMT 2014 English-to-German translation task, improving over the existing best results, including ensembles by over 2 BLEU. On the WMT 2014 English-to-French translation task, our model establishes a new single-model state-of-the-art BLEU score of 41.8 after training for 3.5 days on eight GPUs, a small fraction of the training costs of the best models from the literature. We show that the Transformer generalizes well to other tasks by applying it successfully to English constituency parsing both with large and limited training data.