ST ABILITY OF GRAPH NEURAL NETWORKS TO RELA TIVE PERTURBA TIONS Fernando Gama, Alejandro Ribeiro University of Pennsylvania Dept. of Electrical and Systems Engineering Philadelphia, P A Joan Bruna † New Y ork University Courant Institute of Mathematical Sciences New Y ork, NY ABSTRACT Graph neural networks (GNNs), consisting of a cascade of layers applying a graph convolution followed by a pointwise nonlinearity, have become a powerful architecture to process signals supported on graphs. Graph convolutions (and thus, GNNs), rely heavily on knowledge of the graph for operation. However, in many practical cases the GSO is not known and needs to be estimated, or might change from training time to testing time. In this paper, we are set to study the effect that a change in the underlying graph topology that supports the signal has on the output of a GNN. We prove that graph convolutions with integral Lipschitz filters lead to GNNs whose output change is bounded by the size of the relative change in the topology. Furthermore, we leverage this result to show that the main reason for the success of GNNs is that they are stable architectures capable of discriminating features on high eigenvalues, which is a feat that cannot be achieved by linear graph filters (which are either stable or discriminative, but cannot be both). Finally, we comment on the use of this result to train GNNs with increased stability and run experiments on movie recommendation systems.

Time series forecasting with limited data is a challenging yet critical task. While transformers have achieved outstanding performances in time series forecasting, they often require many training samples due to the large number of trainable parameters. In this paper, we propose a training technique for transformers that prepares the training windows through random sampling. As input time steps need not be consecutive, the number of distinct samples increases from linearly to combinatorially many. By breaking the temporal order, this technique also helps transformers to capture dependencies among time steps in finer granularity. We achieve competitive results compared to the state-of-the-art on real-world datasets.

In this paper, we study reinforcement learning (RL) algorithms to solve real-world decision problems with the objective of maximizing the long-term reward as well as satisfying cumulative constraints. We propose a novel first-order policy optimization method, Interior-point Policy Optimization (IPO), which augments the objective with logarithmic barrier functions, inspired by the interior-point method. Our proposed method is easy to implement with performance guarantees and can handle general types of cumulative multi-constraint settings. We conduct extensive evaluations to compare our approach with state-of-the-art baselines. Our algorithm outperforms the baseline algorithms, in terms of reward maximization and constraint satisfaction. Introduction Recent advances have demonstrated significant potentials of deep reinforcement learning (RL) in solving complex sequential decision and control problems, e.g., the Atari game (Mnih et al. 2015), robotics (Andrychowicz et al. 2018), Go (Silver et al. 2016), etc. In such RL problems, the objective is to maximize the discounted cumulative reward. In many other problems, in addition to maximizing the reward, a policy needs to satisfy certain constraints.

Spiking Neural Networks (SNNs) offer a promising alternative to conventional Artificial Neural Networks (ANNs) for the implementation of on-device low-power online learning and inference. On-device training is, however, constrained by the limited amount of data available at each device. In this paper, we propose to mitigate this problem via cooperative training through Federated Learning (FL). To this end, we introduce an online FL-based learning rule for networked on-device SNNs, which we refer to as FL-SNN. FL-SNN leverages local feedback signals within each SNN, in lieu of backpropagation, and global feedback through communication via a base station. The scheme demonstrates significant advantages over separate training and features a flexible trade-off between communication load and accuracy via the selective exchange of synaptic weights.

Abstract--Graph convolutional networks (GCNs) are vulnerable to perturbations of the graph structure that are either random, or, adversarially designed. The perturbed links mo dify the graph neighborhoods, which critically affects the perf ormance of GCNs in semi-supervised learning (SSL) tasks. Aiming at robustifying GCNs conditioned on the perturbed graph, the present paper generates multiple auxiliary graphs, each ha ving its binary 0 1 edge weights flip values with probabilities designed to enhance robustness. The resultant edge-dither ed auxiliary graphs are leveraged by an adaptive (A)GCN that performs SSL. Robustness is enabled through learnable grap h-combining weights along with suitable regularizers. Relat ive to GCN, the novel AGCN achieves markedly improved performance in tests with noisy inputs, graph perturbations, and state-of- the-art adversarial attacks. A task of major importance at the crossroads of machine learning and network science is semi-supervised learning (SSL) over graphs.

A graph-based sampling and consensus (GraphSAC) approach is introduced to effectively detect anomalous nodes in large-scale graphs. Existing approaches rely on connectivity and attributes of all nodes to assign an anomaly score per node. However, nodal attributes and network links might be compromised by adversaries, rendering these holistic approaches vulnerable. Alleviating this limitation, GraphSAC randomly draws subsets of nodes, and relies on graph-aware criteria to judiciously filter out sets contaminated by anomalous nodes, before employing a semi-supervised learning (SSL) module to estimate nominal label distributions per node. These learned nominal distributions are minimally affected by the anomalous nodes, and hence can be directly adopted for anomaly detection. Rigorous analysis provides performance guarantees for GraphSAC, by bounding the required number of draws. The per-draw complexity grows linearly with the number of edges, which implies efficient SSL, while draws can be run in parallel, thereby ensuring scalability to large graphs. GraphSAC is tested under different anomaly generation models based on random walks, clustered anomalies, as well as contemporary adversarial attacks for graph data. Experiments with real-world graphs showcase the advantage of GraphSAC relative to state-of-the-art alternatives.

We propose an efficient inference method for switching nonlinear dynamical systems. The key idea is to learn an inference network which can be used as a proposal distribution for the continuous latent variables, while performing exact marginalization of the discrete latent variables. This allows us to use the reparameterization trick, and apply end-to-end training with stochastic gradient descent. We show that the proposed method can successfully segment time series data (including videos) into meaningful "regimes", by using the piece-wise nonlinear dynamics.

Certain biological neurons demonstrate a remarkable capability to optimally compress the history of sensory inputs while being maximally informative about the future. In this work, we investigate if the same can be said of artificial neurons in recurrent neural networks (RNNs) trained with maximum likelihood. In experiments on two datasets, restorative Brownian motion and a hand-drawn sketch dataset, we find that RNNs are sub-optimal in the information plane. Instead of optimally compressing past information, they extract additional information that is not relevant for predicting the future. Overcoming this limitation may require alternative training procedures and architectures, or objectives beyond maximum likelihood estimation. Remembering past events is a critical component of predicting the future and acting in the world. An information-theoretic quantification of how much observing the past can help in predicting the future is given by the predictive information (Bialek et al., 2001). The predictive information is the mutual information (MI) between a finite set of observations (the past of a sequence) and an infinite number of additional draws from the same process (the future of a sequence).

We present local ensembles, a method for detecting extrapolation at test time in a pre-trained model. We focus on underdetermination as a key component of extrapolation: we aim to detect when many possible predictions are consistent with the training data and model class. Our method uses local second-order information to approximate the variance of predictions across an ensemble of models from the same class. We compute this approximation by estimating the norm of the component of a test point's gradient that aligns with the low-curvature directions of the Hessian, and provide a tractable method for estimating this quantity. Experimentally, we show that our method is capable of detecting when a pre-trained model is extrapolating on test data, with applications to out-of-distribution detection, detecting spurious correlates, and active learning.

We release the largest public ECG dataset of continuous raw signals for representation learning containing 11 thousand patients and 2 billion labelled beats. Our goal is to enable semi-supervised ECG models to be made as well as to discover unknown subtypes of arrhythmia and anomalous ECG signal events. To this end, we propose an unsupervised representation learning task, evaluated in a semi-supervised fashion. We provide a set of baselines for different feature extractors that can be built upon. Additionally, we perform qualitative evaluations on results from PCA embeddings, where we identify some clustering of known sub-types indicating the potential for representation learning in arrhythmia sub-type discovery. Arrhythmia detection is presently performed by cardiologists or technologists familiar with ECG readings. Recently, supervised machine learning has been successfully applied to perform detection of certain types of arrhythmia (Hannun et al., 2019; Yıldırım et al., 2018; Minchol e & Rodriguez, 2019; Porumb et al., 2020).