Ron Levie

Machine learning models often require large datasets and struggle to generalize beyond their training distribution. These limitations pose significant challenges in scientific and engineering contexts, where generating exhaustive datasets is often impractical and the goal is to frequently discover novel solutions outside the training domain. In this work, we explore the use of dynamical data through a graph neural network-based simulator to enable efficient system-to-property learning and out-of-distribution prediction in the context of uniaxial compression of two-dimensional disordered elastic networks. We find that the simulator can learn the underlying physical dynamics from a small number of training examples and accurately reproduce the temporal evolution of unseen networks. Notably, the simulator is able to accurately predict emergent properties such as Poisson’s ratio and its dependence on strain, even though it was not explicitly trained for this task. In addition, it generalizes well across variations in system temperature, strain amplitude, and most significantly, Poisson’s ratios beyond the training range. These findings suggest that using dynamical data to train machine learning models can support more information efficient and generalizable approaches for materials and molecular design, especially in data-scarce settings.

We study the generalization capabilities of Message Passing Neural Networks (MPNNs), a prevalent class of Graph Neural Networks (GNN). We derive generalization bounds specifically for MPNNs with normalized sum aggregation and mean aggregation. Our analysis is based on a data generation model incorporating a finite set of template graphons. Each graph within this framework is generated by sampling from one of the graphons with a certain degree of perturbation. In particular, we extend previous MPNN generalization results to a more realistic setting, which includes the following modifications: 1) we analyze simple random graphs with Bernoulli-distributed edges instead of weighted graphs; 2) we sample both graphs and graph signals from perturbed graphons instead of clean graphons; and 3) we analyze sparse graphs instead of dense graphs. In this more realistic and challenging scenario, we provide a generalization bound that decreases as the average number of nodes in the graphs increases. Our results imply that MPNNs with higher complexity than the size of the training set can still generalize effectively, as long as the graphs are sufficiently large.

We present an approach for analyzing message passing graph neural networks (MPNNs) based on an extension of graphon analysis to a so called graphon-signal analysis. A MPNN is a function that takes a graph and a signal on the graph (a graph-signal) and returns some value. Since the input space of MPNNs is non-Euclidean, i.e., graphs can be of any size and topology, properties such as generalization are less well understood for MPNNs than for Euclidean neural networks. We claim that one important missing ingredient in past work is a meaningful notion of graph-signal similarity measure, that endows the space of inputs to MPNNs with a regular structure. We present such a similarity measure, called the graphon-signal cut distance, which makes the space of all graph-signals a dense subset of a compact metric space -- the graphon-signal space. Informally, two deterministic graph-signals are close in cut distance if they ``look like'' they were sampled from the same random graph-signal model. Hence, our cut distance is a natural notion of graph-signal similarity, which allows comparing any pair of graph-signals of any size and topology. We prove that MPNNs are Lipschitz continuous functions over the graphon-signal metric space. We then give two applications of this result: 1) a generalization bound for MPNNs, and, 2) the stability of MPNNs to subsampling of graph-signals. Our results apply to any regular enough MPNN on any distribution of graph-signals, making the analysis rather universal.

Graph neural networks (GNNs) are commonly described as being permutation equivariant with respect to node relabeling in the graph. This symmetry of GNNs is often compared to the translation equivariance of Euclidean convolution neural networks (CNNs). However, these two symmetries are fundamentally different: The translation equivariance of CNNs corresponds to symmetries of the fixed domain acting on the image signals (sometimes known as active symmetries), whereas in GNNs any permutation acts on both the graph signals and the graph domain (sometimes described as passive symmetries). In this work, we focus on the active symmetries of GNNs, by considering a learning setting where signals are supported on a fixed graph. In this case, the natural symmetries of GNNs are the automorphisms of the graph. Since real-world graphs tend to be asymmetric, we relax the notion of symmetries by formalizing approximate symmetries via graph coarsening. We present a bias-variance formula that quantifies the tradeoff between the loss in expressivity and the gain in the regularity of the learned estimator, depending on the chosen symmetry group. To illustrate our approach, we conduct extensive experiments on image inpainting, traffic flow prediction, and human pose estimation with different choices of symmetries. We show theoretically and empirically that the best generalization performance can be achieved by choosing a suitably larger group than the graph automorphism, but smaller than the permutation group.

In this article, we present a collection of radio map datasets in dense urban setting, which we generated and made publicly available. The datasets include simulated pathloss/received signal strength (RSS) and time of arrival (ToA) radio maps over a large collection of realistic dense urban setting in real city maps. The two main applications of the presented dataset are 1) learning methods that predict the pathloss from input city maps (namely, deep learning-based simulations), and, 2) wireless localization. The fact that the RSS and ToA maps are computed by the same simulations over the same city maps allows for a fair comparison of the RSS and ToA-based localization methods.

Image classifiers are known to be difficult to interpret and therefore require explanation methods to understand their decisions. We present ShearletX, a novel mask explanation method for image classifiers based on the shearlet transform -- a multiscale directional image representation. Current mask explanation methods are regularized by smoothness constraints that protect against undesirable fine-grained explanation artifacts. However, the smoothness of a mask limits its ability to separate fine-detail patterns, that are relevant for the classifier, from nearby nuisance patterns, that do not affect the classifier. ShearletX solves this problem by avoiding smoothness regularization all together, replacing it by shearlet sparsity constraints. The resulting explanations consist of a few edges, textures, and smooth parts of the original image, that are the most relevant for the decision of the classifier. To support our method, we propose a mathematical definition for explanation artifacts and an information theoretic score to evaluate the quality of mask explanations. We demonstrate the superiority of ShearletX over previous mask based explanation methods using these new metrics, and present exemplary situations where separating fine-detail patterns allows explaining phenomena that were not explainable before.

Global Navigation Satellite Systems typically perform poorly in urban environments, where the likelihood of line-of-sight conditions between devices and satellites is low. Therefore, alternative location methods are required to achieve good accuracy. We present LocUNet: A convolutional, end-to-end trained neural network (NN) for the localization task, which is able to estimate the position of a user from the received signal strength (RSS) of a small number of Base Stations (BS). Using estimations of pathloss radio maps of the BSs and the RSS measurements of the users to be localized, LocUNet can localize users with state-of-the-art accuracy and enjoys high robustness to inaccuracies in the estimations of radio maps. The proposed method does not require generating RSS fingerprints of each specific area where the localization task is performed and is suitable for real-time applications. Moreover, two novel datasets that allow for numerical evaluations of RSS and ToA methods in realistic urban environments are presented and made publicly available for the research community. By using these datasets, we also provide a fair comparison of state-of-the-art RSS and ToA-based methods in the dense urban scenario and show numerically that LocUNet outperforms all the compared methods.

In this paper, we study the localization problem in dense urban settings. In such environments, Global Navigation Satellite Systems fail to provide good accuracy due to low likelihood of line-of-sight (LOS) links between the receiver (Rx) to be located and the satellites, due to the presence of obstacles like the buildings. Thus, one has to resort to other technologies, which can reliably operate under non-line-of-sight (NLOS) conditions. Recently, we proposed a Received Signal Strength (RSS) fingerprint and convolutional neural network-based algorithm, LocUNet, and demonstrated its state-of-the-art localization performance with respect to the widely adopted k-nearest neighbors (kNN) algorithm, and to state-of-the-art time of arrival (ToA) ranging-based methods. In the current work, we first recognize LocUNet's ability to learn the underlying prior distribution of the Rx position or Rx and transmitter (Tx) association preferences from the training data, and attribute its high performance to these. Conversely, we demonstrate that classical methods based on probabilistic approach, can greatly benefit from an appropriate incorporation of such prior information. Our studies also numerically prove LocUNet's close to optimal performance in many settings, by comparing it with the theoretically optimal formulations.