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We have observed the behavior of striations caused by ionization waves propagating in low-pressure helium DC discharges using the non-invasive laser-collision induced fluorescence (LCIF) diagnostic. To achieve this, we developed an analytic fit of collisional radiative model (CRM) predictions to interpret the LCIF data and recover quantitative two-dimensional spatial maps of the electron density, ne, and the ratios of LCIF emission states that can be correlated with Te with the use of accurate distribution functions at localized positions within striated helium discharges at 500 mTorr, 750 mTorr, and 1 Torr. To our knowledge, these are the first spatiotemporal, laser-based, experimental measurements of ne in DC striations. The ne and 447:588 ratio distributions align closely with striation theory. Constriction of the positive column appears to occur with decreased gas pressure, as shown by the radial ne distribution. We identify a transition from a slow ionization wave to a fast ionization wave between 750 mTorr and 1 Torr. These experiments validate our analytic fit of ne, allowing the implementation of an LCIF diagnostic in helium without the need to develop a CRM. 

While the advent of Graph Neural Networks (GNNs) has greatly improved node and graph representation learning in many applications, the neighborhood aggregation scheme exposes additional vulnerabilities to adversaries seeking to extract node-level information about sensitive attributes. In this paper, we study the problem of protecting sensitive attributes by information obfuscation when learning with graph structured data. We propose a framework to locally filter out pre-determined sensitive attributes via adversarial training with the total variation and the Wasserstein distance. Our method creates a strong defense against inference attacks, while only suffering small loss in task performance. Theoretically, we analyze the effectiveness of our framework against a worst-case adversary, and characterize an inherent trade-off between maximizing predictive accuracy and minimizing information leakage. Experiments across multiple datasets from recommender systems, knowledge graphs and quantum chemistry demonstrate that the proposed approach provides a robust defense across various graph structures and tasks, while producing competitive GNN encoders for downstream tasks. 

Graph Neural Networks (GNNs) have been studied through the lens of expressive power and generalization. However, their optimization proper- ties are less well understood. We take the first step towards analyzing GNN training by studying the gradient dynamics of GNNs. First, we analyze linearized GNNs and prove that despite the non-convexity of training, convergence to a global minimum at a linear rate is guaranteed under mild assumptions that we validate on real- world graphs. Second, we study what may affect the GNNs’ training speed. Our results show that the training of GNNs is implicitly accelerated by skip connections, more depth, and/or a good label distribution. Empirical results confirm that our theoretical results for linearized GNNs align with the training behavior of nonlinear GNNs. Our results provide the first theoretical support for the success of GNNs with skip connections in terms of optimization, and suggest that deep GNNs with skip connections would be promising in practice. 

We study how neural networks trained by gradient descent extrapolate, i.e., what they learn outside the support of the training distribution. Previous works report mixed empirical results when extrapolating with neural networks: while feedforward neural networks, a.k.a. multilayer perceptrons (MLPs), do not extrapolate well in certain simple tasks, Graph Neural Networks (GNNs) – structured networks with MLP modules – have shown some success in more complex tasks. Working towards a theoretical explanation, we identify conditions under which MLPs and GNNs extrapolate well. First, we quantify the observation that ReLU MLPs quickly converge to linear functions along any direction from the origin, which implies that ReLU MLPs do not extrapolate most nonlinear functions. But, they can provably learn a linear target function when the training distribution is sufficiently “diverse”. Second, in connection to analyzing the successes and limitations of GNNs, these results suggest a hypothesis for which we provide theoretical and empirical evidence: the success of GNNs in extrapolating algorithmic tasks to new data (e.g., larger graphs or edge weights) relies on encoding task-specific non-linearities in the architecture or features. Our theoretical analysis builds on a connection of over-parameterized networks to the neural tangent kernel. Empirically, our theory holds across different training settings. 

Multi- and hyperspectral imaging modalities encompass a growing number of spectral techniques that find many applications in geospatial, biomedical and machine vision fields. The rapidly increasing number of applications requires a convenient easy-to-navigate software that can be used by new and experienced users to analyze data, develop, apply, and deploy novel algorithms. Herein, we present our platform, IDCube that performs essential operations in hyperspectral data analysis to realize the full potential of spectral imaging. The strength of the software lies in its interactive features that enable the users to optimize parameters and obtain visual input for the user. The entire software can be operated without any prior programming skills allowing interactive sessions of raw and processed data. IDCube Lite, a free version of the software described in the paper, has many benefits compared to existing packages and offers structural flexibility to discover new hidden features.