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  1. This work generalizes graph neural networks (GNNs) beyond those based on the Weisfeiler- Lehman (WL) algorithm, graph Laplacians, and diffusions. Our approach, denoted Relational Pooling (RP), draws from the theory of finite partial exchangeability to provide a framework with maximal representation power for graphs. RP can work with existing graph representation models and, somewhat counterintuitively, can make them even more powerful than the orig- inal WL isomorphism test. Additionally, RP allows architectures like Recurrent Neural Net- works and Convolutional Neural Networks to be used in a theoretically sound approach for graph classification. We demonstrate improved perfor- mance of RP-based graph representations over state-of-the-art methods on a number of tasks.
  2. We consider a simple and overarching representation for permutation-invariant functions of sequences (or multiset functions). Our approach, which we call Janossy pooling, expresses a permutation-invariant function as the average of a permutation-sensitive function applied to all reorderings of the input sequence. This allows us to leverage the rich and mature literature on permutation-sensitive functions to construct novel and flexible permutation-invariant functions. If car- ried out naively, Janossy pooling can be computationally prohibitive. To allow computational tractability, we consider three kinds of approximations: canonical orderings of sequences, functions with k-order interactions, and stochastic opti- mization algorithms with random permutations. Our framework unifies a variety of existing work in the literature, and suggests possible modeling and algorithmic extensions. We explore a few in our experiments, which demonstrate improved performance over current state-of-the-art methods.
  3. Abstract The two-detector design of the NOvA neutrino oscillation experiment, in which two functionally identical detectors are exposed to an intense neutrino beam, aids in canceling leading order effects of cross-section uncertainties. However, limited knowledge of neutrino interaction cross sections still gives rise to some of the largest systematic uncertainties in current oscillation measurements. We show contemporary models of neutrino interactions to be discrepant with data from NOvA, consistent with discrepancies seen in other experiments. Adjustments to neutrino interaction models in GENIE are presented, creating an effective model that improves agreement with our data. We also describe systematic uncertainties on these models, including uncertainties on multi-nucleon interactions from a newly developed procedure using NOvA near detector data.