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Abstract We present deep optical and near-infrared observations of the host galaxies of 34 fast radio bursts (FRBs) detected by the Commensal Real-time ASKAP Fast Transient (or CRAFT) survey on the Australian SKA Pathfinder (ASKAP) to compare the locations of FRBs relative to their host light distributions. Incorporating three additional FRBs from the literature, for a total of four repeating and 33 apparently nonrepeating FRBs, we determine their projected galactocentric offsets and find a median of $4.2_{-2.5}^{+5.7}$kpc ( $1.0_{-0.6}^{+1.5}{r}_e$). We model their host surface-brightness profiles and develop synthetic spatial distributions of their globular clusters (GCs) based on host properties. We calculate the likelihood the observed location of each FRB is consistent with the smooth light of its host galaxy, residual (primarily spiral) substructure, or GC distributions. The majority of FRBs favor locations within the disks of their galaxies, while only 11% ± 5% favor a GC origin, primarily those with galactocentric offsets ≳3r_e. Atz < 0.15, where spiral structure is apparent in 86% of our sample of FRB hosts, we find ≈20%–46% of FRBs favor an association with spiral arms. Assuming FRBs derive from magnetars, our results support multiple formation channels, with the majority of progenitors associated with massive stars and a minority formed through dynamical channels. However, the moderate fraction of FRBs associated with spiral structure indicates that high star formation efficiency of the youngest and most massive stars is not a predominant driver in the production of FRB progenitors. 

While neural models show remarkable accuracy on individual predictions, their internal beliefs can be inconsistent across examples.In this paper, we formalize such inconsistency as a generalization of prediction error. We propose a learning framework for constraining models using logic rules to regularize them away from inconsistency. Our framework can leverage both labeled and unlabeled examples and is directly compatible with off-the-shelf learning schemes without model redesign. We instantiate our framework on natural language inference, where experiments show that en-forcing invariants stated in logic can help make the predictions of neural models both accurate and consistent