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Structure determination is necessary to identify unknown organic molecules, such as those in natural products, forensic samples, the interstellar medium, and laboratory syntheses. Rotational spectroscopy enables structure determination by providing accurate 3D information about small organic molecules via their moments of inertia. Using these moments, Kraitchman analysis determines isotopic substitution coordinates, which are the unsigned $|x|,|y|,|z|$ coordinates of all atoms with natural isotopic abundance, including carbon, nitrogen, and oxygen. While unsigned substitution coordinates can verify guesses of structures, the missing $+/-$ signs make it challenging to determine the actual structure from the substitution coordinates alone. To tackle this inverse problem, we develop KREED (Kraitchman REflection-Equivariant Diffusion), a generative diffusion model that infers a molecule's complete 3D structure from its molecular formula, moments of inertia, and unsigned substitution coordinates of heavy atoms. KREED's top-1 predictions identify the correct 3D structure with >98% accuracy on the QM9 and GEOM datasets when provided with substitution coordinates of all heavy atoms with natural isotopic abundance. When substitution coordinates are restricted to only a subset of carbons, accuracy is retained at 91% on QM9 and 32% on GEOM. On a test set of experimentally measured substitution coordinates gathered from the literature, KREED predicts the correct all-atom 3D structure in 25 of 33 cases, demonstrating experimental applicability for context-free 3D structure determination with rotational spectroscopy., Comment: added software citations

String-based molecular representations play a crucial role in cheminformatics applications, and with the growing success of deep learning in chemistry, have been readily adopted into machine learning pipelines. However, traditional string-based representations such as SMILES are often prone to syntactic and semantic errors when produced by generative models. To address these problems, a novel representation, SELF-referencIng Embedded Strings (SELFIES), was proposed that is inherently 100% robust, alongside an accompanying open-source implementation. Since then, we have generalized SELFIES to support a wider range of molecules and semantic constraints and streamlined its underlying grammar. We have implemented this updated representation in subsequent versions of \selfieslib, where we have also made major advances with respect to design, efficiency, and supported features. Hence, we present the current status of \selfieslib (version 2.1.1) in this manuscript., Comment: 11 pages, 2 figures

Influence functions efficiently estimate the effect of removing a single training data point on a model's learned parameters. While influence estimates align well with leave-one-out retraining for linear models, recent works have shown this alignment is often poor in neural networks. In this work, we investigate the specific factors that cause this discrepancy by decomposing it into five separate terms. We study the contributions of each term on a variety of architectures and datasets and how they vary with factors such as network width and training time. While practical influence function estimates may be a poor match to leave-one-out retraining for nonlinear networks, we show they are often a good approximation to a different object we term the proximal Bregman response function (PBRF). Since the PBRF can still be used to answer many of the questions motivating influence functions, such as identifying influential or mislabeled examples, our results suggest that current algorithms for influence function estimation give more informative results than previous error analyses would suggest., Comment: 28 pages, 6 figures