We combine amortized neural posterior estimation with importance sampling for fast and accurate gravitational-wave inference. We first generate a rapid proposal for the Bayesian posterior using neural networks, and then attach importance weights based on the underlying likelihood and prior. This provides (1) a corrected posterior free from network inaccuracies, (2) a performance diagnostic (the sample efficiency) for assessing the proposal and identifying failure cases, and (3) an unbiased estimate of the Bayesian evidence. By establishing this independent verification and correction mechanism we address some of the most frequent criticisms against deep learning for scientific inference. We carry out a large study analyzing 42 binary black hole mergers observed by LIGO and Virgo with the SEOBNRv4PHM and IMRPhenomXPHM waveform models. This shows a median sample efficiency of ≈ 10% (two orders-of-magnitude better than standard samplers) as well as a ten-fold reduction in the statistical uncertainty in the log evidence. Given these advantages, we expect a significant impact on gravitational-wave inference, and for this approach to serve as a paradigm for harnessing deep learning methods in scientific applications.

Simulation-based inference with conditional neural density estimators is a powerful approach to solving inverse problems in science. However, these methods typically treat the underlying forward model as a black box, with no way to exploit geometric properties such as equivariances. Equivariances are common in scientific models, however integrating them directly into expressive inference networks (such as normalizing flows) is not straightforward. We here describe an alternative method to incorporate equivariances under joint transformations of parameters and data. Our method—called group equivariant neural posterior estimation (GNPE)—is based on self-consistently standardizing the “pose” of the data while estimating the posterior over parameters. It is architecture-independent, and applies both to exact and approximate equivariances. As a real-world application, we use GNPE for amortized inference of astrophysical binary black hole systems from gravitational- wave observations. We show that GNPE achieves state-of-the-art accuracy while reducing inference times by three orders of magnitude.

We demonstrate unprecedented accuracy for rapid gravitational wave parameter estimation with deep learning. Using neural networks as surrogates for Bayesian posterior distributions, we analyze eight gravitational wave events from the first LIGO-Virgo Gravitational-Wave Transient Catalog and find very close quantitative agreement with standard inference codes, but with inference times reduced from O(day) to 20 s per event. Our networks are trained using simulated data, including an estimate of the detector noise characteristics near the event. This encodes the signal and noise models within millions of neural-network parameters and enables inference for any observed data consistent with the training distribution, accounting for noise nonstationarity from event to event. Our algorithm—called “DINGO”—sets a new standard in fast and accurate inference of physical parameters of detected gravitational wave events, which should enable real-time data analysis without sacrificing accuracy.

We provide a dispersion-theoretical representation of the reaction amplitudes γK → Kπ in all charge channels, based on modern pion–kaon P-wave phase shift input. Crossed-channel singularities are fixed from phenomenology as far as possible. We demonstrate how the subtraction constants can be matched to a low-energy theorem and radiative couplings of the K*(892) resonances, thereby providing a model-independent framework for future analyses of high-precision kaon Primakoff data.

Self-attention networks have shown remarkable progress in computer vision tasks such as image classification. The main benefit of the self-attention mechanism is the ability to capture long-range feature interactions in attention-maps. However, the computation of attention-maps requires a learnable key, query, and positional encoding, whose usage is often not intuitive and computationally expensive. To mitigate this problem, we propose a novel self-attention module with explicitly modeled attention-maps using only a single learnable parameter for low computational overhead. The design of explicitly modeled attention-maps using geometric prior is based on the observation that the spatial context for a given pixel within an image is mostly dominated by its neighbors, while more distant pixels have a minor contribution. Concretely, the attention-maps are parametrized via simple functions (e.g., Gaussian kernel) with a learnable radius, which is modeled independently of the input content. Our evaluation shows that our method achieves an accuracy improvement of up to 2.2% over the ResNet-baselines in ImageNet ILSVRC and outperforms other self-attention methods such as AA-ResNet152 in accuracy by 0.9% with 6.4% fewer parameters and 6.7% fewer GFLOPs. This result empirically indicates the value of incorporating geometric prior into self-attention mechanism when applied in image classification.

Deep neural network (DNN) based salient object detection in images based on high-quality labels is expensive. Alternative unsupervised approaches rely on careful selection of multiple handcrafted saliency methods to generate noisy pseudo-ground-truth labels. In this work, we propose a two-stage mechanism for robust unsupervised object saliency prediction, where the first stage involves refinement of the noisy pseudo labels generated from different handcrafted methods. Each handcrafted method is substituted by a deep network that learns to generate the pseudo labels. These labels are refined incrementally in multiple iterations via our proposed self-supervision technique. In the second stage, the refined labels produced from multiple networks representing multiple saliency methods are used to train the actual saliency detection network. We show that this self-learning procedure outperforms all the existing unsupervised methods over different datasets. Results are even comparable to those of fully-supervised state-of-the-art approaches.

We study the quark-mass dependence of ω→3π  decays, based on a dispersion-theoretical framework. We rely on the quark-mass-dependent scattering phase shift for the pion-pion P-wave extracted from unitarized chiral perturbation theory. The dispersive representation then takes into account the final-state rescattering among all three pions. The described formalism may be used as an extrapolation tool for lattice QCD calculations of three-pion decays, for which ω→3π  can serve as a paradigm case.

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