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Mergers of binary neutron stars (BNSs) emit signals in both the gravitational-wave (GW) and electromagnetic (EM) spectra. Famously, the 2017 multi-messenger observation of GW170817 led to scientific discoveries across cosmology, nuclear physics, and gravity. Central to these results were the sky localization and distance obtained from GW data, which, in the case of GW170817, helped to identify the associated EM transient, AT 2017gfo, 11 hours after the GW signal. Fast analysis of GW data is critical for directing time-sensitive EM observations; however, due to challenges arising from the length and complexity of signals, it is often necessary to make approximations that sacrifice accuracy. Here, we present a machine learning framework that performs complete BNS inference in just one second without making any such approximations. Our approach enhances multi-messenger observations by providing (i) accurate localization even before the merger; (ii) improved localization precision by $\sim30\%$ compared to approximate low-latency methods; and (iii) detailed information on luminosity distance, inclination, and masses, which can be used to prioritize expensive telescope time. Additionally, the flexibility and reduced cost of our method open new opportunities for equation-of-state studies. Finally, we demonstrate that our method scales to extremely long signals, up to an hour in length, thus serving as a blueprint for data analysis for next-generation ground- and space-based detectors., Comment: 8+8 pages, 3+7 figures

Binary black holes (BBHs) in eccentric orbits produce distinct modulations the emitted gravitational waves (GWs). The measurement of orbital eccentricity can provide robust evidence for dynamical binary formation channels. We analyze 57 GW events from the first, second and third observing runs of the LIGO-Virgo-KAGRA (LVK) Collaboration using a multipolar aligned-spin inspiral-merger-ringdown waveform model with two eccentric parameters: eccentricity and relativistic anomaly. This is made computationally feasible with the machine-learning code DINGO which accelerates inference by 2-3 orders of magnitude compared to traditional inference. First, we find eccentric aligned-spin versus quasi-circular aligned-spin $\log_{10}$ Bayes factors of 1.84 to 4.75 (depending on the glitch mitigation) for GW200129, 3.0 for GW190701 and 1.77 for GW200208_22. We measure $e_{\text{gw}, 10Hz}$ to be $0.27_{-0.12}^{+0.10}$ to $0.17_{-0.13}^{+0.14}$ for GW200129, $0.35_{-0.11}^{+0.32}$ for GW190701 and $0.35_{-0.21}^{+0.18}$ for GW200208_22. Second, we find $\log_{10}$ Bayes factors between the eccentric aligned-spin versus quasi-circular precessing-spin hypothesis between 1.43 and 4.92 for GW200129, 2.61 for GW190701 and 1.23 for GW200208_22. Third, our analysis does not show evidence for eccentricity in GW190521, which has an eccentric aligned-spin against quasi-circular aligned-spin $\log_{10}$ Bayes factor of 0.04. Fourth, we estimate that if we neglect the spin-precession and use an astrophysical prior, the probability of one out of the 57 events being eccentric is greater than 99.5% or $(100 - 8.4 \times 10^{-4})$% (depending on the glitch mitigation). Fifth, we study the impact on parameter estimation when neglecting either eccentricity or higher modes in eccentric models. These results underscore the importance of including eccentric parameters in the characterization of BBHs for GW detectors., Comment: 36 pages, 14 figures

Atmospheric retrievals (AR) characterize exoplanets by estimating atmospheric parameters from observed light spectra, typically by framing the task as a Bayesian inference problem. However, traditional approaches such as nested sampling are computationally expensive, thus sparking an interest in solutions based on machine learning (ML). In this ongoing work, we first explore flow matching posterior estimation (FMPE) as a new ML-based method for AR and find that, in our case, it is more accurate than neural posterior estimation (NPE), but less accurate than nested sampling. We then combine both FMPE and NPE with importance sampling, in which case both methods outperform nested sampling in terms of accuracy and simulation efficiency. Going forward, our analysis suggests that simulation-based inference with likelihood-based importance sampling provides a framework for accurate and efficient AR that may become a valuable tool not only for the analysis of observational data from existing telescopes, but also for the development of new missions and instruments., Comment: Accepted at the "AI to Accelerate Science and Engineering (AI2ASE)" workshop at AAAI 2024

Neural posterior estimation methods based on discrete normalizing flows have become established tools for simulation-based inference (SBI), but scaling them to high-dimensional problems can be challenging. Building on recent advances in generative modeling, we here present flow matching posterior estimation (FMPE), a technique for SBI using continuous normalizing flows. Like diffusion models, and in contrast to discrete flows, flow matching allows for unconstrained architectures, providing enhanced flexibility for complex data modalities. Flow matching, therefore, enables exact density evaluation, fast training, and seamless scalability to large architectures--making it ideal for SBI. We show that FMPE achieves competitive performance on an established SBI benchmark, and then demonstrate its improved scalability on a challenging scientific problem: for gravitational-wave inference, FMPE outperforms methods based on comparable discrete flows, reducing training time by 30% with substantially improved accuracy. Our work underscores the potential of FMPE to enhance performance in challenging inference scenarios, thereby paving the way for more advanced applications to scientific problems., Comment: NeurIPS 2023. Code available at https://github.com/dingo-gw/flow-matching-posterior-estimation

The ability of an agent to do well in new environments is a critical aspect of intelligence. In machine learning, this ability is known as $\textit{strong}$ or $\textit{out-of-distribution}$ generalization. However, merely considering differences in data distributions is inadequate for fully capturing differences between learning environments. In the present paper, we investigate $\textit{out-of-variable}$ generalization, which pertains to an agent's generalization capabilities concerning environments with variables that were never jointly observed before. This skill closely reflects the process of animate learning: we, too, explore Nature by probing, observing, and measuring $\textit{subsets}$ of variables at any given time. Mathematically, $\textit{out-of-variable}$ generalization requires the efficient re-use of past marginal information, i.e., information over subsets of previously observed variables. We study this problem, focusing on prediction tasks across environments that contain overlapping, yet distinct, sets of causes. We show that after fitting a classifier, the residual distribution in one environment reveals the partial derivative of the true generating function with respect to the unobserved causal parent in that environment. We leverage this information and propose a method that exhibits non-trivial out-of-variable generalization performance when facing an overlapping, yet distinct, set of causal predictors., Comment: Accepted at ICLR 2024

Modern machine learning approaches excel in static settings where a large amount of i.i.d. training data are available for a given task. In a dynamic environment, though, an intelligent agent needs to be able to transfer knowledge and re-use learned components across domains. It has been argued that this may be possible through causal models, aiming to mirror the modularity of the real world in terms of independent causal mechanisms. However, the true causal structure underlying a given set of data is generally not identifiable, so it is desirable to have means to quantify differences between models (e.g., between the ground truth and an estimate), on both the observational and interventional level. In the present work, we introduce the Interventional Kullback-Leibler (IKL) divergence to quantify both structural and distributional differences between models based on a finite set of multi-environment distributions generated by interventions from the ground truth. Since we generally cannot quantify all differences between causal models for every finite set of interventional distributions, we propose a sufficient condition on the intervention targets to identify subsets of observed variables on which the models provably agree or disagree.

Deep learning techniques for gravitational-wave parameter estimation have emerged as a fast alternative to standard samplers $\unicode{x2013}$ producing results of comparable accuracy. These approaches (e.g., DINGO) enable amortized inference by training a normalizing flow to represent the Bayesian posterior conditional on observed data. By conditioning also on the noise power spectral density (PSD) they can even account for changing detector characteristics. However, training such networks requires knowing in advance the distribution of PSDs expected to be observed, and therefore can only take place once all data to be analyzed have been gathered. Here, we develop a probabilistic model to forecast future PSDs, greatly increasing the temporal scope of DINGO networks. Using PSDs from the second LIGO-Virgo observing run (O2) $\unicode{x2013}$ plus just a single PSD from the beginning of the third (O3) $\unicode{x2013}$ we show that we can train a DINGO network to perform accurate inference throughout O3 (on 37 real events). We therefore expect this approach to be a key component to enable the use of deep learning techniques for low-latency analyses of gravitational waves.

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 $\approx 10\%$ (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., Comment: 8+7 pages, 1+5 figures. [v2]: Minor updates to match published version, code available at https://github.com/dingo-gw/dingo

$\beta$-VAE is a follow-up technique to variational autoencoders that proposes special weighting of the KL divergence term in the VAE loss to obtain disentangled representations. Unsupervised learning is known to be brittle even on toy datasets and a meaningful, mathematically precise definition of disentanglement remains difficult to find. Here we investigate the original $\beta$-VAE paper and add evidence to the results previously obtained indicating its lack of reproducibility. We also further expand the experimentation of the models and include further more complex datasets in the analysis. We also implement an FID scoring metric for the $\beta$-VAE model and conclude a qualitative analysis of the results obtained. We end with a brief discussion on possible future investigations that can be conducted to add more robustness to the claims.