This work presents an initial analysis of the estimation of effective temperature and surface gravity for simulated O-type binary systems using a recurrent neural network. The proposed system uses 34 equivalent-width measurements from the optical region of a stellar spectrum. Two methods were applied to observed IACOB spectra before normalization: the addition of a blackbody continuum and the addition of a second observed spectrum. The first method produces only small differences in the normalized line profiles and in the estimated physical parameters over 3700-7000~Å. In the second method, the secondary spectrum is added with contributions of 5, 10, 20, 30, 50, and 75 per cent, as defined relative to the original primary spectrum. The general comparison includes 192 simulated systems and 1152 modified spectra. For most of these spectra, the estimated effective temperature and surface gravity decrease as the contribution of the secondary component increases. Individual examples using HD14947, HD190429, HD48099, and HD206267 show that this behavior is not the same for every combination: some estimated effective temperatures fall below the estimates for both isolated spectra, and some surface gravity estimates increase. Comparisons with previously published values also depend on the physical parameter and reference considered. The results show that the proposed system is sensitive to the addition of a secondary spectrum, but do not establish a unique contribution for the secondary component of an observed binary.
Physics seldom makes breakthroughs when we consider objects only in isolation. Instead we model and measure how objects sit among their neighbours, spatial, temporal, or otherwise: a galaxy in its environment, a halo in its history, a photon hit in a detector. Graphs are ideally suited for encoding exactly these relations, and Graph Neural Networks (GNNs) learn the geometric functions that respect them. This review presents the use of GNNs for astrophysics and cosmology, and argues that GNNs often suit physics and physical data better than any alternative: they fit the native geometry of the domain and the signal, enable the incorporation of the symmetries and prior knowledge we already trust and have toiled to build, and stay flexible enough to capture what we do not yet understand. GNNs' physically intuitive workings also render them more interpretable than other deep-learning architectures. We show how we can begin from general principles of the geometry of deep learning and build the graph and the graph neural network from the ground up, and how other architectures, like the convolutional network and the transformer, can be seen as special cases of one unified geometric blueprint. We survey applications across cosmology, galaxy formation, dynamics, and instrumentation; and we chart the frontier. From this survey, we find that only one in six articles outside instrumentation applies GNNs to data rather than just simulations. We also distil a set of best practices, including when not to reach for a graph. Throughout, we will prioritise physical intuition and foundational principles over mathematical machinery whenever possible.
The Laser Interferometer Space Antenna will observe up to $\sim 10^{7}$ overlapping signals, which have to be characterised simultaneously with a global fit. This is a challenge for model comparison since rerunning the global fit for every physical model of interest, including deviations from vacuum General Relativity, is computationally demanding. An alternative is a two-step post-processing strategy: a first global fit with vacuum models only, after which a selected group of target sources is reanalysed under a different model with all other sources subtracted. We show that in this strategy a beyond-vacuum effect in a target source can be partly absorbed by the overlapping nuisance sources in the first fit, subtracted with them, and never reach the reanalysis. In the linear-signal approximation, the loss is captured by a single number, the masking ratio $\mathcal{R}\in[0,1]$. A deviation the global fit would detect at $n_σ$ is reported by post-processing at $\mathcal{R}\,n_σ$, and bounds in null tests are also reported too tight by the same factor. We show how to compute $\mathcal{R}$ from the posterior samples of the vacuum global fit, and give an algorithm that ranks the nuisance sources by how much of the effect each can absorb, so that only those most correlated with it need to be refitted with the target in a down-scaled reanalysis with a few sources. We validate our method with full Markov-chain Monte Carlo inference on a toy model of 21 overlapping chirping sinusoids, where one carries a small non-linear chirp that represents the missed physics, while the other 20 act as nuisance sources. This method can serve as a basis for tests of General Relativity in realistic LISA mock datasets and can be adapted to study the impact of systematics between different gravitational-wave sources.
With only one confirmed example, namely the Earth, the abundance of life across the universe remains deeply uncertain, and local evidence about Earth's particular circumstances can significantly shape our knowledge of life elsewhere. Such extrapolation is difficult not only because of this sample size of one, but also due to observer selection effects discussed under the Anthropic Principle. In this paper, we describe and apply a framework called Full Indexical Conditioning (FIC) for performing Bayesian inference in this situation. Inspired by, but distinct from, Full Non-Indexical Conditioning, FIC conditions on all evidence available to the reasoner while considering that this evidence could have been otherwise. We address the reference class problem associated with such reasoning, demonstrating that substantive conclusions are unaffected by the choice of reference class provided it is sufficiently large. We apply FIC to several problems in astrobiology, including the Doomsday argument, the early abiogenesis time, and our location around a G-type rather than M-type star, clarifying the foundations of these arguments. We conclude that the early abiogenesis time does not rule out pessimistic possibilities for life's abundance, and that while life around M stars may be uncommon, its temporal distribution could extend far into the future. Ultimately, FIC offers a clear conceptual framework, grounded in straightforward probability theory, for tackling problems involving anthropic selection effects.
Do larger models learn increasingly similar representations of the same world? The Platonic Representation Hypothesis (PRH) predicts that they should, but similar can mean native cosine geometry---nearest-neighbour structure induced by cosine similarity before any learned alignment---or linear recoverability: correspondence revealed by a supervised linear map. Using matched Legacy Survey and Hyper Suprime-Cam (HSC) embeddings across five model families, we find that Ridge alignment strengthens the relationship between model size and cross-dataset neighbourhood correspondence relative to native cosine geometry. The effect appears in all five families and persists when both representations are reduced to dimension, so it is not simply that wider embeddings give alignment more dimensions to work with. The learned maps remain far from rotations or uniform scaling, and Sparse Autoencoder (SAE) and Block-Sparse Featuriser (BSF) features give no advantage over the same alignment applied to dense embeddings. Model scale thus improves linear recoverability more clearly than native cosine-neighbourhood correspondence, without establishing convergence toward a shared native metric geometry.
Bayes factors are a widely used model comparison criterion, but are often quite challenging and computationally expensive to estimate well. We propose a variation of the model-switch thermodynamic integration method for estimating Bayes factors that decreases the variance of the estimator and essentially eliminates integration error. We choose samples whose density in $β$ is proportional to the standard deviation of previously drawn samples. Rather than averaging many samples at each $β$, we use a very dense set of $β$ values, collecting one sample at each in order of increasing $β$ and one sample at each in order of decreasing $β$ to minimize "thermic lag". We study our procedure with a toy model (based loosely on some signal recovery problems). In this model we find that adaptive sampling gives us a 2.7-fold decrease in the spread of the estimated Bayes factor. We test our procedure both drawing directly from the posterior distribution and using a Markov Chain Monte Carlo sampler.
The evidence, $\mathcal{Z} = p(x | \mathcal{M})$, of a data-generating model $\mathcal{M}$ is a powerful tool in Bayesian frameworks: it enables model inference, model misspecification tests, and goodness-of-fit assessment as an alternative to standard discrepancy statistics, e.g. $χ^2$. While versatile, the evidence is notoriously difficult to compute, even when the likelihood is available. In both likelihood-based and simulation-based inference, estimating $\mathcal{Z}$ provides an immediate solution to high-dimensional goodness-of-fit or model misspecification tests: using $\mathcal{Z}(x)$ as the test statistic induces a minimum-volume level-$α$ test. Such tests are essential to assess model fidelity, which is necessary to trust simulation-based parameter inference. Existing learned approaches largely target Bayes factors, which only measure evidence ratios. Instead, we provide accurate, fast, and amortized estimates of the absolute evidence. We present ENFR: Evidence Networks with Flow-matched References. Building on the Evidence Network framework of Jeffrey & Wandelt (2024), the proposed method first learns Bayes factors with respect to a flow-matched reference, from which the absolute evidence is recovered. We show improvement in estimation of $\mathcal{Z}$ over the flow-based baseline in all applications considered and the best performance of all density estimation methods considered in our benchmarks. We furthermore introduce and provide the proof for an architecture that jointly learns the individual evidences of a set of models $\{\mathcal{M}_i\}$. We demonstrate the performance and scaling behavior of these approaches on data from a variety of scientific applications.
Deep learning (DL) models are increasingly being deployed into radiation-challenging environments in spacecraft, particle accelerators, and, soon, space-based data centers. Instantiated as a learned orchestration of numbers stored in persistent memory, models are susceptible to continual degradation as high-energy particles corrupt data. At inference time, new data passed through the network fundamentally break the off-line assumptions and guarantees of a static model determined during training. To preserve the quality and efficacy of the models, fault tolerance against bit flips is a clear objective. In this work we developed a runtime method for repairing the quantized weights of neural networks (NNs) after bit flips on commodity, commercial off-the-shelf (COTS) hardware, without storing extra replicas. Our work extends the well-established Fault-Aware Training (FAT) paradigm by adding an alignment penalty to concentrate undamaged activations and weights into a low-rank subspace, and we then reconstruct flagged corrupted coordinates from the uncorrupted survivors. We call this method {\it Projection Healing} and apply it to six regression benchmarks on quantized NNs. Holding a FAT checkpoint fixed and toggling only the runtime heal gives a further ${\sim}23\%$ reduction in the native-unit excess integral. Across those datasets the method extends the operational scrub interval by a median of $2.04\times$ at a $+5\%$ RMSE degradation and $1.96\times$ at $+50\%$, compared with $1.62\times$ and $1.07\times$ for classical Single Error Correction, Double Error Detection (SECDED). This introduces a new path towards designing resilient data-driven models, complementing established hardware redundancy, ECC, and FAT-based techniques.
Ammonia and hydrogen are major constituents of planets within and beyond the solar system, yet how they interact in planetary envelopes is poorly known. We perform large-scale two-phase coexistence simulations of the ammonia-hydrogen system from 500 to 4000 K and 0.1 to 100 GPa, driven by machine-learning interatomic potentials trained on density functional theory calculations. From these we map the compositions of coexisting hydrogen-rich and ammonia-rich phases, and the critical curve that separates conditions of complete miscibility from those of phase separation. The critical temperature increases with pressure, from 500 K at 0.1 GPa to 2000 K near 30 GPa, and we find no phase separation at 3000 and 4000 K up to 100 GPa. The slope of the critical curve decreases substantially between 0.3 and 30 GPa, and the curve nearly flattens above about 30 GPa and 2000 K, where molecules begin to give way to atomic species. The coexistence curves are asymmetric with an ammonia-rich critical composition. For the expected envelope compositions, the phase boundary lies close to, and intersects, published thermal profiles of Uranus and Neptune, implying ammonia may be raining out in these planets today. In contrast, in warm sub-Neptunes such as TOI-270 d, ammonia and hydrogen are likely miscible in all proportions. Together with previous studies, our results suggest that silicates, water and ammonia separate from hydrogen in sequence as planets cool, with implications for their compositional, thermal and structural evolution.
Many of the most important datasets in the physical sciences live natively on the sphere, and these data often carry no preferred position or orientation. Using methods that do not reflect this symmetry leads to far higher simulation requirements, which can be catastrophic for scientific analyses (forcing reliance on cheap, imperfect models that bias results). We present a novel spherical implementation of a gauge equivariant mesh architecture that is specifically designed for the Hierarchical Equal Area isoLatitude Pixelization (\healpix{}) of the sphere. The $\mathrm{SO}(3)$-equivariant convolution is built from steerable filters, parallel transport and spin-weighted features. The architecture supplies the exact symmetry, so the network does not spend training data learning it. The convolution operations are constructed to give provably exact equivariance, given a band-limit. Our full CNNs can achieve SO(3)-invariance error at per-cent-level and lower, which is controlled through well-understood hyperparameters. On benchmarks, our technique gives the most accurate dense gradient regression and competitive cosmic microwave background foreground removal and denoising. The improved simulation efficiency matters most in simulation-based inference (SBI), where high-fidelity simulations are expensive and neural compressors require large training sets, so a fixed budget forces analyses with less accurate simulators. In cosmology lensing SBI, our technique yields the tightest posteriors at matched simulation count. This approach is a novel method that will enable new convolutional neural network analyses, including generative and inference tasks, for processes and data on the sphere.